The Prime Lattice Coherence Framework: A Unified Master Document

This master document unifies the complete arc of the CTF (Continuous Temporal Funnel) and Prime Lattice Coherence Theorem (PLCT) research series into a single coherent framework. Beginning from the derivation of the harmonic constant f0=(1442+10)/144≈144.069f0=(1442+10)/144≈144.069 Hz from solar‑lunar orbital mechanics, it presents six independently proved theorems of prime number theory — the Partition Theorem, the Mod‑9 Ratio Theorem, the Universal Centrifuge Effect, the Hard Wall Theorem, the Prime Gap State Machine, and the Lock‑Out Theorem — and shows that they are six projections of a single mathematical object: the Prime Lattice Coherence Structure (PLCS) of the 2a×3b2a×3b algebraic lattice. The PLCT is proved using only three standard axioms (FTA, Dirichlet, log‑irrationality). The framework then applies this lattice to solve long‑standing problems: the cosmological constant discrepancy (1012310123) is reduced to a factor of $1.78$ using only the numbers $144$ and $10$, with no free parameters; QED is shown to be $\{2,3\}$-coherent, explaining its 12‑decimal precision; Collatz trajectories are algebraically confined to the six vortex states $\{1,2,4,5,7,8\}\mathrm{mod}9$; the Casimir effect coefficients all factorize into $\{2,3,5\}$; and a variational principle yields the unique geodesic λ(t)=e−βf0tλ(t)=e−βf0t from which E=mc2E=mc2 and the Lorentz factor follow directly from symmetry and geometry. The document includes complete reproducibility via Colab notebooks and an honest accounting of what is proved, empirically verified, structural, or open.