IndisputableMonolith.Chemistry.LaserLinewidthFromJCost
Module packaging the RS treatment of laser linewidth via the J-cost. It defines a domain cost, a positive canonical threshold, and an inhabited certificate that the linewidth bound holds under those cost axioms. Atomic and optical physicists citing RS spectral predictions would reference it. Content is definitional scaffolding plus nonnegativity and positivity lemmas, not a deep existence argument.
claimThe module introduces a domain cost $C$ built from the J-cost $J(x)=(x+x^{-1})/2-1$, a canonical threshold $\theta>0$, and a certificate that laser linewidth is controlled by $C$ relative to $\theta$ in RS-native units.
background
Recognition Science measures mismatch by the J-cost $J(x)=\frac{x+x^{-1}}{2}-1$, forced by the Recognition Composition Law (T5). The Cost import supplies this functional; Constants supplies the RS time quantum $\tau_0=1$ tick and the native unit conventions.
In the chemistry layer, spectral features such as laser linewidth are treated as cost-bounded observables. This module localizes that idea: a domain cost evaluates $J$ on a linewidth-related ratio, a canonical threshold marks the positive scale at which the bound is certified, and a LaserLinewidthCert packages the resulting inequality together with an inhabited witness.
proof idea
Definition module with elementary supporting lemmas. The domain cost is the J-cost specialization to the linewidth ratio; evaluation and nonnegativity lemmas record that it matches $J$ and stays nonnegative. A canonical threshold is fixed and proved positive. The certificate type, a default certificate value, and an inhabitation lemma assemble the claim that the linewidth bound holds at that threshold. No deep tactic development: structure is defs plus positivity.
why it matters in Recognition Science
Places laser linewidth inside the RS chemistry ledger so spectral bounds inherit from T5 J-uniqueness rather than from phenomenological linewidth formulas. Downstream use is not yet wired (no used-by edges); the module is a leaf certificate ready for atomic or optical developments that need a certified RS linewidth bound. It anchors the chemistry domain to Cost and Constants, keeping $c=1$ and related native units available upstream.
scope and limits
- Does not derive a numerical SI linewidth from first principles alone.
- Does not prove uniqueness of any laser model beyond the J-cost specialization.
- Does not connect to experimental linewidth data or fitting procedures.
- Does not discharge forcing-chain obligations outside Cost and Constants.
- Does not supply dynamics or time-dependent lineshape evolution.