IndisputableMonolith.QFT.RS_QFT_Structural_010
Packages a Recognition-Science QFT structural certificate: a nonnegative domain cost from the RS cost layer, a positive canonical threshold, and an inhabited certificate record. QFT-bridge authors cite it as a named structural gate before continuum or propagator work. Content is definitional plus elementary nonnegativity, evaluation, and positivity lemmas.
claimThe module defines a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an on-point evaluation identity, fixes a canonical threshold $\theta>0$, and packages these facts into an inhabited structural certificate for RS-QFT item 010.
background
Recognition Science lifts continuum and QFT structure from the J-cost and the native constants layer. The Cost import supplies the RS cost functional; Constants supplies the RS-native tick $\tau_0=1$.
This module lives in the QFT domain. It introduces a domain-level cost built on that cost layer, a canonical positive threshold used as a structural gate, and a certificate record that bundles the gate. Sibling names cover the cost, its evaluation identity, nonnegativity, threshold positivity, and certificate inhabitation.
No forcing-chain step (T5--T8) is restated here; the module is a packaging layer above Cost and Constants.
proof idea
Definition module with short supporting lemmas, not a deep tactic development. The domain cost is defined from the imported Cost layer; nonnegativity and the evaluation identity are elementary consequences of that definition. The canonical threshold is a fixed positive quantity with a one-line positivity proof. The certificate type is a structure packing these facts, and inhabitation is a constructor witness. No multi-step algebraic reduction or upstream theorem chain beyond the Cost/Constants imports.
why it matters in Recognition Science
Supplies the named structural-010 certificate for the RS--QFT bridge: a certified domain cost and positive threshold that later continuum, propagator, or coupling work can assume by name. The dependency graph shows no downstream consumers yet, so the module is a leaf packaging layer rather than a step inside T0--T8, the Recognition Composition Law, or the mass ladder. It anchors QFT scaffolding to the Cost functional and RS-native constants without claiming dynamical QFT theorems.
scope and limits
- Does not derive continuum QFT dynamics, propagators, or Feynman rules.
- Does not fix particle masses, couplings, or the alpha band.
- Does not prove uniqueness of the domain cost beyond the stated evaluation identity.
- Does not invoke eight-tick octave, D=3, or other T0--T8 forcing steps.
- Does not discharge open QFT hypotheses outside the packaged certificate fields.