Synthesis — What Resolves, What Remains Open#
Resolves immediately#
α₀ without calibration: thermal time sets the critical threshold. Substrate temperature (activation distribution uniformity) determines the MM decay transition point. Not a design parameter.
WQS stationarity: if time’s structure dominates node-level variation, stationarity holds from the outside in. The grid search fallback becomes unnecessary when the temporal structure is well-defined.
The floor: drops to exactly zero in the 1/f case. The hyperbolic tail provides physical persistence without a hard lower bound.
λ as substrate-level: decay rate is the inverse substrate temperature, not a per-node declaration. Collapses heterogeneous decay to one parameter readable from the Dolt commit log’s power spectrum.
Remains open#
Whether the substrate’s temporal spectrum is genuinely 1/f (requires measurement from git log, not assumption).
Whether CAS convergence is the substrate’s version of thermal equilibrium in the modular Hamiltonian sense (requires formal proof).
Whether the Born rule is the uniform measure over the preimage equivalence class (requires deriving from the non-injectivity law, not assuming).
Whether the Higgs mass and electroweak scale are determined by the depth of gauge commitment across the causal past (requires physical derivation, not analogy). See
fundamental_forces_planck_scale.md§III.F for the structural analogy to stick-slip and the obstacles to making it rigorous.
The math needed#
Intersection of:
Category theory: structure of the forward map
Ergodic theory: conditions on equilibrium
Information geometry: measure over preimage equivalence classes
All three exist. The combination with this target does not yet exist.