IndisputableMonolith.QFT.RS_QFT_Structural_002
Structural QFT layer that packages a domain-level cost functional, its nonnegativity and evaluation identities, and a positive canonical threshold into an inhabited certificate. QFT workers cite it when they need a single RS-native cost gate rather than raw J-cost. The module is mostly definitional: identities reduce by unfolding, positivity follows from the Cost import.
claimA domain cost $C(\Omega)$ built from the RS $J$-cost, with $C(\Omega)\ge 0$ and a canonical threshold $\theta>0$, packaged as an inhabited structural certificate for RS-QFT.
background
Recognition Science measures mismatch by the unique cost $J(x)=(x+x^{-1})/2-1$ fixed by the Recognition Composition Law. The Cost import supplies that functional and its elementary inequalities; Constants supplies the RS time quantum $\tau_0=1$ tick used to normalize discrete QFT domains.
This module lifts pointwise $J$ to a domain-level cost $C(\Omega)$ on structural regions of the QFT side, then isolates a single positive scale $\theta$ (the canonical threshold) against which domain costs are compared. Sibling declarations record evaluation at equality cases, nonnegativity of $C$, and positivity of $\theta$.
The certificate bundle RSQFTStructural002Cert is the export surface: downstream QFT lemmas can assume one inhabited cert rather than re-proving the cost and threshold facts separately.
proof idea
Definition module with thin supporting lemmas. domainCost and canonicalThreshold are introduced by definition from Cost and Constants. domainCost_at_eq is an unfolding identity. domainCost_nonneg and canonicalThreshold_pos inherit nonnegativity and positivity from the upstream Cost facts. The certificate record is assembled by packing those fields; cert_inhabited is a one-line constructor application showing the record is nonempty.
why it matters in Recognition Science
Gives the QFT sector a single structural cost-and-threshold certificate instead of ad-hoc appeals to raw $J$. In the RS forcing chain this sits downstream of T5 ($J$-uniqueness) and the Cost library, and upstream of any domain-gate or structural-stability arguments that need $C(\Omega)\ge 0$ and a fixed positive cutoff $\theta$. No downstream consumers are wired in the graph yet; the module is an export stub for later RS-QFT structural theorems that will cite the inhabited cert rather than rebuild the cost layer.
scope and limits
- Does not derive the continuum QFT action or renormalization group flow.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not connect domain cost to particle masses or the phi-ladder.
- Does not establish any dynamical equation of motion on domains.
- Does not claim a numerical value for the threshold in SI units.