IndisputableMonolith.QFT.RS_QFT_Structural_006
Structural certificate module for QFT item 006 in the Recognition Science stack. It packages a domain cost, equality at a reference point, nonnegativity, a positive canonical threshold, and an inhabited certificate record. QFT or RS auditors cite it when a single witness is needed that these side conditions hold. The content is definitions plus elementary positivity facts over the Cost and Constants imports.
claimThe module defines a domain cost $C_{\mathrm{dom}}$, records $C_{\mathrm{dom}}$ at a reference equality, proves $C_{\mathrm{dom}}\ge 0$, fixes a canonical threshold $\theta>0$, and packages these into an inhabited structural certificate for RS QFT item 006.
background
Recognition Science builds physics from a unique cost $J$ forced by the Recognition Composition Law, with supporting infrastructure in the Cost module. Constants supplies RS-native units, including the time quantum $\tau_0=1$ tick.
This file lives in the QFT layer and records structural side conditions labeled 006: a domain-level cost functional, its value at a reference equality, nonnegativity, and a strictly positive canonical threshold used as an acceptance gate.
The certificate type bundles those facts so later QFT developments can depend on one inhabited witness instead of re-proving elementary inequalities at each use site.
proof idea
Definition-and-packaging module, not a deep derivation. The domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the imported Cost infrastructure. The certificate record and its inhabited instance assemble those pieces into a single structural witness. No forcing-chain (T5–T8) argument runs here.
why it matters in Recognition Science
Supplies a leaf structural certificate for the QFT fragment numbered 006. Downstream used-by edges are empty in the current graph, so the module’s role is hygiene and reuse: importers take the inhabited cert rather than re-derive domain-cost nonnegativity or threshold positivity. It does not advance J-uniqueness, $\phi$, the eight-tick octave, or $D=3$; it only locks local side conditions needed by the QFT structural series.
scope and limits
- Does not prove J-uniqueness (T5) or the Recognition Composition Law.
- Does not derive masses, couplings, or the alpha band.
- Does not establish dynamical QFT equations or renormalization.
- Does not claim a unique physical domain; only packages cost and threshold data.
- Does not close scaffolding outside the listed sibling declarations.