IndisputableMonolith.Physics.HiggsDecayWidth3_FromJCost
Module packaging a Recognition-Science certificate for a three-channel Higgs decay width derived from the J-cost. It defines a domain cost, a positive canonical threshold, and an inhabited certificate record tying those quantities together. Physicists checking RS mass/width numerics would cite the certificate; the supporting lemmas are elementary nonnegativity and evaluation identities on the cost.
claimA domain cost $C$ built from the RS $J$-cost, a canonical threshold $\tau>0$, and an inhabited certificate asserting that the three-channel Higgs decay width is controlled by $C$ relative to $\tau$ in RS-native units.
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law. Widths and thresholds are expressed in RS-native units ($c=1$, tick $\tau_0=1$) imported from Constants and Cost.
This module sits in the physics layer: it introduces a domain-restricted cost (nonnegative, with an evaluation identity at equality), a strictly positive canonical threshold, and a certificate bundle HiggsDecayWidth3Cert that packages those ingredients for a three-channel Higgs decay width. No external experimental fit is assumed; the objects are pure RS constructions.
proof idea
Definition-and-certificate module rather than a deep derivation. Domain cost is defined from $J$, then shown nonnegative and to satisfy a pointwise evaluation identity. The canonical threshold is defined and proved positive. The certificate record is assembled from those pieces and shown inhabited by a concrete witness. No multi-step forcing-chain argument appears here.
why it matters in Recognition Science
Supplies a self-contained physics certificate linking Higgs three-channel width numerics to the $J$-cost and a positive threshold, consistent with the RS constant set ($\hbar=\varphi^{-5}$, etc.). Downstream use is not yet wired in this graph (no used_by edges). It is a leaf packaging step: ready for later comparison against the phi-ladder mass formula and the alpha band once width observables are attached higher in the monolith.
scope and limits
- Does not derive the Standard Model Higgs potential or electroweak symmetry breaking.
- Does not claim experimental agreement with measured Higgs widths.
- Does not force the three-channel branching ratios from T0–T8 alone.
- Does not compute numerical GeV values; works in RS-native units only.
- Does not connect to quark/lepton mass rungs beyond the certificate interface.