IndisputableMonolith.Physics.DecoherenceTimescaleFromJCost
Defines a decoherence timescale extracted from the Recognition Science J-cost on a domain, together with a nonnegativity certificate and a canonical positive threshold. Physicists linking RS cost geometry to environmental decoherence rates would cite it. The module is mostly definitional: cost evaluations, threshold positivity, and an inhabited certificate bundle.
claimOn a domain equipped with the RS cost $J$, define a domain cost $C$, a canonical threshold $\theta>0$, and a decoherence-time certificate asserting that the implied timescale (in units of the RS tick $\tau_0$) is controlled by $C$ relative to $\theta$.
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 the Constants module; Cost supplies the $J$-calculus used throughout the monolith.
This physics module packages that cost into a domain-level quantity (domain cost), records that the cost is nonnegative, and fixes a canonical positive threshold against which decoherence is declared. The certificate type bundles the numerical comparison that turns a pure cost evaluation into a timescale claim in tick units.
The local setting is therefore cost-to-time translation: once $J$ is evaluated on the relevant domain data, the threshold comparison yields a decoherence timescale without introducing an external Lindblad parameter.
proof idea
Definition-heavy module. Domain cost is introduced and evaluated at equality cases; nonnegativity is recorded as a lemma. The canonical threshold is defined and proved positive. DecoherenceTimeCert is a structure packaging the cost-threshold comparison; an explicit certificate inhabitant is supplied so downstream code can assume the bundle is nonempty. No deep tactic proof: algebraic identities from Cost plus positivity of the threshold.
why it matters in Recognition Science
Places decoherence on the same $J$-cost footing as the rest of the RS forcing chain (T5 $J$-uniqueness onward), so environmental loss of coherence is not an extra postulate but a threshold crossing of domain cost in tick units. No downstream consumers are wired in the graph yet; the module stands as a physics interface ready for mass-ladder or eight-tick timing arguments that need a cost-derived decoherence scale. It closes the gap between pure Cost lemmas and a usable timescale certificate without leaving the RS-native unit system ($c=1$, $\tau_0=1$).
scope and limits
- Does not derive a master equation or Lindblad operators from $J$.
- Does not fix a numerical decoherence rate in SI seconds without a $\tau_0$ conversion.
- Does not prove uniqueness of the canonical threshold among all positive cutoffs.
- Does not connect the certificate to experimental $T_2$ data or open-system Hamiltonians.
- Does not depend on the eight-tick octave or $D=3$ forcing steps.