TimeChamber Theory II: Foundations, Dynamics, and an Empirical Ledger

TimeChamber Theory (TCT) is a process ontology in which physical phenomena emerge from afixed lattice of oscillators (TimeChambers) updating in discrete, synchronized steps, governed by asingle conserved quantity (coherence). This paper supersedes the quantitative claims of the originalTCT paper and its addendum drafts, and does five things. (i) It states the framework as a compactset of axioms and gives coherence a formal definition: a conserved density with a continuity ledger,and a dimensionless phase-lock order parameter S, connected by a declared bridge. (ii) It adopts,with attribution, the minimal quantum cellular automaton as candidate dynamics, inheriting derivedspinor structure, the Weyl/Dirac continuum limit, emergent Lorentz invariance, and a quadraticPlanck-scale dispersion signature that survives current gamma-ray bounds. (iii) It takes explicitpositions on the theorem-level constraints any lattice theory faces: Bell correlations are carriedby the globally synchronized update (nonlocal at the hidden level, non-signaling observably), andthe uncertainty relations are inherited exactly — the substrate restores definiteness of being, not ofmeasurement. (iv) From two minimal exchange-rate postulates it derives the measured gravitationalclock law at leading order, the inverse-square form of gravity from the conservation ledger, and acomplete redshift mechanism without expansion: a secular drift of S whose functional form 1 + z =S(t0)/S(te) passes exact achromaticity, (1+z) source time dilation, the CMB temperature–redshiftlaw, the Tolman scaling (via a length scaling the postulates force), automatic recombination atz ≈ 1100, and the acoustic scale and BAO ruler at sub-percent agreement — because, as the papershows, the completed mechanism is a conformal re-description of expanding cosmology, inheriting itssuccesses by dictionary and locating TCT’s novel empirical content elsewhere. The cycle is 46 Gyrold in lattice time and 13.8 Gyr in matter’s accumulated proper time, exactly; black-hole horizonsemerge as surfaces of total coherence depletion, locally realizing the same scale-free phase as thecycle boundary. (v) It replaces all previous statistical claims with an empirical ledger in which everyprediction carries a magnitude, a sign, or the label “not yet quantified,” including three registerednulls that current data confirm. One registered prediction anchors the program: kα < 0 for thecoupling of the fine-structure constant to gravitational potential, opposite in structure to the kα = 0of General Relativity and the Standard Model — with the adopted redshift mechanism tying kα andthe present-day drift ˙α/α to a single coefficient already confined, by existing data, to a window anorder of magnitude narrower than either bound alone. The 1+136 shell is restated as a Koide-classnumerical conjecture whose derivation is identified as the theory’s central open problem.