CRR: Candidate Temporal Formalism for Regime Transitions

Status

SPECULATION. CRR is unreviewed, with unverified empirical claims and unpeer-reviewed mathematical proofs. All CRR-derived claims should be graded SPECULATION until independent validation. CRR is not woven through the notebook's core claims, plant model, recursion problem, or regime classification.

What CRR addresses

The notebook's existing regime classification stands on Aston-Jones and Cohen 2005 (LC bimodality, established) plus Arnsten 2009/2015 (steep functional consequences of catecholamine-PFC dynamics, established). These tell you WHAT happens mechanistically but not WHEN transitions occur, how long coherence accumulates before rupture, or what the temporal dynamics of recovery look like. The plant model gap (open problem 5.1) is explicitly about this: the architecture needs dynamical equations, not just mechanism descriptions.

Core definitions

Coherence C(x,t) accumulates as a system successfully implements policies. Rupture occurs when C reaches a threshold parameter Omega. Regeneration is the process by which past coherence is re-weighted into future states.

The rupture condition

C x Omega = 1, where CRR proposes C is accumulated Fisher information and Omega = variance (residual variance = inverse precision). This saturates the Cramer-Rao bound: the system has become an efficient estimator and can extract no further information without structural reorganization.

The regeneration operator

R(x,t) = [integral of Phi(x,tau) x exp(C(x,tau)/Omega) dtau] / [integral of exp(C(x,tau)/Omega) dtau]. High-coherence moments contribute equally regardless of when they occurred. This is coherence-weighted, not recency-weighted memory.

Omega as inverse precision

CRR's Omega IS the FEP's inverse precision formally. If correct:

• Low Omega = high precision = rigid system
• High Omega = low precision = flexible/exploratory system
• Omega approximately 1 = critical = maximally sensitive

Connection to the notebook: catecholamine-mediated precision degradation (Arnsten mechanism) would directly increase Omega, accelerating approach to the rupture threshold.

Empirical claims

CRR predicts CV approximately 0.159 for Z2 (bistable) systems. Sabine claims confirmation by Lampl and Johnson 1998 saltatory growth data (11/11 individual predictions). Post-hoc fits to wound healing (R-squared = 0.9989) and muscle hypertrophy (10/10 consistent). None of these predictions have been independently verified.

Potential connection to the architecture

If CRR's mathematics track real dynamics, they would provide:

1. A temporal model for regime transitions: coherence accumulation (green state stability), rupture threshold (transition to red state), regeneration trajectory (recovery).
2. A formal connection between the Arnsten mechanism and regime timing: precision degradation (increasing Omega) accelerates approach to rupture (C x Omega = 1).
3. A candidate temporal structure for the plant model program: coherence accumulation rate, rupture threshold, and regeneration trajectory as parameters to be identified.

What would break this

CRR would be challenged if: Z2 systems showed CV significantly different from approximately 0.159; regeneration proved Markovian (no path dependence); the Cramer-Rao bound formulation does not predict actual timing of coherence breakdown under stress; peer review identifies mathematical errors in the proof sketches.