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The research aims to provide a comprehensive spectral analysis of the internal space M30 in Dynamics Version 7, focusing on stability and orthogonality.

May 21, 2026Open Access

Informational Foundation of Dynamics Version7

Key Points

The research aims to provide a comprehensive spectral analysis of the internal space M30 in Dynamics Version 7, focusing on stability and orthogonality.
Conducted harmonic analysis incorporating rigorous spectral results.
Established parameters such as α=1 and the spectral gap for charged leptons.
Exclusions of entropic terms without observable consequences.
Derivation of α=1 ensures λmin(L30)=µ1+α, placing the electron correctly.
A positive inter-bandgap (δ1) indicates that charged leptons are isolated spectrally.
Exact relationship between parameters β and α is confirmed at first order.

Abstract

Wecarryoutaharmonicanalysisof the internal spaceM30of IFD (v63), incorporatingtherigorousspectralresultsof 4. Fourresultsareestablished. (1) Derivationofα=1. Reference 4provesσ (S†S) =1, 5onthegoldenratiohierarchical space, withλmin (S†S) =1 (theboundary conditionu−1 =0preventsazeroeigenvaluedespitekerS ̸=0). ThespectrumofL30|C=0isthereforen≥1µn+α, µn+5α, placing the electronatλmin (L30) =µ1+α. Requiringconsistencywithλgeom=4 (SU (2) ×U (1) fibre) andµ1=3 (S3) givesα=λgeom−µ1=4−3=1. (2) Spectral gapandparticlestability. Withα=1, the inter-bandgapδ1= (µ2−µ1) −4α=5−4=1>0: chargedleptonsarespectrallyisolatedbyconstruction. (3) OrthogonalityofHidandHpers. Thescalarharmonicoverlapgid, pers=0, soβ/α=3√5/φisexactatfirstorder. (4) Exclusionoftheentropicterm. Theterm−λ (¯ψψ) ln (¯ψψ) isnonlinear, notderivedfromAxiom0, andhasnoobservableconsequences. ItisexcludedfromIFD. Thecompleteparameter-free structure is: φ (Axiom0), α=1 (spectral consistency), β=3√5/φ (RGfixedpoint), Dhier=110 (tangent-spacegeometryofM34)

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