A WAVE THEORY OF UNIVERSAL RESONANCE: Part FOUR.
Sub-Title: The Decoding of QED Theory; and a Re-Imagination of the Atomic Orbital Model of Orthodox Physics (according to Principles of Universal Resonance).
Part FOUR: An Analysis of the Fine Structure of the Hydrogen Spectrum and Interpretation of Rydberg's Formula.
[Further Thesis on the Physical Basis of Quantum Electrodynamics in the Cohesive Mechanics of a Unitary Universal Field].
Preamble to Part FOUR:
Having established in Volume 1 a model of the 'Unitary Universal Cohesive Field' and the conceivable basis of its correlation with the observations and analytical structure at the foundation of orthodox QED theory, developed more extensively in Part THREE, Volume 2, and principally Part FOUR, proceeds to deal explicitly with a review of the Hydrogen spectrum and reinterpretation of Rydberg's original formula according to those same principles, including a derivation of Rydberg's constant from the number [2Q/137] explained in Appendix J1. More specifically, this is an analysis of the Hydrogen [H1] spectrum according to the principles in cohesive mechanics governing the dynamic frame of 'a-s/c' synthesis within which such an effect is constrained to arise which is then related through a revised interpretation of the 'Rydberg formula' in which the 'Rydberg constant [Ra]' is derived from first principles (and the measurable ‘speed of light c’) to the conventional atomic orbital model of QED theory.
This approach is itself based on the reasoned correlation between a geometric or trigonometric model of rotational 'moments of inertia [Im]' intrinsic to such a frame of empirically-induced 'a-s/c' synthesis--from which H1 spectral frequencies may be inferred--, and a hypothesis upon the basis of the ostensible configuration of the dynamic frame of synthesis which is the substrate of the QED model in that of the synthesis or integration of dominant components in distribution of cohesive force and inertia implicit in such frames. As such, this reinterpretation attributes the configuration of the H1 spectrum to the mechanical relation between a reorienting force applied to the elemental state of hydrogen gas to induce that spectrum and what are imagined as the 'rotational moments of cohesive inertia' intrinsic to that state; and therefore develops a trigonometric model of the elaboration of that spectrum.
Volume 2 further postulates an 'elemental scale' based on the mathematical harmonics implicit in the model of such a 'unitary cohesive field' (Section 4A), while Appendices D and E include discussions of a range of topics, including 'Renormalisation' and the fallacy of 'time dilation' in 'Special Relativity Theory'. Section 4B is a supplementary article entitled, 'The Metaphysics of Coincidence', and incorporates a basic model of Celestial Motion based on the same model.
Section 4A: THE ELEMENTAL SCALE.
General Consideration of the 'Elemental Scale'; including that of 'Actinide' Series Components [Ac89 to Cf98]: Preliminary to Part FOUR.
In considering the elemental scale defined according to the conventional theory of 'atomic number' (of 'protons') and indeed, 'atomic theory' itself, essentially dependent on the theory of 'molar mass'--i.e. according to the principle of Avogadro's constant [Na] governing 'particle number' within 'relative atomic mass or weight'--, as represented in the 'periodic table of elements' and the further revised Bohr-type atomic model which is the foundation of QED theory, the natural first inquiry is upon the basis of the increasing 'relative atomic mass' of 'atoms' comprising successive 'elements' within such a scheme characterised theoretically by successive integer numbers of constituent 'protons' or, broadly, analogues of Hydrogen or H1-nuclei; the further aspect of this question therefore, given the established notion of neutron number, becomes one concerning the fundamental basis--as opposed to a basis in derivative inference from a description of contingencies of structural configuration based on a hypothesis of discrete baryons-- upon which that number of neutrons increases with successive elemental components defined in a scale of regularly increasing 'atomic number', moreover tending to increase at a greater rate than atomic or proton number.
Since in this conception, any such increase in 'relative atomic weight', however it may be characterised according to a theory of 'nucleons', is the function of a graduated transition in 'cohesive resonance' according to which successive elemental states represent effectively reverberant or 'relatively turbulent' forms of the condition represented by the H1 elemental state itself--and secondarily the H1-Ne10 primary scale of transition--, the first consideration becomes that of the representation of the elemental scale itself based on such a principle, in this conception and model, primarily defined by an [88e] scale of 'c' vector recurrence with respect to the [2*2] unit harmonic interval of the archetypal [N-Cn] axis (i.e. according to the equation [88e]=(2*2--[eR])=[2*2--0.002916], thus [eR]=--[0.002916], and [e']--[eR]=[e''], where [e]=[9c--2*2], [e']=[10e--'c'] and [e'']=[10e'--e]) considered to define such a context of graduated resonance or relative alignment of pole components definitive of such forms, and of the mechanics of their imperatives in natural interaction or 'compound synthesis' to form 'chemical compounds' of such states. (Note here the approximation of [eR] to [k+E']).
In this model, since it is supposed that the vector [e] may be understood broadly to correspond to the 'atomic number [Z]', the natural extrapolation of this [88e] scale beyond the point of approximate recurrence of 88e to 2*2 described 88e=(2*2--[eR]), thus 89e, 90e and so on, may be considered to correspond to elements of the 'actinide series', and as will be explained, since this elaboration to 98e represents a condition of 'c' vector recurrence to [2*2+'c'] with a residual [e'']--thus for example such that 99e=[10c+e'']-- rather than 2*2 units itself, and notwithstanding the greater degree of that approximation to 10c represented by 99e, this further 98e and 99e extrapolation should be construed as a secondary elemental scale in the sense discussed in the following: that the 10e and 11e components corresponding to the series of elements from Ac89 to Cf98 and further Es99 are essentially turbulent extremities or 'reverberant aspects' of the condition of relatively higher 'cohesive resonance' manifesting in the H1 to Ne10 states of the primary 88e scale.
Since this further [e''] vector represents a 'higher resolution' aspect of 'c' recurrence such that [e'']=[881c--198*2], and since 98e'' closely approximates [e], that extrapolation to the levels 98e and 99e, corresponding to the Cf98 and Es99 forms, becomes definitive of the extremity of a range within which that further [e''] residual may be directly associated with [e] itself within the synthesised context to imply a similarly multiplying component corresponding to that [e''] which, in incrementally compounding with that [e] vector in that synthesised scale in which both [e] and [e''] may be considered in such direct association*, imaginable as a 'super-position' of 'phase components' in the [N-Cn], represents this further aspect of increasing 'relative turbulence' in which that increase itself, embodied in increasing [e]--and in this analysis in a further periodic vector [ek]=(12k--[e+p']) generally defining the condition of 'lateral phase divergence' of pole components imagined in the [N-Cn] axial component representing the substrate condition of diminished 'alignment' in those components--, is characterised by a further incremental increase therefore represented by this further multiplicity in the [e''] component.
*(For example, in accordance with the principles and method of the model, variably precise approximations of both [e] and [e''] to 2*2 at specific junctures of 'c' recurrence to 2*2 in such a synthesised scale--for example, the approximations of 969e to (22*2+[m]/2), and of [8635e''] to (2*2--[m]/2), by implication of ([98 x 88e]--e)=[8623e]~=[196*2]--['c'+2p''], and thus 94,986e'' to [22*2--p'']--generally permit the inference of a minimally diffuse common origin for [e] and [e''], within a range +/--[m]/2).
It follows therefore that the relation between this [ek] and [e''] becomes particularly significant in defining the transition between elemental states characterised by a concomitant and equivalent multiplicity in both these components, and more particularly therefore, since this further incremental aspect of increasing 'relative turbulence' and thus, it is supposed, the 'atomic weight [AW]' of those states defined by [Z] corresponding to [e], and inevitably to [e''], significant in defining the relation of 'nucleon numbers' traditionally considered primarily to embody such [AW]. As explained in the following, it is the effective 'phase relation' of [ek] and [e''] components which constitutes the basis of the AW/[Z] ratio for successive elemental states comprising such a scale based on dynamics of 'c' and further 'a/c' and 'a-s/c' recurrence in this model.
At the outset it should be observed that the principal features of such an imagined scale of elemental transition, construed here as the function of a corresponding transition in the relative turbulence of successive elemental states He2, Li3 and so on considered with respect to H1 (viz. in its idealised 'quasi-molecular' 2[H1] form in this model), and the increasing 'relative atomic mass' of those successive elements implied by it in this conception, arise by virtue of the arithmetic peculiarity that the relation of these residuals [e], [e'] and [e''] in particular, defining increasing degrees of 'c' recurrence relative to the archetypal frame considered to describe the basic structure of this context of graduated resonance or alignment characterising the elemental scale--thus whose correspondingly graduated reduction implies such a scale of successive elemental forms of increasing 'relative atomic mass' in an atomic theory--, tends to derive in their reiterative multiplication by 9 or 10 to the level of [10e'']=[e''+e''']. As such, since 9c=[2*2+e] and 88e=2*2--([e']--[e'']), where [e']=[89c--20*2], then a basic scale from H1 to Ra88 may be defined by that primary elaboration of 88e, where [e] corresponds generally to the 'atomic number [Z]', including what amounts to a relatively unstable Ac89 component and further 'actinide series' of which 10 principal elemental forms in particular implied by the repetition of such a scale to [2 x 88e] and so on.
Within that basic 88e scale and its extrapolation, a higher resolution aspect broadly defined both by the approximation of 10[e'] to [e], such that [10e'--e]=[e''], and by the further close approximation of 98e'' to [e]--that is, since [10e'--e]=[e'']--, corresponding respectively to the description of definitive levels of 'c' vector recurrence to multiples of 2*2 units at [9 x 88c]* and [10 x 88c] (i.e. these 2*2 unit harmonic intervals represent the idealised 'harmonically-defined' sub-division of the archetype), may then effectively be interpolated to imply a relation between 'atomic number' defined primarily by [e] increments and the characteristics of a property of increasing relative turbulence definitive of successive elemental states and of its transition described according to the relation of those further [e'] and [e''] residuals to [e]; and in particular, as will be explained, to the further aspects of limiting and idealised regularity in progression and recurrence of the fundamental phase vectors definitive of asymmetrical frames imagined within such an archetype to define the determinant configurations of such states of 'elemental turbulence or resonance'.
*Note that in the former case mentioned the specific degree in 'c' recurrence described by [9 x 88c]= 792c recurrence relative to the 2*2 unit harmonic interval considered over 178*2, while less approximate in 'c' recurrence, coincides with a greater definitive degree in 'a' and 'b' vector recurrence over a scale 792a and 792b conditioned by that 792c scale; while the latter aspect is required not only to imply the relation suggested, between 'relative turbulence' and increasing 'atomic weight' and 'atomic number' to be inferred within an extenuation of the primary 88e scale--as explained in the following according to a specific relation implied between [e] and [e''] mediated by a 'transitional factor' ([ek]--e'')=(12k--[e+p'+e'']), where [ek]=([12k--[e+p'])--, but to account for both the anomalous stability of U92 in an oxide form and the evident capacity to induce relatively stable components within the 'actinide series' from Ac89 to Cf98. Certain further secondary relations also define the context of wave recurrence in which these specific components are primarily definitive: notably, since 87 x [e'--k]~=[e--2k], 88 x [e'--k]~=([e--e']+3k), moreover, since [98e'']~=[e] and 10e''~=[e'+m/2], then 88 x ([e'--k]--e'')~=3k and 10[e'--e'']=[e--9e''].
Further, as is discussed later with respect to the specific properties of various primary 2p forms as the function of local [ek] recurrence--notably the case of O8[2p4]--, the anomalous peculiarity of U92 to form such ostensibly stable compounds with O8 in particular is ascribed to several definitive arithmetic properties within the harmonically-defined unitary phase structure in this specific aspect of the integrated description and analysis, primarily those implied by configurations in marginal k recurrence characteristic of these p- and, as is supposed in the case of U92 for reasons given in the following, d-forms in the further context in which these may also be indirectly related according to a conception of [ek] recurrence characterised by such relations in approximation as 8 x ([ek]--e'')=8E'~=(2[ek]--p'') and 6 x ([ek]--e'')=6E'~=[2e''], which become particularly significant in the analysis generally.
For example, according to the supposition that both U92 and O8 may be broadly characterised by the relation of a local 4[ek] component to a specific local origin [k0]' corresponding to s-orbital contexts within the broader framework of elemental transition discussed in the following--in the case of U92 corresponding to the 7s-orbital context defining the Fr87 and Ra88 forms, rather than the 6s or 5s contexts which may conventionally, and in the view of this conception mistakenly be considered appropriate in the QED analysis according to 'electron orbitals'*--, and that in general U92 behaves as such by virtue of the peculiarity that both U92 and O8 are characterised by the effect that 4[ek]=(3[ek]+[ek]) implies a progressive [ek] component arising recurrently with respect to 3[ek]~=(p'+[2p''/3]) within local contexts defined by a local origin [k0]' within archetypal scales of k and [m] elaboration from an idealised origin N=[k0] in the N-Cn axis, as explained in the following, then if U92 is considered 6d4--rather than 5f2 for example--, thus such that 4 x (k+[4y--3x]) for that d4 form and 4 x 2[k--A] for 2p4 [O8], implying a --[8A] resultant relative to 8k, will tend to define the basic configuration of phase continuity in compound synthesis of U92 and O8 (notwithstanding further subsidiary relations implied by consideration of [ek] progression), then since (4 x [4y--3x])--8A approximates [ek], such continuity, therefore conceived to imply such a potential for stable compound synthesis of elemental states, may be inferred with respect to the condition that 4[ek] approximates (3p'+[ek]+2p''/3).
*In this respect, it is important to establish here that in this conception and model, the last s-orbital capable of meaningful designation, both as an s-orbital per se in the QED interpretation of the H1 spectrum, and as an effective reference for the description of L orbital angular momentum or 'lateral phase' resultants designated QN 'l'=0 and in this context for p, d and f-type 'orbital contexts' or ranges in elemental definition and transition, is the 7s-orbital. As such, in this latter aspect of such constraints of conceptual context and framework, not only is the traditional designation of 'actinide series' and further artificially-induced elemental states according to 6d and 5f neither strictly nor essentially valid, but since by the definition of the 88e scale of such states (i.e. primarily H1 to Ra88) according to the recurrence properties of [e]=[9c--2*2] with respect to 2*2, thus 88e=[2*2--eR] where [eR]=[e'--e''], the further extrapolation of that scale to 89e, 90e and so on implies an [e'--e''] shift at that 88e juncture relative to the origin [N]=[k0] of that 88e scale corresponding to the H1 form and the 1s1 and 1s-orbital generally centred around that origin, then the 7s orbital becomes effectively analogous to that 1s and in this case effectively the 2s orbitals with respect to this further elaboration of a second 88e scale; though rather to be considered in character, by virtue of the [m]/2 shift which has occurred at the 4s juncture, a hybrid of 4s and 5s-orbitals. That is, in this instance, the phase relation of that 7s-orbital to subsequent elemental forms is effectively that which suggest its definition as 4s/5s orbital, and it is presumably thus that the 'actinide series' forms assume spectral characteristics akin to the 4f-orbital.
Accordingly, and notwithstanding the implication of such f-orbital characteristics, the Ac89, Th90 etc. forms, although strictly speaking these may be understood as effectively hybrid forms of p, d and f-types considered with respect to that 7s-reference origin, it seems likely that they tend in preponderance to conform to definition in this model as d-forms according to the example suggested by U92 in its synthesis with O8 (though not as suggested 6d-forms, since such description by QN 'n'=6 or 5 loses meaningful context and definition beyond forms designated by QN 'n'=7), and may therefore be treated as such in specific instances, such as in the cases of U92 and further Pu94 in particular (e.g. by applying the modification k+[4y--3x] to consideration of these elemental states in contexts of analysis according to p/k synthesis). It should also be emphasised here that, while the specific details of such aspects of p/k synthesis--such as the relative scale and proportions of components defining these relations in marginal recurrence within the frame of synthesis--are arguable, the essence of this conception and model demands the elaboration of details of this qualitative sort: and all that is further required is the thorough consistency of such a model or framework in description of a unitary dynamic phase structure.
Given then that the relation suggested of a resultant of [ek] defining the context of resolution in compound synthesis in this case of U92 and O8, then since [eR]=[e'--e''], and since [e']=[10e--'c'] may be considered broadly to define both the context of the primary H1 to Ne10 and further Ac89 to Cf98 scales according to 10e progression, then the effect that [eR] approximates (9e''--[m]/2) implies*, relative to the further progression of a 10e'' component definitive of both these scales, a progressive phase component approximating [e''+m/2] in the latter with respect to the former, therefore arising within the phase relation of these H1 to Ne10 and Ac89 to Cf98 aspects of successive 88e scales which may further be imagined to characterise the relation of forms within the latter to those within the former, thus for example, that between Th90, U92, Pu94 and O8 in particular, when the [e'] component is construed as suggested as common to both these 10e scales. *(Note here that since [e'] approximates [10e''--m/2], where [e'']=[10e'--e], then [eR]=[e'--e''] approximates [9e''--m/2]; while the further approximation of that [eR] to 6[ek]+e'', thus implying approximation of 7[ek] to [eR+E'], also presumably assumes some significance in this context).
Conceivably therefore, when this [e''+m/2] resultant--i.e. (9e''--[m]/2) with respect to 10e''-- is considered concomitantly with respect to that [ek] marginal phase differential implied as suggested in the relation of U92 and O8 imagined as d4 and p4 forms respectively (i.e. thus further defined by 4[ek] progression in contexts in which this component is capable of consideration according to a corresponding relation of 'local [k0]' origins', in this case respective 7s and 2s-origins construed with respect to the N=[k0] origin), the further differential resultant ([ek]--e'')--[m]/2=([E'--[m]/2) suggests the implication of that 'transitional factor' E' in this relation, presumably therefore definitive of that facility for oxidation of U92; where that further (--[m]/2) is consonant in that case with the separately arising [m]/2 'phase shift' arising at 4s by virtue of the (14 x [3p''--m]) elaboration of disparity between [m] and p'' scales in the N-Cn characterising the frame of synthesis and its analysis in this model; where that [m]/2 'phase shift' is also negative (viz. in the context discussed later of transition in the AW/[Z] ratio, this [m]/2 phase shift implies a relative progression in [I] transition amounting to a disjunction within that transition). The cases of Pu94 and Th90 (as a phosphate) will be related to that of U92 to the extent that d2 and d6 forms generally are related in behaviour to d4 forms in such tendencies to compound synthesis with O8 (where a similar reasoning applied to the relation of elemental forms within the primary 88e scale proper should take account of the relation of respective s-orbital reference origins).
As such therefore, this perspective not only presupposes the particular relation between the primary H1 to Ne10 scale and what is construed as its definitively turbulent aspect in the succeeding scale proceeding Ac89 to Cf98 in this scheme--such that a specific definitive relation exists between the N=[k0] origin for H1 and the local [k0]' origins definitive of the 7s-orbital context--, but that these forms, by virtue of this inference from the behaviour of U92, are primarily d-variants, as is evident in the spectral and implied electronic configurations for Ac89 and Th90, rather than f-variants as in the conventional analysis; and not unreasonably, as suggested, capable of consideration as both in this model. The further effect that (8 x [4y--3x]) approximates [4p'--3m/2] is also presumably of some significance in any such imagined context of resolution implicit within such contexts of compound synthesis, in this case of U92 and O8, mediated by the relations of [A]=4m to k and p' in particular; while, since (3 x 4 x [4y--3x])=0.007473384 and 32A=0.008321428, the approximation of the difference 0.00084804 to (2[ek]+3m), and similarly, since the difference between (12 x [4y--3x]) and 48A approximates [p'+p''], then these indicate further possible determinant aspects within such resolution between U92 and O8 elemental aspects, manifesting for example in the further observation of a [U3/O8] configuration of compound synthesis between these states.
In considering the further aspect of an extenuated 'elemental scale' beyond Ra88 principally implicating artificially rather than explicitly naturally or 'primordially' occurring elemental forms (such as U92 in particular), it is therefore necessary, as mentioned, to consider further the manner in which the primary scale from H1 to Ra88 itself is conceived to derive in the elaboration of 88 x [e] variants successively describing degrees of increasing turbulence, each arising according to a diminution in such alignment described by the basic relation [9c--2*2]=[e]; and therefore not only to conceive a simple extrapolation of the primary 88e scale describing the range H1 to Ra88 to imply a second 88e component commencing at Ac89, but, in order to describe this context according to various ranges in relative turbulence as the function of 'relative alignment' defined according to 'c' vector recurrence and the elaboration of [e], [e'] and [e''] phase vectors, to infer within such a primary 88e scale--and effectively its extrapolation to 97e and 98e-- a further aspect which is essentially that of a higher resolution or marginal range within such a context of relative alignment implying 'relative turbulence' represented by the [e''] residual implicit in each specific degree of such relative resonance or turbulence within that primary scale, essentially as a residual construed relative to [e] itself corresponding to the 'atomic number [Z]': viz. naturally, the H1 form would be characterised by a singular [e], [ek] and [e''] component, while increasing 'relative turbulence' would be defined by corresponding increases in those components.
Inevitably therefore, since it is observed that 98e'' closely approximates [e] itself, where [e'']=[881c--198*2], then by virtue of this peculiarity, further implicating the (--[eR]) phase disparity between such successive 88e scales, a particular relation between the initial H1 to Ne10 and Ac89 to Cf98 components of each such 88e scale, the 'higher resonance forms' of each, will be defined by this relation of 98e'' to [e], more especially when the scale of [eR] is taken into account. For example, in the following, the elaboration of [98 x 88e] overlaid within a common 2*2 unit context permits this relation to the inferred with respect to given components in [e] progression by virtue of the approximation of (98 x [e+e'']) to 99e, where [e+e'']=10e' and where in that scheme, 98e'' components are interpolated within a singular [e] according to that overlaying in synthesis of these recurrent 88e constituents of the higher resolution aspect of 'c' recurrence defined by [e'']; thus such that 98 x (--[eR)=(98 x [e'--e'']) approximates [98e'--e] implied by the structure of this synthesised effect within the harmonic 2*2 unit interval, thus, since [e']=[89c--2*2], implying ['c'--e] in each such [98 x 88e] operation with the same degree of approximation as that of 98e'' to [e] itself; and representing the basis of further higher resolution.
Accordingly for example, since the scale of 'relative turbulence' itself simply elaborates according to [e] progression, thus extrapolating here to imply Cf98, and since this higher resolution [e''] aspect may be inferred with respect to [e] progression over a corresponding scale, thus implying a particular aspect of recurrence dependent on the approximation of 98e'' to [e], then the more specific relation between the primary H1 to Ne10 and Ac89 to Cf98 forms becomes the function of the disparity [eR] between these 88e scales, and its incidental approximation to [9e''--m/2] mentioned.
As such, in general, it is the resultant [e''+m/2] component which describes the relation in relative turbulence between the H1 to Ne10 and Ac89 to Cf98 forms, more particularly when the latter are construed as effective extremities within the range of relative turbulence implicit in the primary 88e scale, moreover imaginable as the function of that effect of higher resonance itself within H1 to Ne10 forms: that is, not only is it generally imagined in this conception that all elemental forms succeeding from H1 are effectively turbulent reverberations of or within it, but the 'elemental states' Ac89 to Cf98 may more specifically be understood as essentially reverberant manifestations of or effectively within that higher primary scale H1 to Ne10 according to which reasoning, outlined in the following, if the properties of forms succeeding from that initial scale, fundamentally defined both by the relation of 10 x [e] components to 'c' to imply [e'], and by the further relation of 10e'' to [e'], are construed, as is inferred in the structure of the 'periodic table', to derive in the elaboration of the basic properties of those H1 to Ne10 forms, then the same principle may be applied to the observed properties of those 10 constituents of the 'actinide series' with the qualifications implied by the [eR]=[e'--e''] phase disparity between the Ac89 and H1 forms, and by its approximation to [9e'--m/2].
As such for example, while the basic structure of elemental transition H1 to Ra88 is defined by 88e components considered in a sequential progression within a commonly synthesised scale within which any such [e], [e'] and [e''] residuals in 'c' recurrence, represented by their similarly schematic sequential elaboration from a common origin N=[k0] may be considered with respect to those arising within 'a-s/c' and a/c aspects of the frame, principally to [p'], [p''], k and [m] components (viz. thus within a further component [ek]=[12k--e--p'] discussed in the following), where Ac89 is implied as a more-or-less unstable component defined with respect to the point of [88e] recurrence to [2*2] represented by the residual [89e--2*2]=([e]--[eR]), where as mentioned [eR]=[2*2--88e]=([e']--[e'']), the further effects that 98e'=['c'+0.000035453]~=('c'+[m]/2) and 98e''= ([e]--0.0000081685344)~= ([e]+[m]/8), summarised, since 98e=[2*2+'c'+e''], by 98([e]--[e'])~=(2*2+[e'']), suggest and permit the definition of a further aspect within this transition which is at once definitive of nuances of degree within higher resonance, and of relative turbulence corresponding to the definition of elemental forms themselves both within that primary 88e scale and in its elaborated extenuation to 98e, more especially within the 10 initial 'actinide series' components considered to imply this manifestation as such turbulence of the higher resonance H1 to Ne10 scale.
This circumstance may be summarised generally according to the observation that, since 98([e]+[e''])~=99e=[2*2+'c'+e+e'']=[10c+e'']), then the direct relation of [e] and [e''] in that context may be considered to imply the arithmetic basis of that surmise. Further, as is evident from the following, since it is this [e] component which primarily corresponds to the 'atomic number [Z]' of successive elements while the further component [ek]=(12k--[e+p']) broadly describes the substrate in diminishing alignment for an incremental increase in relative turbulence definitive of such forms according to the inference of the relation of successive multiples of [e] comprising the 88e scale to 12k and p' aspects of the limiting symmetrical frame representing the condition of limiting uniformity in distribution of cohesive force--and corresponding regularity in p' progression in particular--with respect to which such a progressive reduction in alignment represented by [e] increments may be defined, then a more explicit context of transition in such 'resonance' or conversely 'relative turbulence' between elemental states may be described according to the relation of such [ek] to the [e''] vector embodied in a 'transitional factor' E'=([ek]--e'') discussed in the following.
The Primary 88e Scale: and the Periodic Component [ek]=(12k--[e+p']):
Commencing with the basic or primary scale of 88e over 2*2 units with a remainder [eR]=(2*2--88e)=(178*2--792c)=0.002915996746~=0.002916 (bearing in mind that 792c recurrence with respect to the 2*2 unit harmonic at this level of resolution is consistent with comparable degrees for the 'a' and 'b' vectors similarly elaborated to multiples of 792; which, notwithstanding that [881c--198*2] represents a higher order of 'c' vector recurrence further described by the relation of 99e to 10c, thus 99e=[10c+e''], and the equivalence of 98e to [2*2+'c'+e''], is not the case for that context of 98e recurrence), and interpolating within it from the same origin N=[k0] of archetypal synthesis or recurrence of all such vectors in the linear N-Cn axis--therefore implying the idealised equivalence of N and Cn as its aspects, harmonically-defined by the 2*2 unit interval-- further [e'] and [e''] scales related by [e']=(10e--'c') and [e'']=(10e'--[e]), consider that, if for each 88e regarded relative to 2*2 units, a residual (--[eR]) arises which is implied by the relation given [eR]=([e']--[e''])=([10e--c]--e''), then in the further elaboration [98 x 88e], if an aspect (98 x 10e')=(98 x [e+e'']) is considered implicit within the context which both implies and corresponds to a further aspect of [e] recurrence itself, compounding within the 88e scale construed entirely within a synthesised 2*2 unit interval, which is effectively that of a condition of 99e recurrence--i.e. the effect that 98e=[2*2+'c'+e''] means that 99e may be represented by ('c'+[e+e'']) within as opposed to extrapolated from that 2*2 unit interval*--, thus within which, since the definitive context of that relation is 'c', one [e] component within the approximation of that resultant ['c'+e''] correspondingly implied by 98e in that context which may be equated with 98e'' may also be construed to define the distribution of this effect in increasing turbulence or resonance within the 98e scale extrapolating from 88e, therefore according to what amounts to a progressive [e''] component considered relative to that context of [e] progression and further [ek] elaboration. *(NB: 99e=([10 x 10e]--e)=10 x (['c'+e]--e)=[10c+e'']=2*2+'c'+[e+e'']).
Additionally then, a secondary aspect of such a scale or continuum of evolutionary transition in cohesive resonance, therefore conceived to inhere in the transition between elemental forms, may correspondingly be inferred from this interpolation according to which, since [e''] arises from ([e']--[eR]) over 98 elaborations of [2*2--88e]=(--[eR]) to imply [98e'']~=[e], 10 such [e''] within that [98e''] aspect of the synthesis or interpolation will be variously associated with 10 x [e'] aspects arising from [10 x 10e] to imply that [99e] resultant; and indeed, what must be presumed, as suggested, to be capable of definition and representation within that 'c' vector resultant deriving in the elaboration of 99e from an origin N according to the approximation mentioned of [98e'] to 'c' (i.e. 98e'~=['c'+[m]/2]); where that 'c' resultant may also be understood to correspond primarily to a recurrent vector effectively superimposing in the model, upon the the basic 10e=(c+[e']) defining the context of H1 to Ne10 forms.
As such, as explained below, [88e] may be imagined to define the basic scale of elemental transition on the basis of diminishing resonance conceived within the archetypal configuration according to 'c' vector recurrence relative to the [2*2] unit axis harmonic of [N-Cn] (i.e. [9c--2*2]=[e]), to be regarded in this conception as definitive of the primary aspect of a transitional scale H1 to Ra88 which then inclines to a repetition within a similar aspect proceeding from Ac89, and to imply within that context the further elaboration of an [e''] component which may be expressly related to that [e] vector considered definitive of the traditional 'atomic or proton number' over that extenuated 98e scale. That is, since the transition itself within such a scale, moreover in which it is the [e] component which is considered here to correspond explicitly to 'atomic number [Z]', is defined both by that further higher resolution aspect [e''] within the range of 'relative alignment' defined according to 'c' recurrence and its relation to a component [ek]=(12k--[e+p']) representing the basis of an imagined progression in 'relative turbulence' definitive of such a scale of elemental transition (viz. in which that component [ek] is considered to describe a condition of lateral phase divergence defined by the relation of incrementally increasing [e] to a context of regularity in p' and k or 12k progression and recurrence considered within and with respect to the N-Cn axis), then it is more correctly both [e''] and the further component [ek] deriving in and representing that [e] or effectively 98e aspect which, more especially when expressed in their relation E'=([ek]--e''), describes the condition of increasing 'relative turbulence' according to which the scale of transition between elemental forms may be defined and comprehended.
The further aspect of this description is the implication mentioned of [e'] as an effectively intermediary component such that, since 10e''~=([e']+[m]/2) and 10e=['c'+e'], then the H1 to Ne10 primary component of such a scale may be consistently be described in an integrated N-Cn axis both according to a range 10e'' and by its relation to 10e mediated by the transitional factor E'=([ek]--e'') suggested; according to a method of the sequential elaboration of these constituent components of the frame of synthesis, in its 'a-s/c' and a/c aspects, from a common origin N=[k0]. The approximation 98E'=98 x ([ek]--e'')~=[p--p''] is considered particularly significant, more especially in the context in which the 'atomic number [Z]' and the 'fine structure constant' based on the substrate ratio p/[*2] are related in equations describing the Hamiltonian energy of H1 in the QED model.
In general therefore, it is the differential [E']=([ek]--e'')=0.0001052279 which, since it defines the relation between principal aspects of a synthesised scale of transition in 'c' recurrence within 'a-s/c' synthesis, becomes definitive of elemental transition; moreover that defined here principally by 98e progression from which, and within which context the [ek] component is implied as suggested; and according to which the 98e'' scale interpolated within 98e may be construed to describe the context of increasing 'atomic weight' with respect to the traditional theoretical succession of 'atomic number', interpreted as 'proton number' representing such transition, effectively as its numerator in the traditional SM. As mentioned, the conception therefore is that that aspect within the primary scale, generally H1 to Ne10 when that succession is considered according to an approximation of 10e'' to [e'] imagined in the context in which [e'] itself derives as [e']=[10e--'c'] (i.e. such that as mentioned this primary component of the scale may be consistently defined according to a range incorporating both such aspects), is therefore capable of manifesting the residual component represented Ac89 to Cf98.
That is, to reiterate, the inference of this relation between [e] and [e''] mediated by [e'] and implicating [ek] in the analysis is that the primary relation of 10e'' components to [e'] representing the higher resonance aspect within the such a context corresponding to that primary scale H1 to Ne10 (i.e. whose further aspect is represented by the relation [10e'--e]=[e'']; also bearing in mind that 10[e'--e'']=[e--9e'']), implies within the elaborating scale of relative turbulence generally (thus conversely, the scale of 'evolutionary transition' towards H1), the capacity for the manifestation of the so-called 'actinide series' from Ac89 to Cf98 in particular, effectively as the turbulent aspect and intermediate extremity of that H1 to Ne10 scale when this elaboration of [e'] is construed with respect to the progressive incremental elaboration of [e] representing increasing relative turbulence, thus described by the [ek] component. As such, the [e''] component may be considered to represent the higher resolution component within this context which at the extremity of relative turbulence considered within such a scale (thus effectively representing the 'reverberant aspect' of the H1-Ne10 component of that scale) defined by the [ek] component embodying [e] within E', manifests as that Ac89 to Cf98 transition. It may also be noted that with respect to [e], the distinction between these contexts of 'c' recurrence at which [eR] and [e''] arise is effectively that between [9 x 88e] and [10 x 88e], or equivalently, [88 x 9e] and [88 x 10e], the latter case permitting the explicit expression of the definitive relation [e']=[10e--'c'] within the integrated scale of 'c' recurrence defined by [e'']=[881c--198*2]=[10e'--e]. As is evident, in a general sense, since [e'']=[10e'--e], it is 10e' which mediates the relation of [e] and [e''], where [e']=[10e--'c'].
This scale of evolutionary transition in 'relative alignment or cohesive resonance' therefore corresponds to that of a transition between elemental components comprising the general context of their compound 'chemical synthesis' within which these ordinarily arise and are defined by techniques of their isolation as discreet ostensibly homogeneous 'states': viz. thus from such states of chemical synthesis which may be understood to manifest, according to the supervening exigencies of 'cohesive polarity resolution' or equilibration within the universal unity, the process of evolutionary resolution of the turbulence implicit within formal asymmetrical reality, considered with respect to an archetype, of which such elemental forms are the definitive aspects and conceivably more-or-less discrete stages. This resolution towards an idealised 'cohesive resonance' represents the inclination of such a process towards an idealised alignment of components or resultants in distribution of cohesive force or polarity with an archetype within which the configuration of such a scale of transition is intrinsic--and of which these 'elemental forms' are merely specific definitive aspects, in a general sense corresponding to stages within such a process conceivable in terms of 'phase transition' within a 'unitary phase structure'--, and with respect to which such states of turbulence remain variably disparate (i.e. the configurations described in the QED model are essentially inferred within the H1 state).
It is important to note therefore that since [ek] defines that aspect of transition based primarily on a scale of [e] and [12k--e] transition, then it is the continual elaboration of an [e''--p''/2] disparity implied by the approximation of [3E']=3 x ([ek]--e'') to that [e''--p''/2] arising by virtue of the inter-relation of 12k, [e] and p' components (similarly 4E' approximates [ek]--p''/2), therefore defining the basis of a periodicity in progression and recurrence within the context of 'a-s/c' synthesis, which in concert with the further relation of 3[ek] to p' with a ~[p''/3] resultant, thus 3[ek]~=(p'+[p''/3]), and the basic relation of [ek] to [e''] mentioned, 4e''~=3[ek], principally accounts for the commonly recurring properties of elements defined according to such variably regular relations in periodicity implicit within such a framework of synthesis.
As a general principle therefore, what may be regarded as definitive of the higher resonance condition of the primary scale H1 to Ne10 --the disparity between [ek] and [e''] aspects of a dynamic of phase transition corresponding to that within the condition of such alignment primarily defined by [ek], and by inference transition within the elementary continuum or scale generally (viz. as explained later, the effective 'phase relation' of these [ek] and [e''] aspects or components may be understood within a transition embodied in the AW/[Z] ratio)--, may be imagined to manifest in a corresponding component of the scale characterised by a relative extreme in that reverberant effect of 'turbulence' or diminished 'equilibrating polarity resolution' at and in extrapolation from a point of approximate synthesis of definitive 'phase vectors' at what is therefore the diffuse 'origin' or point of synthesis of respective phase vectors, therefore defining that Ac89 to Cf98 scale, represented by the relation of the specific residuals implied by that definitive primary degree of 88e recurrence with respect to 2*2, thus 88e=(2*2--[eR]) where [eR]=[e'--e''], when considered with respect to the idealised origin N=[k0]. (To reiterate, while 99e and 98e equivalence to [10c+e''] and [2*2+'c'+e''] respectively represent the higher resolution aspects of [e] recurrence relative to 'c', it is the 88e aspect which not only defines the primary scale of [e] recurrence relative to 2*2 itself but is associated with comparably precise degrees of such recurrence for 'a', 'b' and 'c' vectors).
This extrapolation may then be construed within a scale of recurrence of [e''] with respect to [e] defined by the further 98e'' scale in order to permit the definition of this effect with respect to the 'atomic number [Z]' corresponding explicitly to [e] itself, and effectively to [e''] in this model; such that for that [e] considered with respect to the resultant (--[eR]) arising as the residual of 88e recurrence relative to 2*2 to imply the relatively diffuse aspect of the idealised origin suggested, the 10 components of that Ac89 to Cf98 scale may in a general conceptual sense be inferred to correspond more-or-less directly with the primary H1 to Ne10 scale as its relatively turbulent extremity, where, as mentioned, it is essentially the phase discrepancy [eR]=[e'--e'']) which defines the extent of this disparity between those 'local contexts', each of which may be defined by 10e, 10e'' and further 10[ek] and 10E' transition.
As mentioned, since (--[eR])~=(--[9e''--m/2]), and since 10e'' is implied within the progression of 10e 'atomic number' forms Ac89 to Cf98, then considered with respect to the idealised N=[k0] origin, then because this implies an approximate [e''+m/2] resultant disparity between H1 to Ne10 and Ac89 to Cf98 scales, transition Ac89 to Cf98 corresponding to E' components 10E'=10 x ([ek]--e'') is effectively defined by the 10[ek] component construed with respect to the 2*2 unit harmonic interval representing that idealised origin, with a disparity of ~[m]/2; therefore for example with particular respect to the components E' within the 10E' representing the range in transition in 'relative turbulence' within the primary H1 to Ne10 scale.
Properties of Elemental States:
To attempt further to explain the specific properties of various elemental forms on this basis, moreover therefore to account for the tendency for these to conform to a variably regular periodicity within the condition of 'elemental transition' which may meaningfully be related to such a dynamic of transition--thus, for example, broadly consistent or commensurate with both the description of electron L orbital angular momentum and the 'atomic weight' of elemental 'atoms'--is a complex and arduous task indeed. In order for example to appreciate the sense in which the 'reactivity' of the [s1, s2] metals in particular represents the definitive primary aspect of the more general configuration of 'reverberation' or 'relative turbulence' within the H1 state itself according to which the natural proclivity of these metals is to form salts with the various halogens may be conceived as the analogue of a primary dynamic of alignment corresponding to the relation of H1 to He2 of which, by virtue of the peculiarities of O8, the [H2O] aqueous form constitutes a definitive and characteristic aspect of optimal regularity within a condition of oscillatory turbulence characterising that relation of H1 and O8 which may be imagined as one such primary aspect of that fundamental H1-He2 relation, it is necessary to identify several inter-dependent aspects of these dynamics (outlined in the following) suggesting the approach more generally. (The identity of He2 as a 'rare gas' therefore permits the further idea that the p6 or Ne10, Ar18 and Kr36 forms in particular may be regarded as further aspects of that primary definitive relation).
The Distinction between Elemental States Characterised by Successive Orbital Components [p1, p2,..p6] and [d1, d2, d3,...d9/d10]:
[NB: This facet of the model is explored further in Parts THREE and FOUR].
In the light of this analysis then, and given that designation by the QN 'l' suffices to describe a common definitive lateral phase relation between electron S phase cycles, thus L orbital angular momentum corresponding to given orbitals (2p, 3p, 3d etc.) and common to their electron components, therefore to the description of these lateral phase relations considered with respect to given ranges [m] within 7m scales designated by the principal QN 'n', the further question arises regarding the basis of the distinction between these successive components of such orbitals, and the relation of this to the phenomenal properties of corresponding elemental forms according to 'atomic number [Z]': in this conception generally conceivable as the function of the state of resonance or 'alignment' of those respective elemental forms within a scale primarily defined by 'c' recurrence.
Moreover, if it is supposed that [6k/12k] components define the context within which the basic structure of the p-orbital arises (thus, as explained in the following, as a progressive incremental wave effect defined by [ek] components considered with respect to an effectively local origin [k0]'), then in this analysis some further aspect within dynamics must be identified in order to account for the evident regularity with which theoretical electron components--defined spectrally--occur within such a context as (p1, p2,...p6) while retaining a common definition consistent within common properties or invariant parameters of definition, the electron S angular momentum and 'charge e'; thus effectively a manner of subdividing this context of k recurrence within the a/c aspect of synthesis into 6 components capable of definition by a common harmonically-defined increment, in this case the [ek] component equivalent to ([12k--e]--p') implied in the integrated N-Cn axis, supplanting methods based on the use of a common multiple (say 60k within which such p-orbital components would correspond respectively to factor multiples of k, 60k for p1, 30k for p2 and so on to 12k for p5 and 10k for p6), and relating these separately to [e] and p' (notwithstanding the analogous construction of a 'harmonically-subdivided scale' as a variation on this idea mediated by [e''] to define the relation of increasing 'atomic weight' to 'atomic number' and the definitive condition of lateral phase divergence characterising elemental forms, represented generally by [e], explained in the later sub-heading, 'A Conjecture on the Neutron/Proton Mass Ratio').
As such, in this model of p/k synthesis, these considerations translate to the supposition of a fundamental basis for the context of the distinction between elemental forms in 'c' vector recurrence defined by those specific residuals, [e]=0.032108081, [e']=0.003243566, and [e'']=0.0003275501272 for 'c'=[*3--*2]=0.317837245196, therefore defining a more-or-less regular repeating scale or continuum of elemental transition H1 to Ra88 further extrapolating from Ac89 to Cf98 according to which primary k recurrence, thus further [m] recurrence (relative to 'a' and 'c' components in horizontal a/c synthesis; therefore the marginal relation of those 'a' and 'c' components) defining the basic numerical configuration of p6 and d10 components described in QED theory, is further defined both with respect to the archetypal frame, principally through the relation of k to [e] and [e'] considered with respect to a variable local [k0]' origin and to the p' vector definitive of 'a-s/c' recurrence relative to that frame; therefore according to the relation of the residuals arising in the relation of k to the [e] residual phase vector in particular through the relation of 12k=0.0338324 to [e] expressed, as is possible in this model, by the difference [12k--e]=(0.0017243173), and in certain secondary instances, in the relation of k itself to the [e'] vector, [e'--k]=0.0004242.
The further relation of [12k--e] to [p'] itself effectively embodies a description of the relation between such conditions of 'lateral phase divergence' described by multiples of [12k--e] within the a/c aspect of the frame of synthesis, its symmetrical aspect in the archetype, and the 'a-s/c' aspect represented by limiting p' recurrence in the N-Cn axis of the limiting symmetrical frame: thus, ([12k--e]--p')=[ek]=0.000432778; where it is of some importance to note the approximate equivalence of [12k--e] with 4[ek], since p'~=3[ek]+[p''/3] and the equivalence [12k--e]=p'+[ek] (and indeed of both y=[9k--J/2]=0.0004302675 and 7m to that [ek] component). As explained, the 'atomic number [Z]' itself ascribed to these elemental forms in 'atomic theory' corresponds to the elaboration of successive primary [e] residuals within the context of an archetypal frame of synthesis defining the basic configuration according to which such a scheme of elemental forms is imagined to conform.
That is, since the distinction between elemental forms is essentially the function of degrees in resonance, thus primarily the status of relative alignment of 'pole components', or degrees in precision and regularity in 'wave recurrence' defined primarily by 'c' and therefore [e] recurrence, then the distinction between electron components within given p, d and f-orbitals characterised by increasing 'atomic number' is inevitably the function of the primary relation of [e] and k--expressed here for convenience of scale by [12k--e] --, and an incremental progression in the relation of that differential between 12k and [e] which, when considered relative to p' according to a definitively progressive vector [ek] in the integrated [N-Cn] axis (viz. progressing and recurring with respect to its constituents p' and k in particular: viz. in the latter case primarily with respect to [6k/9k] recurrence, thus 36k components in the a/c aspect) defines those orbital contexts within which 'elements' are described in the QED model.
Eventually this [ek] component may be comprehended either with respect to [e] itself and thus further [e''], or to p'; within the more general context in which that [ek] component may as explained be considered to define the context in which the effectively resultant state of 'relative turbulence' corresponding to the elaboration of the extrapolated elemental scale H1 to Cf98 may be described according to the relation of [ek] to [e''] expressed by the 'transitional factor' E'=([ek]--e'')=0.0001052279. Since in the further correlation of this disparity [12k--e]=0.0017243173 with the definitive p' vector it is evident that the difference in that relation ([12k--e]--p')= [ek]=0.000432778 closely approximates that between [e'] and k expressed [e'--k]=0.0004242 where (8 x [e'--k])~=[e']--(2 x 0.00009665), then, exemplifying the character of such a frame of synthesis--in which for example 4[e'']~=3[ek]~=[p'+p''/3] --, the configurations in recurrence suggested by the former are reinforced within the lateral synthesis by the latter.
As such, while the essential numerical configuration of p6 and 10d-orbital types in particular depends primarily on dynamics of [6k/9k] recurrence with respect to 'c' itself, the specific (p1, p2, p3...p6) and further (d1, d2, d3d10) components of such orbitals are distinguished according to the specific intricacies of k recurrence with respect to the frame which may be defined by the relation of [e] and [e'] to k, and to the context of 'a-s/c' synthesis effectively according to the relation of [12k--e] to p' represented by [ek]: such that, for example, since 3[ek] closely approximates [p'+p''/3], 6[ek]~=[2p'+2p''/3], and 9[ek]~=[3p'+p''], and since [12k--e] defining the primary increment in lateral phase disparity definitive of transition in states of alignment or resonance, thus between elemental forms--as opposed to the lateral phase disparity between constituent electron S phase cycles; a distinction exemplified in this context by the exceptional case of QN 'l'=0 [s1, s2] forms--, this relation in harmonic recurrence may be understood to define the essential framework of such transition within the more general context in which asymmetrical frames are characterised by disparate a/c and 'a-s/c' aspects of vector synthesis capable of broad reconciliation through this consideration of relations, in particular those between [e], k and p' embodied in the [ek] component, and the [e''] vector; moreover for example by virtue of the effect that various definitive inter-relations between these phase vectors and synthesised components [ek] condition the context generally; and in particular, in addition to the approximate equalities mentioned, a close approximation between 7m and [ek] which permits the relation between [ek] and k to be defined within the context of an [m] scale comprising essentially sequential 7m components constituting the basis of the imagined resolution between such disparate 'phase components' within the synthesis. (Refer to Diagrams K1d and K1e).
NB: In this context, it should be emphasised that those 'electron aspects' within such a model corresponding to QN 'l'=1, 2 and 3 designations, regardless of the further characteristics implied by disparate definitive components of recurrence associated with orbital-type, are defined by the k vector; neglecting in this case the [s1, s2] orbital defined principally by transition in the (3p''--[m]) with respect to k, as opposed to 'by' such a modification of k, and in this context, with respect to 'local origins' [k0]' for consideration of p-, d- and f-type 'orbital contexts' of 'elemental definition' from which they are distinct (refer to discussion of 'Local Origins' below). As such, bearing mind this method of modification of k by A for the p-orbital electron, [k--A], and of k by [4y--3x] defining the d-type electron (i.e. k+[4y--3x])*, each such designation as p, d and f-type is in this model defined by a specific aspect of marginal recurrence within definitive transition in dynamics of primary k recurrence itself, and in the case of the f-type, that further associated with the relation of k to 14.85 x (3p''--[m])~=[m]/2 implied by that approximation and representing the transition represented by the relation of 3p'' and [m] defining the [7 x s2] scale generally. (t may be supposed for instance that the description of 'actinide series' components following Ac89 and Th90 according to 5f14 designation derives in this effect, that the initial configurations evident are inclined to manifest this latter 14.85 x (3p''--[m]) component as an essentially reverberant effect amounting to ‘d-orbital’ variants; presumably according to the explanation given above, and further by virtue of the approximation between [4y] and both 4[ek] and [12k--e] mentioned within the context suggested in which such relations tend to condition the configuration of the frame of synthesis generally).
While the ‘s-’ or [s1,s2]-orbital is, as explained, implied within this general effect by this specific marginal aspect representing [m] recurrence relative to both the frame and 'a-s/c' synthesis by that relation of 3p'' to [m], and to arise according to a progression in that definitive [m] locus relative to the archetypal p'' scale of the N-Cn axis defined by the progressive residual (3p''--[m]), therefore according to which these [s1, s2]-type elemental forms are defined by that [ek] component representing the condition of increasing relative turbulence in successive elemental forms with respect to a local [k0]' locus defining an effectively 'local origin' for p, d and f-type contexts with which they are disparate according to this (3p''--[m]) component (where, to reiterate, that [ek] incorporated within the E'=([ek]--e'') component is broadly definitive of transition between elemental forms characterised by any QN 'l'=0, 1, 2 and 3), the essential distinction between these s-orbital types and further p, d and f-orbital types is that, while the latter may be described directly by the relation of an [ek] component to a local origin [k0]'--effectively a locus of k/p' synthesis-- according to which successive p- and d-orbital components may be defined as the function of respective multiples of such [ek] relative to that origin, that 'local [k0]' origin' itself is distinct or disparate from the specific [m] component of the 7m and [m0] scales corresponding to the definition of the s-orbital by a persistent disparity (3p''--[m]).
As explained in the following, this case for the consideration of 'elemental transition' according to 'orbital-type context' differs from that in which specific s-orbitals are defined in the QED model according, in this conception, to the QN 'n' which therefore ordinarily functions as a local reference in description of those p, d and f-orbitals according to the QN 'l' quantifying the 'lateral phase disparity' between electron S phase cycles in multiples of approximation to p''. The implication is therefore that while elemental transition itself may generally be defined according to the 'phase relation' of [ek] and [e''] described by the factor E'=([ek]--e''), since these [s1, s2] orbitals defined by [m] loci are not explicitly defined by points of k/p' synthesis, any consideration of [ek] and E'=([ek]--e'') transition within p- and d-type orbitals with respect to the definition of a local [k0]' origin--i.e. relative to which the [12k--e] component of such [ek] is imagined to arise--, is to be distinguished from the context in which those [s1, s2] reference points ordinarily define the QN 'l'=0 origin of further QN 'l'=1, 2 and 3 orbitals, and may therefore be defined with respect to a 12k component and local [k0]' origin of periodic k/p' synthesis only indirectly.
This elaboration of multiples of (3p''--[m]) components successively defining 1s to 7s electron orbitals in QED (i.e. such that 14.85 x [3p''--m] approximates [m]/2 representing the maximum extent of divergence between p'' and [m] aspects of p''/[m] synthesis definitive of the frame and these various periodic reference origins) to imply an [m]/2 resultant 'phase shift'* remains intrinsic to the dynamic frame and, it is argued, represents the basis of the QED model according to its QN 'n' designation of s-electron orbitals; and while it is fundamentally implicit both within the evolving phase relation of [ek] and e'' characterised by dynamics of periodic k/p' synthesis and thus within the its further representation in the effect of transition in the AW/[Z] ratio mediated by p'' and [I] (discussed in the following), the relation of local [s1, s2] and [k0]' origins, since these are periodically arising loci in [m]/p'' and k/p' and further k/p''/[m] synthesis respectively whose correspondingly periodic relation is therefore defined by instances of p''/[m] synthesis itself arising within a range of divergence between these [m] and p'' vectors of +/--[m]/2, is not characterised explicitly by this incrementally progressive (3p''--[m]) component (viz. rather by a singular [3p''--m] component implicit within an oscillatory effect defined by that [m]/2 range itself) in consideration of contexts of elemental transition according to 'orbital-type' in the same way that it necessarily defines the description of s-electron orbitals according to the QN 'n' in the QED aspect of the integrated description. *(Refer to the appropriate sub-heading below).
Nor therefore does such (3p''--[m]) progression characterise transition in the AW/[Z] ratio for discrete elemental forms defined by such AW and [Z] as an incremental effect; rather, this transition in the AW/[Z] is characterised more generally by an [m]/2 shift implied within the frame itself of intermittent periodic k/p''/[m] synthesis required to define the context in which such elemental states may themselves be defined and accordingly related effectively by the inference of these 'local origins' for [ek] progression [s1, s2], and [k0]' for further p-, d- and f-types, thus as an oscillatory [m]/2 resultant imaginable with respect to an idealised origin N=[k0] which reflects itself both +[m]/2 in the 12[I] disjunction in transition evident in that AW/[Z] ratio and a corresponding regression (--[m]/2) in the respective ratios for 4s and 5s-forms considered within the scale of its transition; and within which [m]/2 shift the 14.85 x (3p''--[m]) components embodied in the QED description in the QN 'n' and associated QN 'l'=0 dependent on such 'n' represent the incrementally progressive aspect.
That is, in this context of elemental transition, the relation of what may be considered s-type forms according to that QED description and associated p- and d-types in particular is not expressly defined by the QN 'n' as in the QED model in which that designation is required in order to permit further specific QN 'l' designation for description of resultants in the L orbital angular momentum ascribed to electrons. In these differing contexts of QED description and AW/[Z] transition corresponding to that between elemental states, this [m]/2 shift is therefore evident as a +/--[m]/2 oscillation within which the 14.85 x (3p''--[m]) components definitive in QED and of its requisite context of QN description in which those incremental components are implicit, are not explicitly ostensible other than as a singular effectively synthesised (3p''--[m]) component amounting to a correspondingly oscillatory marginal resultant therefore imagined persistently and recurrently to define the relation of [s1, s2] and k0]' origins.
As explained in the following, this [m]/2 'phase shift' implicit in the QED description and corresponding to the elaboration of those 14.85 x (3p''--[m]) components arising within a dynamic of periodic [m]/p'' synthesis definitive of these [s1, s2] origins in the further aspect of the model considering elemental transition (and in the case of QED defining the context in which progressive s-electron orbitals designated QN 'n'=[1, 2, 3, ...7] may also be consistently designated by a QN 'l'=0), is pertinent to this further context only insofar as it implies, by virtue of this inference of that effect within the scale generally, the corresponding centralisation of the [5p''/3] range within the 2p'' idealised range definitive of transition within the AW/[Z] ratio mediated by [I]; and, as suggested, appears to account both for the effect of a 12[I] disjunction in transition of that AW/[Z] ratio over the range 45[I] to 57[I] discussed later, and for the observation that transition in that AW/[Z] ratio for s-type forms is typically constrained to a 6[I] range implied by a persistent (3p''--[m]) phase relation between [s1, s2] and [k0]' origins definitive of respective contexts of 'orbital type' in the characterisation of elemental states in this scheme.
In this respect, it is of some significance that 74 [ek] closely approximates [e] to define the range in which such transition may be understood as a range of 'relative turbulence' described by basic 'c' recurrence, [9c--2*2]=[e], modified to [ek]; since in general, an essential symmetry between perpendicular components in 'c' recurrence defined by [e] --or any 'phase vector' within the symmetrical a/c aspect of the frame of synthesis, and thus its context of idealised 'horizontal phase symmetry'-- therefore also defines the basic range of asymmetry within the context generally; thus in 'lateral phase divergence' corresponding to the condition of alignment or resonance manifesting as such elemental forms and broadly represented by the [12k--e] aspect of [ek] in such a conceptual context.
The Principle of Orbital Aspects as 'Wave Components': a 'Deconstruction' of the QED Model, and Further Elaboration of the Model of Elemental Transition according to E'=([ek]--e'') Transition.
All elemental forms (defined according to a theory of 'atomic number [Z]' and 'relative mass [AW]'), however further characterised theoretically according to an 'atomic model', are in principle to be regarded fundamentally as 'relatively turbulent', effectively 'reverberant' aspects of the H1 form as it is identified empirically as a discrete state here imagined to manifest optimal uniformity in distribution of cohesive force and inertia, in this conception corresponding to the condition of the limiting symmetrical frame representing limiting optima in cohesive resonance implying those optima in uniformity of distribution, effectively of 'cohesive polarity'; and by a reasoned inference, such elemental forms may also be construed as such aspects of the primary scale H1 to Ne10 characterised in this model according to the relation of [e], [e'] and [e''] vectors or resultants in 'c' recurrence to k described primarily by both the [ek]=0.000432778 and [e'--k]=0.0004242 components within the synthesis; bearing in mind that it is the [ek] component in particular which may be considered, in the manner suggested, to define transition between forms described by successive components of s, p, d and f-type orbitals. Regarding this distinction between [ek] and [e'--k] components and the pertinence of their relation to a description of transition in 'relative turbulence' within an elemental scale which is principally dependent upon the relation between [ek] and [e'']--where, as explained, it is the [e] and [e''] components which are conceived as explicitly definitive of traditional 'atomic number [Z]'--, the essential idea is that, since [e'--k] more directly relates k and [e'], moreover in the context in which the approximate equivalence of 10e'' and e' (i.e. 10e''=[e']+[m]/2) facilitates the mediation by [e'] of the description of the 'reverberant effect' of increasing turbulence definitive of the scale of elemental transition generally according to the relation of [e] and [e''] vectors described by the relation of 88e and 98e'' in that context, then it is [e'--k] which, in specific instances, is more directly pertinent to the description of properties associated with that transition itself.
At the same time, since [ek] further incorporates the p' vector within the basic description of this relation of [e] and k, effectively disparate aspects in 'a/c' recurrence (viz. [e] defines 'c' recurrence relative to the frame, and is therefore analogous to p' in 'a-s/c' synthesis; while k describes the a/c relation itself in its principal aspects), then it is considered pertinent to the effect of elemental transition generally, and more particularly between components within specific p, d and f-type orbitals: that is, while [ek] may also be considered appropriate to elemental transition generally, it is also capable, by virtue of the capacity to define a specific origin with respect to both p' and k--since p' is incorporated within it--, to infer the character of such transitions within those orbitals and between respective elemental forms described as such relative to such local origins; essentially according to the relation of [ek] to p' defined by 3[ek]=p'+[p''/3]: i.e. 9[ek]~=[3p'+p'']. It is especially intriguing to note here that (98 x [ek]--e'') =[98E']~=[p--p'']; in addition to the observation mentioned that 74[ek]~=[e]; where, since 98e''~=[e], this also describes the approximate ratio of [ek]/[e'']~=98/74). Moreover, since 8 x ([ek]--[e'--k])~=3p'', it is likely that this specific relation is implicated in various local transitions between p6 and s1 orbital designation.
Additionally, the progressive relation of [ek] and [e'--k] within the scale of [e], [e'] and [e''] recurrence--viz. according to the inter-relation of these aspects within 'c' vector recurrence defined by that of 88e, 98e''; and further 98e'~=['c'+m/2] --accentuates the effect generally, representing a variant aspect of the description of the frame of synthesis of the relation of its symmetrical a/c and asymmetrical 'a-s/c' aspects; although eventually both components [ek] and [e'--k] may be considered to represent aspects of this transition and their variant relations to p' and p'' components of 'a-s/c' synthesis and recurrence as essentially equivalent descriptions of this effect. At the same time, since [e'--k] more directly relates [e'] to k, and since [e']=[10e--c], and inasmuch as that [e'--k] may then be directly related to p', then it represents a more direct method of relating the specific 2p, 3p and 3d orbital forms whose atomic numbers are broadly related by primary 10e increments within the recurring 88e scale.
With respect to the description of this imagined correspondence between an inference of decreasing alignment or resonance, thus implying increasing 'relative turbulence' and the manifestation and elaboration of successive elemental forms--ordinarily within compound states representing the tendency to resolution of such turbulence towards idealised alignment or cohesive resonance--in a scale or continuum primarily defined by these 88e, 98e and 98e'' aspects, the same principle may be applied to its representation in this model as that governing the analytical inference of the 'lateral phase relation' of electron S phase cycles according to approximations to components of p'' phase disparity laterally between such integrated cycles (i.e. described by the QN 'l') to a regular scale of [m] recurrence within the [N-Cn] axis of the idealised archetype; therefore applied to a framework of resonance defined by a limiting symmetrical aspect corresponding to the H1 state and its 'idealised electron' [1s1] defined by limiting p' recurrence in which, while the definitive laterally progressive disparity analogous to [m] is in this case [e] itself modified to [12k--e] construed in relation to p' in the integrated N-Cn axis, thus embodied in [ek]=(12k--[e+p']), that [ek] component becomes determinant in the description of an incrementally progressive elaboration of such diminishing alignment of 'pole components', represented as [FPN/N-Cn] components, and representing the basis, when construed with respect to further [e'] and [e''] components, of increasing 'relative turbulence' conceived as the function of a real range in phase disparity laterally.
This range is therefore primarily defined according to multiples of [12k--e] which when related to p' representing the condition of limiting regularity in the N-Cn axis of the limiting symmetrical frame may be considered to define the effect in progressive asymmetry within the frame (according to which elemental forms may be successively implied) in terms of corresponding multiples of [ek] in that integrated N-Cn axis; therefore in a definition of that scale of elemental transition capable of correlating the QED description of QN 'l' orbitals with the 'atomic number' of respective elements characterised as such, according to the common L orbital angular momentum component of such orbitals representing the lateral phase relation between constituent electron S cycles construed distinctly from the condition of lateral phase divergence itself implying the manifestation of such elemental states.
This presupposes what appears self-evident in this conception that this QED electronic configuration inferred theoretically from the H1 spectrum must be presumed to correspond directly to the configuration of dynamics generally within such elemental states and their putative nuclei, and which are intrinsic to the common frame of synthesis (as explained later (in consideration of the 'Nuclear Shell Model'). The further assertion here is, as mentioned, that concerning the notion that s-type orbitals are primarily defined by a (3p''--[m]) transition, the effect that the elaboration of 74 components of [ek] progression characterising the p, d and f-type orbitals to Ra88 translates to a range closely approximating [e] itself might reasonably be surmised to suggest the distinction between the implication of [ek] within those orbital types considered with respect to local [k0]' origins, and [ek] transition directly involving those s-orbital forms.
In this respect, and as a general principle concerning the description of elemental properties defined according to the identity of given orbital components--e.g. [p1, p2, … p6] types in particular throughout the elemental scale--, what is supposed is that the distinction between elemental forms of corresponding 'orbital designation' pertains principally to the [ek] component within the transitional factor E'=([ek]--e'') construed with respect to such local origins [k0]' representing loci of approximate periodic k/p' synthesis, thus with respect to a point of approximate recurrent synthesis between p'' and [m] components (where [m] represents the fundamental increment or 'phase vector' in the definition of a margin in k recurrence with respect to 'a' and 'c' components in a/c synthesis) defining the resolution of this essential disparity between the archetypal [m] and p'' scales according to the incrementally progressive component (3p''--[m]) defining progression of that [m] scale and its constituent [m] loci representing these specific [s1, s2] orbitals. At the same time, since this resolution according to the progressive relation of p'' to [m] in the N-Cn reference axis only periodically coincides with the p' component of an imagined 'local origin' [k0]' required for the consideration of [ek] and further E'=([ek]--e'') transition with respect to that [k0]' generally definitive of transition between p, d and f-orbital elemental states--and indeed elemental states generally, as defined by the 98e and 98e'' scales--, then the further treatment includes a method of relating these [ek] and e'' components to both p' and p'' according to a ratio of 'atomic weight [AW]' to 'atomic number [Z]' discussed below. (Refer to Diagrams K1e).
That these p6 and d9/10 configurations in particular and the properties associated with the periodic recurrence of such components tend to recur with such characteristic periodicity within such an effect--a 'reverberant aspect' of H1--or frame of synthesis depends, as suggested, on the fundamental character of relations in a/c synthesis whose component intervals (J=[c--a], and [a--5J] in particular) may be defined by primarily by 6k and 9k components and their specific multiples, with margins of k recurrence further defined by the marginal residuals x, y, A=[k--7x] and B=[7y--k], thus [m].
The initial task however, in addition to that of proposing, according to this conception, a unitary dynamic structure itself on which the common definition of the 'electron' may reasonably be based and consistently applied to the QED theory of electron angular momentum, is to represent the manner in which a commonly arising component within the unitary wave dynamic--identified in QED theory as the 'electron' representing a definitive aspect of limiting regularity within that dynamic (i.e. optimal for H1 [1s1]) and in this model of a frame of 'a-s/c' synthesis corresponding to the p' vector (i.e. defining the electron S angular momentum in various interdependent aspects)--elaborates in successive elemental forms according to a more-or-less regular multiplicity which is the function of 'atomic number [Z]'; such that at the same time, within a given QN 'l' orbital type, successive elemental components arise--for example, corresponding to [p1, p2, ...p6] for the p-orbital-- with what amounts to a dynamic regularity within that context, which in this conception is inevitably the function of disparities in 'phase' defined within the frame of synthesis according to specific invariant 'phase vectors', and in the case of the description of lateral phase disparity between electron S phase cycles, approximations to them (i.e. to p'' in particular).
The essential conundrum is therefore effectively that originally addressed by De Broglie theory: to relate a 'frequency' or 'wavelength' to what is inevitably a structure of oscillatory angular momentum and 'energy' mediated by a common 'particle', constrained in that case by the conception of an orbital spatial model of the nucleo-centric 'atom'. The further aspect of the problem is to relate this effect to the condition of elemental transition itself suggested by the 'atomic number', theoretically reduced from an empirical determination of 'atomic weight', on the basis suggested that this is essentially the function of a condition of 'cohesive resonance' or 'alignment' capable of description according to 'c' vector recurrence--thus by [e] and [e''] vectors in particular-- in the diverse or disparate aspects of 'a-s/c' and a/c synthesis in which it is determinant; and to suggest a model in which this relation of 'atomic weight' to [Z] is capable of further fundamental correlation with 'neutron number' according to the common singular basis of this conception.
Given that it is the relative scale of the 'phase vectors', since this inevitably translates to some specific degree of recurrence with respect to p', and therefore to the 'photon wavelength' of visible light in empirical contexts (in this conception), which is ordinarily interpreted in QED theory to infer relative 'frequency' of definitive components corresponding within the integrated description to the definition of the angular momentum of 'particles' (as is generally so for the L orbital component ascribed to electrons within equations) described within and with respect to their 'wave functions' as a variable quantity, then it is necessary to 'deconstruct' this theoretical interpretation, in this case to its basis in the relation of constituent 'phase vectors', at the same time as permitting a description or representation of the same effect according to the principle that successive elemental forms H1 to Ra88 and beyond, are aspects of turbulence, effectively 'reverberation' within a wave dynamic characterised by optimal or limiting regularity within the H1 form or state of optimal uniformity in distribution of cohesive force, and by inference, of 'cohesive inertia' (recalling that this latter aspect of distribution may be conceptually equated with the electron angular momentum; in that case of the limiting symmetrical frame equated with the definitive S angular momentum and corresponding uniform electron S phase cycle dependent for the definition of its comprehension as an oscillatory principle characterised by such a periodicity in 'phase' upon both p' and on this inference of optimal or limiting regularity in p' progression and recurrence definitive of the limiting frame of symmetry which is the fundamental context of the QED theoretical analysis).
This may be accomplished by conceiving that specific degrees of recurrence within and with respect to a frame of synthesis, of variably disparate 'phase vectors' deriving in the relation of 'fundamental phase vectors' ('a', 'b', 'a-s' and 'c') arising with a common 'actual frequency' in this model*, defining as wave components specific aspects of a unitary dynamic of progressive wave recurrence, thus an approximation to synthesis of these disparate 'residual phase vectors' ([e], [p'] etc.) which is therefore dependent on their relative scale within a common harmonically-defined context (i.e. the [N-Cn] axis)--eventually that inferred by the reference frame of limiting symmetry corresponding to oscillatory light dynamics in 'free space'--, strictly defines their relation in 'cohesive phase' within that context; and therefore the configuration of the unitary phase structure as it is empirically apprehended. (*NB: it is only this basic condition or premise of the model which eventually permits the inference of a correspondence between relative scale and relative frequency of residual phase vectors in QED theory). These common specific degrees of approximate synthesis between 'phase vectors' or their relative recurrence are those ostensible relative to an inferred reference, evident as an effect in synthesis corresponding to properties of wave recurrence described in the QED model by 'particle dynamics', eventually defined with respect to light and its properties of oscillatory regularity naturally and implicitly, and effectively necessarily, representing a frame of reference or 'relativity'.
The method therefore proposes, to reiterate, a common context 12k, capable of representation either as an interval of 12k recurrently overlaid upon itself or a progression sequentially of those 12k components, for example in further 36k scales (Diagram K1e), and proceeds to interpolate equivalent components [ek] within it deriving in the inference of a variable relation to that 12k represented by multiples of [12k--e], thus for a repeating or reiterating 12k scale defined [k0]'+12k, multiples of [e] representing divergence in 'alignment' or resonance amounting to the essential or primary basis of a condition of 'relative turbulence' construed as the function of 'c' recurrence and definitive of successive elemental forms (by increasing 'atomic number' and 'weight': as mentioned, it is effectively [e] and [e''] which correspond to 'atomic number [Z]' in this interpretation), arising with respect to a regularly progressive component [p'] in the archetypal [N-Cn] axis in corresponding multiples: thus [12k--e]--p'=[ek]=(12k--[e+p']), where k, [e] and [p'] represent definitive aspects of idealising regularity within an archetypal frame of synthesis.
The representation of the corresponding components of the p-orbital for example is then based on the relation of [ek] to its components [e] and p' in particular in the context in which the relation of a definitive succession of recurrent [ek] components characterising the condition of resonance of a given elemental form (e.g. such that [ek], 2[ek], 3[ek], ... to 6[ek] components considered from a given 'local origin' [k0]' or aspect of N=[k0] imputed to some given 12k component in synthesis with a transitional p' --such [k0]' thus related by the recurrent component [3p''--m] in this variant description to a local 's-orbital reference' given by an [m] component--, correspond to [2p1, 2p2, … 2p6] elemental components), therefore appearing as a variably oscillatory configuration or 'cluster' relative to a limiting regularity in p' vector progression and recurrence--thus effectively to a given p' vector component--definitive of conditions of light dynamics representing the effective reference frame, is interpreted according to the inference of a correspondence between the state of 'relative turbulence' definitive of such elemental forms with the specific configuration, considered as an aspect within the 'unitary phase structure' of the frame of synthesis, implied by the description of such QN 'l' orbitals in the QED model; while the relation of such [ek] to [e''] construed over the greater scale itself from an idealised origin [k0]=N, primarily represented by the linear component E', may be understood to define the more general transition of such elemental forms, where as explained, incremental [e''] describing the higher resolution aspect of transition in 'relative turbulence' effectively represents the relation inferred within a context of graduated resonance or turbulence defined by the essential range in 'c' vector recurrence described between [e], embodied in [ek], and [e''] components of such a transition in resonance or 'relative turbulence' for elemental forms--viz. in a relation further embodied in [E'] and the AW/[Z] ratio-- to the traditional 'atomic number' corresponding to [e], [e''] and implying a corresponding number of 'electrons' in neutral atoms within the 'atomic orbital model', including those elemental states described by such a 'local reference [s1, s2] orbital' which in the QED aspect of description is further described by the QN 'l'=0.
The model therefore permits that the p1 orbital component for example may be represented with respect to a common local origin [k0]', thus also periodically an [m] reference in k/[m] and p' synthesis (thus in effect by periodic k/[m]/p'' synthesis), by [ek], p2 by 2[ek] components and so on, therefore in practice with respect to an origin incorporating that p' (and intermittently p'') component within that reference relative to which the p' component within [ek] may be construed effectively and periodically to arise (viz. while this inference of such a local [k0]' origin for consideration of [ek] progression is, to the extent that p'' is implicated, analogous to the context in which the QN 'l' describes lateral phase disparity between electron S cycles based on approximations to p'' disparity in that lateral phase relation considered with respect to the QN 'l'=0 of the s-orbital itself, it is distinct from that QED aspect of the description in the manner mentioned: that the relation between such [k0]' and [s1, s2] reference origins is distinction from that in which the QN 'l' values are ascribed with respect to an s-orbital defined in the QED model necessarily by both QN 'n' and further QN 'l'=0 values).
Within such [ek] components, both [e] and p' components are therefore considered to arise concomitantly with [ek] itself, with respect to which an incrementally progressive resultant deriving expressly in the higher resolution aspect of [e] recurrence also capable of definitive relation to the reference frame, in this case principally the residual [e'']=[10e'--e], arises to imply and define a further progressive component representing that higher resolution aspect. That is, while these ideally regular disparate components of [ek], 12k, [e] and p' clearly arise within a dynamic of a/c and 'a-s/c' synthesis at disparate rates, it is an essential principle within this conception that not only will these components, considered in sequential elaboration from an idealised origin N=[k0], periodically coincide (in approximate synthesis) at or relative to specific points of reference, but that this coincidence in 'vector synthesis' defining a specific aspect of the 'unitary phase structure' of the frame is progressive, both with respect to its specific components and more generally to the frame of reference itself*.
Moreover, within this periodic effect of 'wave recurrence' in which that progressive component is effectively that of ([e]+p') with respect to recurrent 12k--i.e. in this case, that ([e]+p') component is actually retrogressive (See Diagram K1e)--, a further progressive effect is implied according to the recurrence properties of its components, therefore further implicating the [e''] and p'' vectors in particular. These [ek] components will therefore arise successively in integer elaboration, thus with respect to local [k0]' origins which are effectively defined by 12k and further 36k components within such a frame of synthesis, in these specific definitive multiples [ek], 2[ek], 3[ek] and so on (where 78[ek]~=12k) as the function and representation of progressive 'relative turbulence' within the idealised condition of archetypal cohesive resonance or symmetry, thus within and with respect to the limiting discernible condition corresponding to the H1 elemental state, of which such degrees of 'turbulence' are effective aspects; therefore defining a primary progressive wave aspect characterised by further incrementally progressive components --thus [e''] and p'' in particular--, according to which a transition between discernible or discrete elemental states may be defined by the relation E'=([ek]--e''), and the configuration of that dynamic according to the relation of that factor both to p' and to [ek] itself; noting that ([ek]/[e''])~=[4/3]. For example, the relation of this progressive aspect E'=([ek]--e'') to both [ek] and [e''], and to further p' and k becomes the basis for the inference of the effect that multiple orbital components identified in QED theory arise with a progressive 'wave-like' character (suggested by the mathematical description) while maintaining the appearance of a relatively discrete 'cluster' of such 'electrons' defined and correspondingly capable of description relative to p', effectively therefore relative to the frame of limiting [Qp'] recurrence.
As such, with respect to an ostensibly limiting regularity in p' progression and recurrence represented by the frame of reference (i.e. in practice corresponding to the frame of visible light dynamics), given definitive multiples [ek], 2[ek], 3[ek] etc. arising in the definition of successive elemental forms within the context of that definition by E'=([ek]--e'') will appear as 'clusters' comprising these [ek] components as effectively oscillatory resultants relative to that regularity in p' progression and recurrence, therefore effectively to the p' component of [ek] itself, with the further progressive wave aspect suggested arising by virtue of the relation 3[ek]~=(p'+[p''/3]). These 'clusters' comprising such multiples of sequentially-related recurrently arising [ek] components characterised by such a progressive component--within the further or prevailing context of the definitive relation of [ek] and [e'']-- therefore define the elaboration of successive elemental forms considered as components within contexts of 'orbital type', thus according to these definitive relations of such [ek] multiples to p' itself, at the same time as the broader relation of [ek] to p' may be thought to characterise given orbital types according to the reasoning discussed: of the basic correspondence between the foundation of a QED description of 'orbital component numbers', traditionally based on the mathematics of Laplace's spherical harmonics, in what is conceived in this model as the specific character of [6k/9k] aspects of k recurrence, and the elaboration of corresponding 6[ek] and 9[ek] components of orbital contexts in elemental definition; with the qualification that, in this context of 12k recurrence, the specific components of those electron orbital types represented by modifications of k defining margins in k recurrence may also generally be considered definitive of these elemental components of p, d and f-type 'orbital contexts'.
That is, the progressive component implied in the relation of [ek] and p' according to 9[ek]~=[3p'+p''], thus effectively of [12k--e] to its p' component, suggests the basis not only of the context of elemental transition within and between so-called 'orbital contexts', but of the primary effect of such 'electron orbital' elaboration itself. For example, 2p3 implies 3 specific [ek] components defined with respect to a regularly progressive p' vector which will therefore appear as an approximate 'cluster' or aggregate of those [ek] components successively arising and considered with respect to local origins [k0]', with a further progressive component defined explicitly by the approximation of 3[ek] to (p'+[p''/3]) similarly considered with respect to such [k0]'; while 2p4 corresponds to an approximation of 4[ek] to (p'+[ek]), according to which condition that orbital and the elemental state itself (e.g. primarily O8) will be characterised by dynamics implied by the progressive and recurrent relation of that [ek] resultant to p', with a [p''/3] residual accruing periodically (i.e. according to p'=58.4077p''). The implication therefore is that a common basis for description of the 'atom' generally according to a common configuration in p/k synthesis intrinsic to the frame, thus capable of relating the QED description to a scheme of 'nuclear structure', is suggested by this aspect of the frame embodied in [ek] and e'' progression demanded, to reiterate, by the necessity to explain the basis on which a characterisation of 'atoms' according to 'electron orbitals', thus according to successive numbers within those 'electron orbitals' corresponding to the inference of increasing [Z], may further imply a succession in elemental states.
In this respect, it is of note that, if 9[ek]=0.003895002 approximating [3p'+p''], then since this is also similarly approximate to 6[ek]+ (3 x[12k--e])+p'' and since (3 x [12k--e]) approximates (2k--[ek]--3p''/2) such that 9[ek] approximates (5[ek]+2k--p''/2), a 10th [ek] component (consistent with the elaboration of a 10th d-electron component in this scheme of the correspondence between the QED electron orbital and further 'orbital contexts' of elemental definition and transition) is implied as a further aspect of resolution within this context of [ek] recurrence between [ek] and 12k, more specifically within that aspect defined by the relation of 9[ek] and thus 10[ek] to 6[ek], according to which 10[ek] approximates (6[ek]+2k--p''/2), thus which in multiplicity represents the basis of that resolution: for example, 6 x 10[ek]=60[ek] approximates 36[ek]+12k--3p''. Note also that, particularly when an accommodation is included for the relation of these [ek] and k-aspects in synthesis, this is a variation on the definition of p, d and f-type electron components according to modification of k for marginal k recurrence which further incorporates the p' component within the 'a-s/c' aspect of the frame within this corresponding aspect of p/k synthesis.
* The typical case is that of 'a-s/c' synthesis itself in which a condition of 'a/c phase parity' induced empirically--meaning the elaboration of disparate ['a-s'] and 'c' vectors at equivalent rates in specific axes of the frame, in this case vertically and horizontally as opposed to laterally--permits that that the scalar difference between these fundamental vectors represented by the progressive 'phase vector' p=(['a-s']--'c'), in defining the relation of ['a-s'] and 'c' and its further oscillatory aspect when construed within and with respect to the *2 unit interval of the N-Cn axis and frame, describes dynamics of 'phase progression' within the wave effect defined by those primary 'a-s' and 'c' components and their relation. The case of [ek] considered with respect to its constituent components is merely analogous; with the further qualification that the condition of 'phase parity' governing the elaboration of [ek] as a specific recurrent resultant, thus of further E'=([ek]--e''), is implicit in the fact of its approximate recurrence as a periodically progressive effect relative to the initial coincidence in occurrence at an origin of synthesis of 12k, [e] and p'; further incorporating the [e''] component within a greater context of such dynamic recurrence defined by the principal relations mentioned: 98e''~=[e], the further secondary relation [98e']~=('c'+[m]/2) and 98E'=98([ek]--e'')~=[p--p''], this latter, given the relation 98e''~=[e], suggesting the implication of the 'fine structure constant or 'M-ratio' based on p/[*2] in equations relating the 'atomic number [Z]' to [En] and the Hamiltonian energy for H1.
With respect to 'a-s/c' synthesis describing the relation of 'a-s' and 'c' vectors arising on the FPN or 'pole' and N-Cn respectively, and considered in such synthesis in the N-Cn axis, the model of 'phase parity' permits that these harmonically-defined components of the unitary wave dynamic are ascribed the same 'rate of occurrence' relative to the cardinal loci of that axis which, were these equivalent components elaborating from a common origin [N], would imply common 'phase' or 'phase synchrony', and that their 'phase relation' may be defined by the scalar relation of these invariant 'phase vectors' in a common axis; as such, 'phase progression' is defined by the [p] vector within the limiting constraints of the [*2] unit harmonic interval of that [N-Cn] axis representing its converse phase aspect, thus [N-Co], according to the further relation 137p=[*2+p'].
Concerning the 'Rare or Noble Gases'; the 'Heavy Gases':
In particular for example--and in concert with a description according to [ek] and [e''] components; and noting the relations mentioned [10e''--e']~=[m]/2 and [98e']~=('c'+[m]/2)--, considering the case of the relation of He2 to Ne10 and further Ar18 (Kr36, Xe54), if the initial He2 and Ne10 forms are imagined to be defined primarily according to the E'=([ek]--e'') 'transitional factor' conceived to define transition between discrete elemental states within the elemental scale generally, thus by subsidiary 2[ek] and 10[ek] components respectively--bearing in mind that the respective 'atomic numbers' explicitly correspond to [e] components, 2e and 10e, and that the latter is secondarily or locally defined according to 6[ek] pertaining to the definition of the p6 orbital component with respect to a local reference or origin [k0]' (where the definitive [k--A] component for that p6 is also characterised by the relation [k--A]--2p'~=[p''])--, then, presupposing, according to this conception, a 'reverberant aspect' within archetypal resonance corresponding to the elaboration of any such elemental forms to be defined principally according to that relation of [ek] and e'' embodied in E'=([ek]--e'')=0.0001052279 and its approximate multiples--i.e. 10E' for Ne10--, and inferring from the relation stated of 10e'' to ([e']+[m]/2) that [e'] therefore effectively mediates this principal relation of [ek] and [e''] at specific junctures in transition at which the elaboration of both [ek] and E'=([ek]--e'') as resultants may be considered components within such [e'] approximating [10e''--m/2], such as in the case of Ne10 according to the relations 8[ek]--[e']~=2E', where then the implication of the relation of 8[ek] to [e'] expressed as such (8[ek]--[e'])~=2 x ([ek]--e'')=2E' in both the elaboration of He2 (i.e. since this is defined by 2E') and in the further elaboration of Ne10 effectively upon it (i.e. since the 8[ek] component mediates the transition; and noting that 8E'~=2[ek]--p'') not only suggests the relation between He2 and Ne10 according to such a notion of increasing turbulence construed as a 'reverberant effect' defined by that transition and the 'transitional factor' E'=([ek]--e''), but the further basis on which the Ar18 and Kr36 forms in particular may reasonably be understood as further manifestations of that same reverberant effect at diminishing degrees of resonance. That is for example, within the primary scale H1 to Ne10, the bounds of the turbulent or reverberant aspect may be represented by the relation 10[ek]--[e']~=10E'~=[3e''+E'], since [ek]~=4E'+[p''/2], and 3E'~=(e''--[p''/2]), and where 4e''~=(3[ek]+p''/2), while 9[ek]~=[3p'+p''].
NB: y=(9k--J/2)=0.0004302695 and [ek]=0.000432778. Note also, to reiterate, [10e''--e']~=[m]/2 and 8e''~=(2p'+[m]/2).
Further, since [k--A]~=(2p'+p''), 6[ek]~=(2p'+[2p''/3]), and, following from the preceding arguments--bearing in mind that 8E'~=(2[ek]--p'') and 8e''~=(6[ek]+p''), and since 15[ek]~=2e', then 31E'~=[e'+p''] --, then the implication of the following is that this 31E' pertains to the elaboration of Rn86 upon Xe54. (Note also that 36E'~=[3p'+3p''] while 9[ek]~=[3p'+p'']).
It is of some importance therefore to observe that, by virtue of the ratio ([ek]/[e''])=1.32127, the further elaboration of [8e] and a subsidiary [8e''] to imply Ar18;
where  since 6[ek]~=[2p'+2p''/3], then its approximation to [8e'']~=[2p'+2p''] corresponds broadly, with a disparity of ~[4p''/3], to the context in which that 6[ek] component may be considered definitive of transition to imply that 3p6 elemental form construed with respect to an origin [k0]', at the same time that;
 the further elaboration of 8E'~=(2[ek]--p''), and 6[ek] construed from that local origin to imply Ar18, with a disparity ~[4p''/3] relative to that 8e''; in concert with the observation of the disparity ~[p''] between [k--A] and 2p', supports the supposition that Ar18 represents such a further reverberant aspect of both He2 and Ne10 aspects of the elemental transition, or scale of 'evolutionary resonance'.
More generally, it may also be observed that, since 18E'~=([3p'/2]--[3p''/2]) and thus 36E'~=[3p'--3p''], then a simple proliferation of 18e'' components, where 17e''~=2k+[m], while it does not of itself imply the elaboration of these successive Ar18, Kr36 and further Xe54 states, nevertheless tends to amplify the effect in the manner characteristic of the dynamics of vector synthesis and dynamics of progression and recurrence generally mediated by such phase vectors; where the approximation 18e''~=[2k+A] implies a particular consonance with the character of the p6 orbital component itself, characterised by the [k--A] modification to k recurrence.
At the same time however, the properties of the 3d6 form (Fe26) and the intercession of the 10d-type elemental forms generally within such an effect of simple 18E' elaboration --interpolated within the scale of [e] vector succession implying increasing 'atomic number'-- must therefore be presumed to derive both in the peculiarity of transition of the local origin represented by the [s1, s2] orbital (viz. the more complex description in Part FOUR suggests an [m]/2 transition at that specific juncture, sustained in 4s2; in addition to a further transition arising by virtue of 14 x (3p''--[m])~=[m]/2), and primarily in the effect that these p- and d-type orbitals represent disparate principal components within a/c synthesis described according to [6k/9k] recurrence within a common [12k/36k] scale of such k recurrence; thus described in this model by variant modifications of k corresponding relative degrees of marginal recurrence (with respect to 'a' and 'c' components), [k--A] for the p-orbital components and (k+[4y--3x]) for d-electrons.
This disparity between these modified components within the archetype implies an accrued disparity recurring with respect to k of k+([4y--3x]+A)*, thus effectively with respect to 12k and 36k components defining the symmetrical frame of a/c synthesis, in the respective elaboration of what are designated p and d-'electrons'--or regularly recurrent wave components described as such--, broadly with respect to a 12k component of the scale of regular k vector recurrence; which in the framework in which such a 12k component of [ek] in particular may be ascribed a 'local origin' [k0]' effectively between contexts of marginal recurrence locally, represents the basis on which the archetypal configuration conceived over the greater scale (representing the greater universal context itself towards which the resolution of 'real turbulence' within asymmetrical reality naturally inclines) may be considered both locally and generally.
*(As explained in greater detail below, this resultant locally derives by virtue of the effect that 10 x (k+[4y--3x])~= (12k+[4y--3x]--[m]/2) and 6 x 2[k--A]~=[11k--A]), and will therefore tend to resolve within the greater context with respect to such 12k according to the relation of those residuals, [4y--3x] and [A] to k and 12k). In general, it is this configuration which is essentially implicit in the configuration of the H1 spectrum itself according to this conception and analysis; and whose interpretation in QED theory may be understood to anticipate the structure of this relation between local and general aspects within a unitary wave dynamic and its frame of synthesis according to these common interdependent aspects of that frame of vector synthesis characterised by the inter-relation of these definitive 'phase vectors'.
Representation of p, d and f-type Electrons and Further 'Orbital-type Contexts' of Elemental Definition:
*As explained at length in Part FOUR, the description of p-type and d-type electrons according to modifications of k, such that the p-electron is represented by an incremental component [k--A] within a 12k context of k progression and recurrence reducing from 2[k--A], and the d-type by (k+[4y--3x]), where [4y--3x] =0.000622782, derives in the necessity both to imply the distinction between these specific p- and d-components based on that inferred within the spectral analysis of H1, and to establish a common framework in k-recurrence for those respective definitions, minimally the 36k scale within which [3 x 12k] and [4 x 9k] components, according to which [x, y] and further A and B are defined (e.g. y=(9k--J/2], A=[k--7x]), may be commonly accommodated; and through which their intrinsic interdependence may be established, principally by virtue of the close approximation between (9 x [4y--3x]) and 2k --and in the further aspect of this model and scheme of [ek] progression and recurrence, the approximation of the sum (A+[4y--3x]) to 2[ek] --, and the further approximation of 11A to k (bearing in mind the approximate equivalence of 4y itself to both 4[ek] and [12k--e]). It is essentially the necessity to infer this inter-relation between components commonly defined by [ek] progression generally and those arising specifically within the context of k recurrence within a/c synthesis in the horizontal plane of the model, thus to establish the further basis of continuity between d- and p-type elemental forms evident in the structure of that phase transition defined by [ek] progression, which requires that this distinction be made: thus, as suggested, that the basis for that inter-relation may be established, principally for example by virtue of the correspondence of the difference between [k--A] and (k+[4y--3x]), equal to that sum of A and [4y--3x], to 2[ek]. (Note also: [4y--3x]--[m/2]~=[e''+A]).
Within this further context of inter-relation between [ek] and k recurrence, the further aspect of this inter-dependence between [k--A] and (k+[4y--3x]) aspects implied within the synthesis with respect to the scale of k recurrence--viz. a simple sequential elaboration of the k vector from an origin N-- derives in the specific effects that 10A approximates 2p' with a disparity of p'', thus, 10A~=[2p'--p''], and further that 6[ek]~=2p' approximates [k--A] itself with a similar disparity of [2p''/3]: that is, 2p'~=([k--A]+p'') and 6[ek]~=[2p'+2p''/3]; where this is only to state that 11A~=k. The implication of the latter in the peculiar properties of 'chemical inertia' of the p6 forms (Ne10, Ar18, Kr36 and so on) defined by 6[ek] locally, and therefore characterised by its definitive approximation to 2p' in the context of the vector synthesis, is that, since this p'' disparity between [k--A] and 2p' is specific to the p6 form in which 6 x 2[k--A] components elaborate to define a progressive wave effect defined by that basic [k--A] component--as shown in Diagram K1d1, this is peculiar to the elaboration of such a 2[k--A] component, that, by virtue of 44m~=k, where A=[4m], the effect that 6 x 2[k--A])=(11k--A) yields the characteristic resultant A with respect to a multiple of k, moreover [k--A] with respect to the definitive 12k component with the scale of regular k vector recurrence, implies the tendency for this elaboration in multiples of 6 to perpetuate locally--, then the associated p'' lateral phase disparity definitive of the p-orbital generally (i.e. described by QN 'l'=1) implies a relative symmetry between these perpendicular components; those of the lateral phase disparity and the definitive p'' disparity implied between the progressive [k--A] component and 2p' within that recurring or reiterative elaboration of the p6 effect.
That is, a further principle of the model is that, according to the meaning of '[6k/9k] recurrence' discussed, primarily within a common 36k component within the greater scale of k recurrence, the integrity of specific electron orbital types, particularly the p- and d-types, is defined by approximations to common approximate degrees of k recurrence within the context in which k is thus modified to the [k--A] and (k+[4y--3x] components mentioned, these marginal components therefore mediating the description of such recurrence and the configurations in synthesis implied by it within those greater scales of k and [m] recurrence (See Diagrams K). To reiterate, the 12k component therefore functions as a reference context within which definitive p' and [e] vectors may be related, noting the role of p' generally as an effective 'unit of integration'. (Refer to subheading below, 'On Integration'). As such, 6k and 9k components--noting the further effect of the relations of 6[ek] and 9[ek] to p'-- are conceived to recur within a common context, primarily an interval 36k within which the 9k and 18k components correspond in the synthesised context of such recurrence to the elaboration of the 9d/10d-orbital; while the 6k and 12k components correspond to the elaboration of the p-type orbital of 6 electron aspects.
These common or basic 36k components are therefore reducible to subsidiary 12k components with respect to which it is convenient to relate [e] and p' as explained, while those specific k components within these common [12k/36k] contexts definitive of all such orbital types are themselves, modified by [A] in the case of the p-type components, thus [k--A] in 6 x 2[k--A] components to describe such orbitals according to corresponding 'marginal progression', and similarly by [4y--3x] for the d-orbital such that 9 x (k+[4y--3x]), since 9 x [4y--3x] approximates (2k--[m]/2), implies the necessity for a further d-component to define the 10d orbital configuration according to these degrees in marginal progression within and with respect to the basic [12k/36k] context; both of which are to be understood within the context suggested in which it is the further [ek] component which defines the distinction between these successive components in correspondingly successive or discrete elemental forms. Additionally, the 14f orbital may be defined in the same way by the modification of k to k+(3p''--[m]) for such components to imply over 14 elaborations of that marginally progressive component a resultant of (2k+[m]/2) relative to 12k, naturally resolving to recurrence with some multiple of 12k according to the relation in approximation of 44m to k: that is for example, since 88 x (2k+[m]/2) approximates 177k=[180k--3k], such resolution to a multiple of 12k requires 4 multiples of those 88 to imply such approximate resolution; thus [4 x 88]=352=[11 x 32] such multiples of (2k+[m]/2). Of some significance here therefore is this specific approximation of 88m to 2k, and its consonance with the relation of 88e to 2*2.
Similarly, since 10d implied by 10 x (k+[4y--3x]) further implies a resultant approximating ([4y--3x]--[m]/2) relative to 12k, while the elaboration of 6 x 2[k--A] approximates [11k--A] to define the p-orbital implying a resultant of minus [k+A] relative to 12k, then such resolution to equivalence with the 12k component of these respective resultants arising relative to 12k will be the function of the respective relations of those resultants to 12k, thus to be expressed as factors of multiples of 12k. As such for example, since 11A approximates k, for [A]=4m, then a disparity [k+A] will 'resolve' simply according to the approximate equivalence of 11 x [k+A] to 12k; while the ([4y--3x]--[m]/2) resultant requires the more complex elaboration suggested by the original relation itself, of the approximate equivalence of the elaboration of (9 x [4y--3x]) to 2k--[m/2], thus, since that latter value multiplied by 6 equals (12k--3m)=(12k--[B]), in [9 x 6 x 132]=[9 x 792] elaborations of that ([4y--3x]--[m]/2) resultant. The relation between these respective aspects of resolution for p, d and f-orbital types is generally mediated by the common factor 11, and as is evident generally, common multiples of these effective 'phase factors' emerge within the integrated synthesis based on the principal relations between dominant phase vectors, and in these cases in particular, complicated by the modification of k by 'marginal phase vectors' [A] and x, y.
Further, since a disparity ([k+ A]+[4y--3x]--[m]/2)=0.000845477 is also implied by those resultants in the relation of these conditions or orbital states with respect to 12k which implies a condition of further resolution over some appropriate multiple of that relation and context, then for example--further noting that ([A]+[4y--3x]) approximates 2[ek]--, since (40 x 0.000845477) approximates 12k, 40 multiples of the 12k context of synthesis in which those resultants may be commonly related according to such a disparity or marginal phase differential 0.000845477, will resolve within that 12k component in the synthesised context. And while the significance of this effect is questionable, it may relate to the effect that approximately 40 elemental states separate the conditions in which d10 and p1 orbitals define sequential states, thus between Ga31 [4p1] following Zn30 [3d10], and Lu71 [5d1], and similarly, between the 5p1 form [In49] following Cd48 [4d10], and Ac89, given as a '6d1 form' (bearing in mind that the designation by QN 'n'=6 in this context is considered dubious: refer to further su-headings below). Generally then, as is evident, all such local disparities in marginal recurrence considered relative to 12k will be similarly resolved generally within the greater context of p/k synthesis to imply its definitive configuration, and thus that of the 'fine structure' of the H1 spectrum, from which the further context of an elemental scale may be inferred which is consistent with the conception of such forms as 'relatively turbulent' aspects of or within that H1 state of limiting cohesive resonance, or 'uniformity in distribution of cohesive force'.
With respect to the further aspect of such a context in which resolution between multiples of [ek] and p' tends to amplify the configuration of this harmonically-defined phase structure--and indeed constitutes one principal aspect of that dynamic structure--, it may further be observed that were an effect in [ek] progression for instance interpolated, as in this model, within a common synthesised 12k scale, therefore further approximating a description of the relation of p' and k in that context, then the approximation of [k--A] to [2p'--p''], where [A]=4m, becomes secondarily definitive of continuity within the context of the p-orbital whose configuration is primarily defined by the approximation of 6[ek] to (2p'+[2p''/3]). Since it is also noted that since the component [4y--3x] in (k+[4y--3x]) defining the d-orbital electron as a progressive component--such that (9 x [4y--3x])~=2k-- is approximately equal to ([p'--2p'']/2), further noting that 9[ek]~=[3p'+p''], the likely significance of these specific p'' and 2p'' residuals relative to p' in the cases of [k--A] and (9 x [4y--3x]) is that they are respectively consonant with the approximations to [p''] and [2p''] lateral phase disparity definitive of the L orbital angular momentum in QN 'l'=1 and 'l'=2 respectively for p- and d-type orbitals. In this regard, it might also be supposed here that the effect that 15[ek]~=2[e'] generally reflects itself in the direct continuity observed between 10d and 6p orbital contexts (at d9/d10-p1), presuming, in the context discussed, its essential basis in that of a corresponding continuity in that aspect of the configuration of synthesis in which such a continuity arises between definitive [6k/9k], thus over [9k+6k]=15k components, with respect to a local origin [k0]' corresponding to the definition of the 4s2 orbital.
Regarding the 4f14 orbital in particular, what is supposed is that, while the context of the orbital is primarily defined as suggested according to the elaboration of 14 x [(3p''--[m]) residual components, it is the further elaboration of 14[ek] in approximation to (2k--2m)+[ek], since 13[ek]~=(2k--2m), which implies that a definitive progressive component [ek] with respect to 2k is modified by this 2m disparity; the resolution of which, implied over an elaboration of the basic context itself by 14 to 28[m]=(4 x 7m)~=4[ek], is therefore generally consonant with the resolution of the disparity 2m arising between k and the elaboration of (6 x 7m)~=[k--2m] when considered generally within the synthesis. As such, in this specific aspect of the analysis in which [ek] is related to k and [m] components of a/c synthesis rather than p' and p'', the resolution of the disparity between 6[ek]~=(k--[7m/2]) defining the context of the p-orbital type elemental states and the disparity implied between 14[ek] and such k, [m] components is generally consonant with that between the contexts of the p- and f-type orbitals, mediated by the common component [ek] implied by 14 x ([2k--2m]+[ek])=(10[ek]+28k). At the same time, in simple consideration of differing contexts of elemental definition itself according to such 'orbital types', it is sufficient and more straightforward in the description of the actuality of an asymmetrical frame principally defined according to the 'a-s/c' aspect of the synthesis of which these further relations of [ek] to k and [m] are subsidiary components within the a/c aspect, merely to regard 14[ek] as (12[ek]+2[ek]), and to imply a common context of 84[ek] within which 6[ek] and 14[ek] components may be related with respect to [p'] and [p''].
Regarding the implication of an approximation to a [p''] lateral phase divergence associated, by virtue of the relation 9[ek]~=[3p'+p''] within the context discussed in which 10[ek]=(9[ek]+[ek]) may be correlated with the 'd10' effect in this model, with a transition from the d10 to p1 elemental forms (e.g. Zn30 to Ga31 etc.) when considered in a context of continuity in [ek] elaboration with respect to the respective 4s2, 5s2 or 6s2 'reference orbitals' (that is, since p-orbitals follow directly from d-orbitals and orbital types, and given that the p1 component may be excluded in this case from the effect of the approximation of 6[ek] to [p'+p''/3] defining the 'p-orbital context' itself), a specific and definitive consonance is also supposed between that p'' phase disparity implied between 9[ek] and 3p' components considered in the integrated N-Cn axis of p/k synthesis, thus within that synthesised effect generally, and that defining the specific distinction between QN 'l'=2 and 'l'=1 designations for those respective d- and p-type orbitals themselves made, it is argued, on the basis of an approximation to [p''] lateral phase disparity similarly ostensible in the 'lateral synthesis' inferred within the integrated [N-Cn] axis, and in this case further considered to distinguish those respective conditions of the lateral phase relation of integrated N-Cn components described in the QED aspect of the conventional model by electron S phase cycles which may therefore be imagined to characterise the definition of such p- and d-type orbital contexts (viz. presumably according to the inference of a corresponding L orbital angular momentum component inherent within the conventional 'nuclear structure' conceived to define the lateral phase relation of proton S phase cycles: refer to later subheading on the 'Nuclear Shell Model').
Bearing in mind the condition in which an elaboration of 10 x [k+(4y--3x)] implies, since 9 x [k+(4y--3x)]~=(2k--[m]/2), a resultant approximating (k+[4y--3x]) when this is construed within a context in which the [m]/2 component may be distinguished as an [m]/2 phase shift implied at those s2 junctures with respect to the 7m scale which is consonant with the scale of the accrued 14 x (3p''--[m]) transitions mentioned, and further noting the approximation of [4y--3x] itself to [2e''--p''] effectively overlaid on that effect, it is also supposed that this continuity within effectively marginal 'phase transition' between d10 and p1 components and thus d- and p-type 'local orbital contexts' defined within the scale of elemental transition, since it is effectively mediated by a tendency to resolution implicit in the disparity in the elaboration of 10 x (k+[4y--3x]) and 6 x [2k--2A] components construed in a synthesised context and frame of elaboration of such 'phase vectors' within a common harmonically-defined scale of their recurrence with respect to 12k and [ek] in particular, thus in which the effect that such a disparity is eventually more-or-less seamlessly accommodated becomes definitive of the configuration of the synthesis, will, as mentioned, principally implicate and depend on these specific relations in marginal k recurrence within the further context of k and [ek] recurrence.
A Note on the Method of Analysis of the Frame of Synthesis: as applicable to a model of [ek] and [E'] progression and recurrence.
As a general principle in this model therefore, this scheme of [ek] progression considered within and with respect to local contexts of k and [12k/36k] recurrence may be understood, to the extent that it defines tendencies to compound 'chemical synthesis' of such elemental states according to the exigencies of cohesive equilibration or resolution of 'relative turbulence' corresponding to continuity in phase transition within those local compound contexts or states, to constitute the basis of the traditional theory of 'chemical valency': according to the idea that such continuity represented by that in [ek] progression implied in such compound states of synthesis also implies tendencies to horizontal phase symmetry within the resultant context corresponding to that in the relation of [ek] to p' in particular; and while it is sufficient here to imply such a tendency to symmetry in the continuity of complementary relation between [ek] components of respective elemental states within such local contexts of orbital definition according to 6[ek] and 9[ek], thus 10[ek], and their relation to multiples of p', in order to infer such a correlation with the notion of 'valency', this is to be understood more correctly in the further context in which p' defines the electron S phase cycle itself. (NB: the H1 state itself, thus the limiting symmetrical frame, is defined within such a scheme by both [ek] and E' as singular initial components arising from an idealised origin of archetypal synthesis N=[k0]).
In order to appreciate the context of such reasoning however--bearing in mind its intention to elucidate a correspondence between the configuration of the 'fine structure' of the H1 spectrum, and its analysis in QED theory--, it is necessary to consider that a scale of k progression and recurrence be elaborated from an origin N which defines a sequential elaboration of these k vector components describing the relation of fundamental phase vectors 'a' and 'c' in the N-Cn axis and which, when incorporated within an integrated [N-Cn] axis of both 'a-s/c' synthesis and [e], [e'] recurrence, effectively superimposed within such a synthesis, therefore such that 'c' components are common to both 'a-s/c' and that a/c aspect of the synthesis defined by the k vector, may be directly related to 'c' recurrence with respect to the frame, which is itself defined by [e] and [e'] recurrence, through the relation of k, and in this scheme 12k, to those latter 'phase vectors'.
This method of juxtaposition of disparate scales or series from a common origin on the N-Cn axis in such a framework of vector synthesis is considered feasible in the description of dynamics of 'wave recurrence' implicit in such frames of synthesis and defined by primary 'phase vector components' because, while these fundamental vectors 'a', 'a-s', 'b' and 'c'=[b--a] are posed within the scalar model to arise with a common actual frequency, the real disparity represented by that between their harmonically-defined scalar magnitudes (when each such vector is itself imagined to represent the translation of a fundamental cohesive disparity in cohesive potential in the FPN to an effective 'frequency differential' when imputed to linear cubic axes of such a scalar model) may also be construed as a 'phase disparity or differential' within a given common harmonically-defined context represented by a common 'harmonic interval' in a definitive model axis--in this case the [*2] unit interval of the N-Co component of the N-Cn axis principally definitive of any such empirical frame of synthesis in which wave dynamics are to be apprehended and analytically described--, therefore represented by secondary or residual 'phase vectors' defining the relation of such vectors: for example, the vector p=['a-s'--'c'] in the case of 'a-s/c' synthesis and J=[c--a] in a/c synthesis, where further [19a--16c]=2k represents the minimum practicable common 'phase currency' in that a/c aspect of the synthesis (i.e. [c/a]~=[19/16]); to be distinguished from further 'progressive phase vectors', such as p', p'' and [e], [e'] and [e''] etc., when define the relations in recurrence either of those differential resultant vectors or the fundamental vectors themselves to the framework or axes of the model.
Accordingly, since [e] and [e'] represent the basic vectors defining resultants in 'c' recurrence relative to the N-Cn framework in both 'a-s/c' and a/c aspects of the synthesis, and since these residuals simply elaborate with respect to the 2*2 unit harmonic interval--thus its multiples in the extended scale of recurrence-- from successive multiples of 9c and further 89c, 881c etc., these may be represented in scales of elaboration from a common origin N along a synthesised 2*2 unit axis in which both are effectively spatially concurrent--that is, the [e'] residual arising [e']=[89e--2*2] is simply permitted to elaborate successively from a common origin N to imply the relation in scalar magnitude [10e--e']=[e''], where [e''] represents an even higher order of 'c' recurrence, specifically [e'']=[881c--198*2] --, thus in common juxtaposition with scales of k and [m] recurrence similarly elaborating from that common origin of their synthesis at N, provided that the real frequency occurrence of these respective residual vectors, k, [e], [e'], and p' in particular, neglected in the explicitly scalar model of the frame of synthesis, is effectively accounted for in further aspects of the QED analysis: for example, through the use of the 'fine structure constant' which, it is argued here, effectively embodies the basic frequency relation between p and p' components expressed by the relation 137p=[*2+p']; moreover whose derivation from that relation p/[*2] incorporates and depends on the application of various z-ratios describing the relative frequencies of actual occurrence or elaboration of [e], [e'] and further [e'']=[10e'--e] vectors. A common frame of p/k synthesis comprising such juxtaposition of disparate scales is therefore established to describe the configuration of an effective hierarchy of archetypal resonance with respect to which tendencies in real 'resonance/turbulence' are naturally defined, and corresponding to that which is effectively described within the QED model according to the simple scalar differentials of these residuals, with the qualification suggested regarding the actual frequencies of their elaboration as resultants within an integrated dynamic context of 'distribution of cohesive force'.
To clarify the basis of such a method, since the elaboration of 2k depends on that of 16c relative to 19a, thus such that 2k=[19a--16c], such that, within a context of synthesis this 2k component, and implicitly k itself, will tend to predominate as a sequential elaboration defined by 1003k~=2*2 within that frame of synthesis when that approximation is permitted to define a recurrent local 'origin' with respect to which other phase vectors may be considered--and are in fact apparent within the lateral synthesis--, and since the elaboration of [e] from 9c=[2*2+e] depends on the primary elaboration of that 9c according to which further 88e implies a similarly approximate recurrence relative to 2*2 in that aspect of 'c' recurrence, then in general, the common relation of [e] and k to 2*2, while it derives in aspects characterised by a disparity in the real frequency of occurrence both of 'c', in a ratio ~[9/8], and of those specific k and [e] phase vectors, may be expressed according to both the relative scale of those k and [e] represented by [12k--e], and by the further relation of that [12k--e] to a common component p' in the 'a-s/c' aspect which may be considered here to represent that common context of recurrence relative to 2*2 units (i.e. through the inference of [ek]); therefore according to which that real frequency differential in the elaboration of k and [e] with respect to 'c' implied by that ratio [9/8], k occurring more frequently in that context, may be understood variously to resolve within further aspects of the synthesis mediated by [ek], with the qualification that 'amplitudes' evident within the lateral synthesis arising by virtue of this real frequency disparity may, since apparent 'frequencies' ascribed to such 'phase components' in the conventional analysis are ordinarily the function of this relative scale, be related, as in such analysis to those 'amplitudes' (as in the case of the 'path integral formulations' of QED).
Notably, this resolution consists principally, since [10e--'c']=[e'], in the periodic relation of [e'] to k represented by [e'--k], and in particular in the further aspect of such dynamics that, since the factor [9/8] corresponds broadly to the relation of 98e to 88e, then, if 9c is construed to arise within a 10c scale of recurrence such that, regarding the incremental component of [e] implied in that further elaboration of 'c' as 10c=(2*2+'c'+[e]) plus an increment implied by that further progression of 'c' upon 2*2 considered to be embodied in the relation of [e] and [e'] expressed 10e'=[e+e''], thus by 99e=[10c+e'']--permitting that the elaboration of [e] may be considered to arise with respect to 'c' according to a rate approximating ([88/98]) x 9~=8.1, where for (98 x [e+e''])~=99e, that 8.1 becomes ([88/99]) x 9 =8 --, and since the consideration of [e] in these components permits that the combined or integrated elaboration of [e] construed as such in these [e] and [e''] aspects may be considered within a correspondingly integrated synthesis to be broadly commensurate with the rate of elaboration of k with respect to 8c, then the further relation of close approximation between [98e''] to [e] discussed may be incorporated into the analysis of elemental transition according to an interpretation of the factor E' as definitive of this aspect of resolution between disparate components k and [e] within 'c' recurrence; more generally permitting that, since the essential configuration of this inherent tendency to resolution within the synthesis towards a condition of cohesive equilibration may be imagined to derive in that of the relation in synthesis of these disparate 'phase vectors' and residuals in recurrence, in this case implicit within this further dimension of 'c' recurrence represented by the relation of [e] and [e''], then a description based on these relations is adequate to the integrated description, presumably, it is argued, that implicit in the QED model: moreover since it is only the relative predominance of these harmonically-defined aspects of periodic resolution--thus of relations in the scale of 'phase vectors' and in their real frequency together implying relative 'phase' itself between fundamental components (viz. as opposed to 'phase relations' inferred between specific aspects within the frame of synthesis defined by common phase vectors, in particular, that imagined between 'particles')--which becomes definitive within the real effect of 'wave interference' or 'a-s/c' and p/k synthesis and its integrated description naturally constrained, as in the QED model, by such dynamics of synthesis and recurrence.
Additionally, since it is supposed in this model that the measurable configurations within the H1 spectrum interpreted as 'wavelengths' are principally the function of these relations, represented as ratios, between dominant component 'phase vectors' within p/k synthesis--thus for example, [k/p'], [p'/m] and so on--, then Part FOUR develops a scheme in which these are considered to correspond directly to the squares of a specific trigonometric ratio defining the relation of sides in a right triangle representing the intrinsic 'rotational moments of inertia [Im]' within the integrated 'a-s/c' plane itself--thus a trigonometric function of its definitive angle D2, further implicating the QN 'n' defining the relative scale of that triangle, and represented by a factor [F]2-- with respect to which a reorienting force, operating in components corresponding to such Im over a definitive range, induces transitions corresponding to and ostensible as configurations in p/k synthesis capable of interpretation according to the relation of the ratios mentioned to a specific context representing the frame of synthesis embodied in the 'Rydberg constant', derived in this model according to a revised idea of its basis as definitive of the context in which such a factor might meaningfully be applied to imply the H1 spectral wavelengths.