IndisputableMonolith.Physics.Compton5
Module packaging the RS-native Compton domain cost and its positivity threshold at the φ^5 scale set by ħ. It exposes a non-negative cost functional, a strictly positive canonical threshold, and an inhabited certificate record that the cost sits at the threshold. Physicists tracing mass or length ladders cite it when they need the Compton gate in RS units. The file is mostly definitions plus elementary non-negativity and positivity lemmas.
claimDefine a domain cost $C$ on the Compton sector, prove $C \ge 0$ and $C(a)=C(a)$ pointwise, fix a canonical threshold $\theta>0$ tied to the $\varphi^5$ scale, and package an inhabited certificate that the cost meets that threshold.
background
Recognition Science works in native units with $c=1$ and $\hbar=\varphi^{-5}$. The Compton length of a mass therefore carries an explicit $\varphi^5$ factor once the mass is placed on the $\varphi$-ladder. This module sits in the Physics layer and imports only Constants (for the tick $\tau_0$ and $\varphi$) and Cost (for the underlying $J$-cost calculus).
The local objects are a domain cost functional on the Compton sector, its evaluation identity, non-negativity, a strictly positive canonical threshold, and a small certificate record asserting that the cost equals the threshold. No forcing-chain step (T0–T8) is re-proved here; the module only specialises the cost language to the Compton gate.
proof idea
Definition module with thin lemmas. The cost is introduced by definition; equality at a point is definitional unfolding. Non-negativity follows from the imported cost axioms. The canonical threshold is a positive constant expression in $\varphi$; positivity is a one-line arithmetic check. The certificate is a structure instance whose fields are exactly those facts, shown inhabited by assembling the preceding lemmas.
why it matters in Recognition Science
Supplies the Compton-scale cost gate used whenever RS mass or length formulae must pass through $\hbar=\varphi^{-5}$. Downstream physics developments that quote a Compton threshold or a certified domain cost are expected to import this file; the present graph lists no direct used_by edges yet. It does not advance the forcing chain (T5 $J$-uniqueness, T6 $\varphi$, T7 eight-tick, T8 $D=3$) but keeps the Compton sector aligned with the same $J$-cost and $\varphi$-ladder conventions.
scope and limits
- Does not derive the Compton wavelength from QED or special relativity.
- Does not prove mass-ladder or $\alpha$ bounds; only the local cost threshold.
- Does not re-prove $J$-uniqueness, $\varphi$ fixed-point, or $D=3$.
- Does not claim experimental Compton data fits beyond the certificate equality.