IndisputableMonolith.QFT.RS_QFT_Structural_007
Structural certificate module for Recognition Science QFT item 007. It packages a domain cost functional built from the RS J-cost, a positive canonical threshold, and an inhabited certificate record tying those facts together. QFT bridge authors cite it when they need a named, non-negative cost-and-threshold pair rather than ad-hoc inequalities. The module is mostly definitions plus short positivity and equality lemmas.
claimDefine a domain cost $C$ from the RS cost $J$, prove $C\ge 0$ and an equality form at matched arguments, fix a canonical threshold $\theta>0$, and package these into an inhabited structural certificate for RS-QFT item 007.
background
Recognition Science routes continuum and field structure through the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law. The Cost import supplies that $J$ and its elementary inequalities; Constants supplies the RS-native tick $\tau_0=1$ used as the discrete time unit when QFT statements are later discretized.
This module sits in the QFT layer and does not re-derive $J$. It introduces a domain-level cost built from $J$, records non-negativity and an evaluation identity, and names a positive canonical threshold against which domain costs can be compared. The certificate record is the export surface: downstream QFT lemmas can assume one inhabited certificate rather than re-proving the same positivity facts.
proof idea
Definition-heavy module. domainCost is introduced from the imported Cost primitives; domainCost_nonneg and domainCost_at_eq are short algebraic or rewriting lemmas. canonicalThreshold is a named positive constant (canonicalThreshold_pos). RSQFTStructural007Cert bundles those fields; cert and cert_inhabited supply a concrete inhabitant so the certificate type is non-empty. No deep tactic scripts: the argument is packaging plus elementary cost inequalities.
why it matters in Recognition Science
Gives the QFT bridge a single named structural certificate (item 007) for domain cost and threshold data instead of scattered local lemmas. That matches the RS pattern of forcing chain landmarks (T5 J-uniqueness, RCL) feeding reusable certificates rather than one-off inequalities. No downstream edges are recorded yet in the graph, so the module is presently a leaf export: parent QFT structural or continuum-limit theorems are expected consumers once wired. It does not itself force dimension, the eight-tick octave, or coupling constants; it only stabilizes the cost-threshold interface those results need.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law; those are imported.
- Does not prove continuum QFT dynamics, scattering, or renormalization statements.
- Does not fix numerical values of c, hbar, G, or alpha.
- Does not claim D=3, eight-tick structure, or mass-ladder formulae.
- Does not list downstream consumers; used_by is currently empty.