IndisputableMonolith.Physics.PhotonStatisticsFromRS
Module that ties photon counting statistics to the Recognition Science cost J. Coherent light sits at J = 0 and is declared Poissonian; other regimes are classified by the same cost. Optical and quantum-statistics workers in the RS stack would cite it when connecting ladder cost to count distributions. Content is mostly regime definitions and a small certificate, not a deep derivation.
claimPhoton counting regimes are classified by the RS cost $J$. Coherent light corresponds to $J = 0$ and is Poissonian: the count distribution is that of a Poisson process. The module supplies a regime type, a count map, a coherent-Poissonian fact, and a certificate packaging that claim.
background
Recognition Science measures mismatch with the cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$), unique under the Recognition Composition Law and the forcing chain (T5). The global minimum is $J(1) = 0$.
In quantum optics, coherent states produce Poissonian photon counts. This module places that fact inside RS units: the coherent regime is identified with vanishing cost $J = 0$, imported from IndisputableMonolith.Cost. Sibling names indicate a regime enumeration, a count functional, an explicit coherent-Poissonian statement, and a certificate wrapper.
The local setting is the physics layer of the monolith: translate RS-native cost into laboratory photon statistics without re-deriving $J$ uniqueness.
proof idea
Definition-and-certificate module rather than a long proof chain. It introduces a regime type for photon statistics, a count map, and a named fact that the coherent ($J = 0$) regime is Poissonian. A small certificate structure packages that claim for downstream use. No multi-step tactic development is indicated; the argument is classification by cost plus the standard coherent-state Poisson law.
why it matters in Recognition Science
Gives the RS physics layer a clean handle on coherent light: $J = 0$ means Poissonian counts. That links the T5 $J$-uniqueness landmark to everyday quantum optics without extra postulates. Downstream used-by edges are empty in the graph, so the module is a leaf exporter for optics and statistics consumers rather than an internal forcing step. It does not touch mass ladders, $\alpha$, or the eight-tick octave; it only specializes cost to photon counts.
scope and limits
- Does not derive the Poisson law from first principles; it classifies coherent light as Poissonian at $J = 0$.
- Does not treat thermal, squeezed, or number-state regimes beyond naming hooks.
- Does not connect photon statistics to the mass ladder, $\alpha$ band, or $D = 3$.
- Does not prove uniqueness of $J$; that is assumed from the Cost import and T5.