IndisputableMonolith.Physics.CoherenceTimeFromJCost
Defines a domain-level cost from the RS J-functional and a positive canonical threshold, then packages a coherence-time certificate that the cost stays below threshold. Physicists tracking decoherence bounds in RS-native units would cite the certificate and nonnegativity lemmas. The module is mostly definitional: nonnegativity and positivity are short algebraic facts; the certificate is an inhabited structure.
claimFrom the RS cost $J$, form a domain cost $C$ with $C\ge 0$, fix a canonical threshold $\theta>0$, and certify coherence time by the inhabited structure asserting that the domain cost remains below $\theta$ on the relevant regime (in units where the fundamental tick is $\tau_0=1$).
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law. Time is counted in the fundamental RS tick $\tau_0=1$ from Constants. Coherence here means the accumulated $J$-cost on a domain stays below a fixed positive threshold before the configuration is treated as decohered.
This module sits in the Physics layer and imports only Constants and Cost. It introduces a domain cost built from $J$, records that the cost is nonnegative and agrees with pointwise evaluation where defined, and names a canonical positive threshold. The certificate type packages the claim that cost remains under threshold, with an inhabited instance supplying a concrete witness.
proof idea
Definition module with light algebraic lemmas, not a deep derivation. domainCost is introduced from the Cost layer; domainCost_at_eq and domainCost_nonneg are short equalities and nonnegativity facts inherited from $J\ge 0$. canonicalThreshold is a named positive constant; canonicalThreshold_pos is the positivity proof. CoherenceTimeCert is a structure; cert and cert_inhabited supply and inhabit the certificate. No multi-step forcing argument appears here.
why it matters in Recognition Science
Gives Physics a reusable coherence-time certificate tied directly to $J$-cost rather than an external decoherence model. Downstream consumers (none linked in the current graph) can assume an inhabited CoherenceTimeCert instead of re-proving threshold comparisons. In the broader RS chain this sits after T5 $J$-uniqueness: once $J$ is forced, coherence windows are just sub-threshold cost budgets in tick units. It does not yet close mass-ladder or eight-tick timing theorems; it only standardizes the cost-to-time interface those results would use.
scope and limits
- Does not derive a numerical coherence time from first principles beyond the named threshold.
- Does not prove uniqueness of the canonical threshold among all positive cutoffs.
- Does not connect coherence certificates to the eight-tick octave or $D=3$ forcing steps.
- Does not supply experimental bounds or SI-unit conversions for the threshold.
- Does not claim decoherence dynamics; only a static cost-below-threshold certificate.