Informational Foundation of Dynamics Version7

Wecarryoutaharmonicanalysisof the internal spaceM30of IFD(v6[3]), incorporatingtherigorousspectralresultsof [4].Fourresultsareestablished.(1)Derivationofα=1. Reference [4]provesσ(S†S)=[1,5]onthegoldenratiohierarchical space, withλmin(S†S)=1 (theboundary conditionu−1 =0preventsazeroeigenvaluedespitekerS ̸={0}).ThespectrumofL30|C=0isthereforen≥1[µn+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)