IndisputableMonolith.Physics.PhotonStatisticsFromRS
Module that ties coherent-state photon counting to the Recognition Science cost: Poissonian statistics are identified with vanishing J-cost. Physicists working the RS optics bridge cite it for the regime labels and the certificate that coherent light sits at J = 0. The file is mostly definitions and a thin certificate wrapper over the Cost import, not a deep derivation.
claimCoherent light is the Poissonian photon-counting regime, identified in Recognition Science with vanishing cost $J = 0$. The module introduces a regime enumeration, a counting map, the coherent-Poissonian case, and a certificate object asserting that identification.
background
Recognition Science measures mismatch with the cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$), forced unique by the T5 step of the unified forcing chain and obeying the Recognition Composition Law. The Cost module supplies that $J$ and its elementary identities; this physics module only imports that layer plus Mathlib.
In quantum optics, a coherent state yields Poissonian photon-number statistics (variance equals mean). The module's short doc-comment states the RS reading of that fact: coherent light corresponds to $J = 0$. Sibling names indicate a discrete regime type, a counting function, an explicit coherent-Poissonian constructor, and a certificate pair that packages the claim for downstream use.
proof idea
Definition-and-certificate module rather than a multi-step derivation. It introduces a regime enumeration (including the coherent/Poissonian case), a photon-stat counting map, and a certificate structure whose witness is the identification of coherent light with $J = 0$, drawing only on the imported Cost layer. No substantial tactic proof is indicated; the argument is by definitional packaging of the optics fact against the RS cost.
why it matters in Recognition Science
Places standard coherent-state photon statistics inside the RS cost language so later physics layers can treat Poissonian light as the zero-cost baseline. That baseline matters wherever RS compares optical regimes to nonzero $J$ (thermal, number-squeezed, or ladder-offset states) and wherever certificates are required for the optics side of the monolith. No downstream consumers are recorded yet in the graph; the module is an entry point for photon-statistics claims rather than a leaf of a named parent theorem. It does not itself invoke T6--T8, the mass ladder, or the alpha band, but it sits in the same Cost-rooted physics stack those landmarks use.
scope and limits
- Does not derive the Poisson distribution from the RS functional equation.
- Does not treat thermal, Fock, or squeezed photon statistics beyond regime labels.
- Does not compute optical constants, cross-sections, or detector models.
- Does not prove uniqueness of J; that lives in the Cost/forcing chain.
- Does not connect to the mass ladder, eight-tick octave, or alpha band.