M2DE/THEAD v7.8 - Honest Three-Layer Framework with Priors (for universe-4646708)

M2DE/THEAD v7.8 - Honest Three-Layer Framework for manuscript universe-4646708 (Final Submission Version) This is v7.8 final honest version, replacing v7.2 It adopts a three-layer structure as suggested by independent review and corrects mathematical errors in v7.6/v7.7. Layer I - Derived Geometry (no tuning):- BMS charge Qf = 1/4πG ∫ f mB (Iyer-Wald Noether charge)- Kerr area factor F(a*) = 2/(1+√(1-a*²)) from Kerr horizon area- Anomaly inflow form S_inflow = π⁻¹ ∫ C_J J_f J_Skyrme, coefficient C_J not derived here Layer II - Phenomenological Priors (explicit, with quantitative uncertainties):- II.1 α_sky RG: One-loop β(e) = -e³(1-2/Nc)/32π², e(1 GeV)=5.45, ln(Λ_BH/Λ_QCD)~44 → Δe/e~4.0, so e=5.45±4.0, ΔC_J/C_J~2. C_J=0.59(M1/M_Pl)F(a*)- II.2 S_ent prior: Single-mode S≈0 for 2πE/H=7.85e13. Multimode Stot=Neff ln(2πE/H), ln(2πE/H)=32.0. Taking Neff=0.5 (observable half) gives Seff=16.0±2.0. Prior S_ent~U[10,40]. Posterior from Fermi-LAT f1>1e-12 requires S_ent=14-18. f1(Sent=16)=4.1e-11, f1(Sent=32)=1.7e-18 too small → need extra decoherence. This is honest tuning, reported as prior.- II.3 ξ0 as initial condition: ξdot=Γent ξ - H ξ, Γent= T_GH * Sdot. If Sent=const, no growth. ξ0=n0-1/3 ηc1/3 fixed by aT=0.76 as initial condition, not dynamical result.- II.4 μ(k,a): Pure percolation n(s)=s-τ, τ=2.18, Df=2.52 → μ-1 ∝ kDf(3-τ)-2=k0.07 too flat to explain S8. Including bending rigidity κ → μ-1 ∝ k0.07 sqrt(1+(lb k)²) → k0.57≈k0.5_eff with lb~ξ0~10 Mpc. Adopt k0.5 as effective phenomenological fit, free index α=0.48±0.12 preferred over 0.07 at 2.8σ. Layer III - Statistics and Falsifiability:- COLA FastPM convergence: 256³ vs 512³ Δ=0.004, 40 vs 80 steps Δ=0.003- DES Y3 3x2pt: Δχ²=-8.2, Δk=6, ΔAIC=+4.2, ΔBIC=+12.1, logB_M2DE/Λ=-2.1±0.4 (weakly disfavored, odds 1:126, not ruled out)- Fisher Euclid DR1: σ(dS8/dlnk)=0.004, prediction -0.05 → 12.5σ separation from ΛCDM. P(k) bump at 0.6h/Mpc 8σ. GRB coherence Ncoh~1e21. Corrections to v7.6:- ln(2πE/H)=32.0 not 16.1, previous confusion between 2πE/H and ln(2πE/H) fixed- Df(3-τ)-2=0.07 not 0.5, angular average does not change exponent, admitted as phenomenological Concept DOI: 10.5281/zenodo.23236400 (always resolves to latest version)This version DOI: v7.8 (new)Manuscript: Universe journal submission universe-4646708License: CC-BY-4.0 Files: M2DE_THEAD_v7.8_ThreeLayer_Honest.pdf (Appendices A+B+C full)