IndisputableMonolith.QFT.RS_QFT_Structural_005
Structural certificate module for RS-QFT item 005: a nonnegative domain cost functional and a strictly positive canonical threshold, packaged as an inhabited certificate. QFT bridge authors cite it when a cost-versus-threshold comparison is needed. The module is mostly definitions plus elementary nonnegativity and positivity lemmas over the RS cost layer.
claimThe module introduces a domain cost $C(\cdot)\ge 0$, a canonical threshold $\theta>0$, and an inhabited certificate $\mathrm{RSQFTStructural005Cert}$ asserting that these objects are well-formed for the RS-QFT structural checklist item 005.
background
Recognition Science routes continuum QFT claims through discrete cost and tick structure. The Cost import supplies the J-cost family (the unique symmetric generator of the Recognition Composition Law); Constants fixes the RS time quantum $\tau_0=1$ tick. This module sits in the QFT domain and defines a domain-level cost functional together with a canonical numerical threshold against which that cost is compared.
Sibling names indicate the local API: domainCost and its evaluation identity, nonnegativity of the cost, a positive canonicalThreshold, and a certificate type RSQFTStructural005Cert with an inhabited instance. No forcing-chain step (T5–T8) is re-proved here; the module only packages cost/threshold structure used by later QFT bridge lemmas.
proof idea
Definition-heavy module. Cost and threshold are introduced as defs; nonnegativity and positivity are short lemmas (likely direct from Cost/Constants inequalities). The certificate is a structure or Prop bundle; cert_inhabited supplies a witness so downstream code can assume the 005 structural package without rebuilding the data.
why it matters in Recognition Science
Fills RS-QFT structural checklist slot 005: a reusable cost-versus-threshold interface for discrete-to-continuum arguments. No downstream edges are recorded yet in the mirror graph, so it is presently a leaf certificate rather than a proved parent theorem. It keeps QFT scaffolding aligned with the RS cost layer (J-cost, tick units) without claiming mass formulae, $\alpha$ bounds, or forcing-chain uniqueness.
scope and limits
- Does not prove any continuum QFT dynamical equation or renormalization identity.
- Does not derive J-uniqueness, $\phi$, eight-tick period, or $D=3$.
- Does not fix numerical particle masses or the $\alpha^{-1}$ band.
- Does not assert that every domain cost exceeds the canonical threshold.
- Does not record downstream consumers in the current dependency graph.