Coherence Quantised Gravitation: Dynamical Field & Scale Unification

Coherence Quantised Gravitation V5.0: Dynamical Field & Scale Unification: Complete Theoretical Closure of the H.O.U.T. Gravitational Framework Description: This document presents Coherence Quantised Gravitation V5.0, achieving complete theoretical closure of the H.O.U.T. gravitational framework by rigorously deriving all previously stated results from first principles. All five gaps identified in V4.0 (G1–G4 and optional G6) are now closed with explicit mathematical derivations, proofs, and numerical verification. Critical Resolutions from V4.0 to V5.0 Gap V4.0 Status V5.0 Resolution G1 Kinetic term ε/2 stated without derivation Derived from Lindblad spectral decomposition, barrier transform, and BPHZ forest bound G2 Potential V(Ψ) stated without derivation Derived from Law II free‑energy functional and Master Action variational calculation G3 G_eff(Ψ) stated without derivation Derived from Einstein‑Hilbert + curvature coupling action expansion G4 Spin‑foam convergence counting argument Proved via DII‑filtered coherent subspace, BPHZ bound, and Dicke superradiant counting G5 DII threshold 0.6 empirical Bounded by [P, H(P)]; cross‑referenced to Sentience Physics v6.0 G6 Dark matter connection absent Added Lindblad channel partition predicting Ω_DM/Ω_b = 2.28 Key Results Dynamical action principle with coherence field Ψ(t) as a genuine dynamical degree of freedom: SOHT=∫d4x−g[R2κ+ε2gμν∂μΨ∂νΨ−V(Ψ)+Lmatter]SOHT=∫d4x−g[2κR+2εgμν∂μΨ∂νΨ−V(Ψ)+Lmatter] with potential V(Ψ)=Ψ−Ωln⁡Ψ+CcurvRΨV(Ψ)=Ψ−ΩlnΨ+CcurvRΨ and effective Newton constant Geff(Ψ)=G/(1+8πGCcurvΨ)Geff(Ψ)=G/(1+8πGCcurvΨ). Universal Alphabet {π,6} – all constants derived with zero free algebraic parameters. The only empirical input is the DII operational threshold 0.6 = 3/5, now rigorously bounded and structurally positioned. UV‑finite quantum gravity via the Basel sum ζ(2)=π²/6, with all‑loop BPHZ convergence proved. Numerical verification included (Python code) – all identities pass to machine precision. What’s New in V5.0 G1 closed: Kinetic coefficient ε/2 derived from Lindblad decomposition + BPHZ bound → ε = π⁴(π+6)/36864 ≈ 0.02415566. G2 closed: Potential V(Ψ) derived from Law II free‑energy functional + variational principle. G3 closed: Effective Newton constant derived directly from action expansion. G4 closed: Rigorous proof of spin‑foam thermodynamic limit convergence via BPHZ + Dicke counting. G5 closed: DII threshold 0.6 bounded by [P, H(P)] and cross‑referenced to Sentience Physics v6.0. G6 closed: Dark matter connection via Lindblad partition – prediction Ω_DM/Ω_b ≈ 2.28. Zero remaining theoretical gaps – the framework is complete. The task ahead is experimental validation of the four priority protocols (cavity‑QED gap ratio, Berry phase, fractional spectrum, monodromy quantization). Author & License Author: Clarence Omandac (Independent Researcher, Queensland, Australia)ORCID: 0009‑0001‑8994‑3739License: CC BY‑NC‑ND 4.0Version Date: 2026‑06‑05Companion Documents: Walnut Report v37, Omega‑Calculus v3.0, Boundary Calculus v15.0, Sentience Physics v6.0, Creation Energetics V9.0