Imhotep Infinity — A Proposed Unified Framework from Ψ = 100/99: Papers 1–12, Final Referee-Cleaned Edition

This record contains the complete twelve-paper Imhotep Infinity series, Final Referee-Cleaned Edition (May 2026). All papers are Iron Rule clean: derivation-layer mathematics flows only from the 45 Vision postulates and the single arithmetic generator Ψ = 100/99 (ε = 1/99). No measured physical constant enters the derivation layer. External comparison appears only in separated final sections. PAPER SERIES OVERVIEW Paper 1 — The Binary Architecture and the 45 Vision PostulatesEstablishes the foundational framework: the binary road (0-side / 1-side), the two fields ΦG and ΦH, the Z6 symmetry structure, and the 45 Vision postulates. The master generator Ψ = 100/99 and coupling ε = 1/99 are defined. Paper 2 — The Z6 Spectrum, CP Violation, and the Integer 137Derives the Z6 spectral sector assignment j = 0, 1, 2, 3, 4, 5, proves Z6 uniqueness via the Chinese Remainder Theorem, establishes the integer 137 = N²−9N+1 at N = 17, and derives the structural CP-violation source from χ₁ (g¹³⁷) = e^ (−2πi/6) ∉ ℝ. Paper 3 — The QFT of ΦG: Action, Propagator, and Effective ActionConstructs the complete quantum field theory of the ordering field ΦG: the Gaussian action SG, the 11D propagator G̃G (k) = 1/|k|², and the effective action SeffΦH via functional integration. Paper 4 — Gravity: Newton's Law, Einstein Equations, and Classical SolutionsDerives Newton's law via Kaluza–Klein reduction of the 11D propagator to 4D, giving GN = ε²/ (4πV7). Lovelock's uniqueness theorem applied to the Vision structural premises (P-2, P-12, P-39, P-45) gives the Einstein equations. Six classical solutions are recovered: Schwarzschild, Kerr, flat universe, Friedmann equations, vGW = c, and two GW polarisations. Vision correction to GR of order ε² ≈ 10⁻⁴ is a falsifiable prediction. Paper 5 — The Standard Model Gauge Group and Matter SectorThe Z6 centre theorem selects the SM gauge group SU (3) ×SU (2) ×U (1). The six Z6 sectors give the proposed SM fermion-content structure per generation. Three generations from P-14 give 48 Weyl fermions. EWSB arises from the projection P-33. The Z3 cyclic symmetry on three generations gives the leading tribimaximal PMNS structure. CP violation has a structural source from 137 ≡ −1 (mod 6). Seesaw mechanism supported by three gauge-sterile νR candidates. Paper 6 — Gauge Coupling Running, Weinberg Angle, and UV CompletionBeta coefficients b3 = −7, b2 = −19/6, b1 = +41/6 are pure arithmetic from the Vision-derived matter content. New result: b1 − b2 = 10 = NU + 1 exactly (NU = 9 from P-15). The Z6 unification condition gives sin²θW = 1/2 at ΛKK exactly. Conditional running to MZ gives sin²θW (MZ) ≈ 0. 231. The ε coupling is UV stable with βε ≈ 0 from P-13. Above ΛKK the exact Gaussian ZG provides the proposed UV-completion structure for the Vision ε sector. Paper 7 — The G2 Manifold: Constraints, Candidate, and Volume V7Develops eight Vision constraints on the hidden G2 candidate manifold MH. Rules out the Kovalev TCS family (b3 ≥ 22). The Joyce orbifold T⁷/ (Ẑ2×Z3) satisfies constraints C1–C7. The Z3 action on the G2 three-form φ is verified term by term. The Iron-Rule algebraic target volume V7 = ε²/ (4π) ≈ 8. 12×10⁻⁶ ℓPl⁷ is computed. Full geometric verification (b3 = 3 persistence, intersection form, volume) is Open Construction 3. Paper 8 — Black Hole Thermodynamics, Information Preservation, and the S-MatrixP-8 binary road gives area scaling S ~ A for BH entropy (coefficient 1/4 conditional on Im-4 normalization). Information preservation: P-8 + P-37 + P-5 guarantee no information loss — pre-manifest component X⁽⁰⁾ ∈ ΦG is never localised behind the horizon. Recycling operator R0 releases information at rate ε per Hawking cycle. Structural S†S = 1 factorisation established; full Lorentzian proof in Paper 10. Paper 9 — Cosmology: Dark Energy, Dark Matter, Baryogenesis, and the Arrow of TimeDark energy: w = −1 at leading order from P-5 (∂tΦG = 0) ; falsifiable prediction |w+1| ~ ε² ~ 10⁻⁴. Creation-time cosmological constant ΩΛ (creation) = 1/100 from P-6. Dark matter: j = 3 gauge-sterile sector provides candidate with mDM ~ CDM·ε·ΛKK (CDM open). Three Sakharov conditions structurally represented. Arrow of time derives from binary road direction 0→1 at the Big Bang (P-34/P-8). Paper 10 — G2 Cohomology, Intersection Form, ALE Resolution, V7, and S†S = 1Algebraic result: dim H³ (T⁷;Q) Z6 = 3, proved by explicit representation theory. Intersection form I = δ + εJ with J uniquely determined by Z3-antisymmetry. Conditional ALE assignment r = √ε from Eguchi–Hanson model gives target volume V7 = ε²/ (4π). Lorentzian S†S = 1 proved in six steps under stated analytic assumptions, with P-5 performing the central role in Wick rotation. Paper 11 — Yukawa Couplings, Higgs VEV, and the Fractional Fine-Structure ConstantAlgebraic Higgs VEV: v = √ (4π/ε) MPl conditional on Im-10 target volume. Yukawa eigenvalues of I = δ + εJ: λi = 1 + εμi with μi ∈ −√3, 0, +√3, giving within-generation splitting of ±ε√3 ≈ ±1. 75%. Fractional α formula structure f = (b1/2π) ln (ΛKK/me) derived; numerical value open pending blind G2 computation of ye. Paper 12 — Problem Statement for a G2 Differential Geometer (Blind Protocol) NOT A JOURNAL PAPER. A blind collaboration document for G2 differential geometers. Presents three questions: Q1 (compute V7 independently), Q2 (compute Yukawa matrix yij from the G2 metric), Q3 (compute individual Yukawa scales yf0). No target values are provided. Comparison to observed physics occurs only after computation is complete. HONEST STATUS SUMMARY (A) Algebraic results established without the G2 metric: • Integer 137 = 17²−9×17+1 exactly from Ψ = 100/99• b3 = 3 = Ngen: algebraic theorem from Z6 representation theory• Intersection form I = δ + εJ with J uniquely determined• S†S = 1 under stated Lorentzian analytic assumptions• Sakharov conditions structurally represented• Dark energy w = −1 at leading order; |w+1| ~ ε² falsifiable prediction• SM gauge group structure SU (3) ×SU (2) ×U (1) from Z6 centre theorem (B) Algebraically derived — awaiting independent geometric verification: • GN = ε²/ (4πV7): formula derived; geometric proof of V7 open• mf = yf√ (ε/V7): structure derived; Yukawa values yf open• 1/α = 137 + f: integer exact; fractional part open until ye computed blindly IRON RULE: All derivation-layer mathematics flows only from the 45 Vision postulates and the arithmetic generator Ψ = 100/99. No measured physical constant enters the derivation layer in any of the twelve papers. Version history: This is Version 5. 0, superseding all earlier versions of this record. The series has been systematically referee-cleaned with overclaiming language replaced throughout.