IndisputableMonolith.QFT.RS_QFT_Structural_008
Structural QFT module packaging certificate 008: a domain-level cost, its nonnegativity and pointwise evaluation identity, a strictly positive canonical threshold, and an inhabited certificate record. Physicists assembling RS-QFT structural obligations cite it as a self-contained unit. Content is mostly definitional, with short positivity and equality lemmas.
claimThe module defines a domain cost $C$, proves $C \ge 0$ and a pointwise evaluation identity, introduces a canonical threshold $\theta > 0$, and supplies an inhabited structural certificate for RS-QFT item 008.
background
Recognition Science builds QFT structure on the same cost calculus used in the forcing chain. The imported Cost layer supplies the J-cost (the unique symmetric generator of the Recognition Composition Law), while Constants fixes the RS-native tick $\tau_0 = 1$.
This module sits in the QFT domain and packages a single structural obligation labeled 008. Sibling objects introduce a domain cost, record that it is nonnegative, fix a canonical positive threshold, and wrap those facts in a certificate type with an inhabitation witness. No dynamical field equations are stated here; the setting is purely structural bookkeeping for later QFT assembly.
proof idea
Definition-heavy module rather than a deep theorem chain. Domain cost and the canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas; the evaluation identity is an equality lemma at specified points. The certificate record is assembled from those pieces and discharged by an inhabitation proof (cert_inhabited). No multi-step tactic development beyond elementary real inequalities and def unfolding.
why it matters in Recognition Science
Gives a named, checkable unit for RS-QFT structural item 008 so downstream QFT assembly can require an inhabited certificate rather than ad-hoc side conditions. Imports only Constants and Cost, keeping the dependency surface minimal. No used-by edges are recorded yet, so this module is a leaf in the current graph: it is meant to be consumed by higher QFT structural or certification layers once those wire in. It does not itself touch T5-T8, the mass ladder, or the alpha band; it only standardizes a cost-plus-threshold certificate shape for the QFT side.
scope and limits
- Does not derive dynamical QFT equations or scattering amplitudes.
- Does not prove uniqueness of the domain cost or the threshold.
- Does not connect to the mass ladder, alpha band, or T5-T8 forcing steps.
- Does not discharge any sorry outside this module's own certificate record.
- Does not assert numerical bounds beyond positivity of the canonical threshold.