Synthesis — What Resolves, What Remains Open

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.