IndisputableMonolith.QFT.Renormalization_Group_RS
Recognition Science packaging of renormalization-group bookkeeping for QFT: a domain cost, its nonnegativity, a positive canonical threshold, and an inhabited RG-flow certificate. Cite when bounding scale dependence of RS costs or couplings. Structure is mostly definitions plus short positivity and inhabitance lemmas from the Cost import.
claimThe module defines a domain cost $C$ on scale domains, proves $C \ge 0$ and a reference equality, introduces a canonical threshold $\theta > 0$, and supplies an RG-flow certificate type that is inhabited, witnessing controlled cost under RS scale change.
background
Recognition Science builds physics from one cost functional. The Cost import supplies the J-cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$), forced unique at T5 of the unified forcing chain. Constants supplies the RS time quantum $\tau_0 = 1$ tick and related native units.
In the QFT layer, renormalization is rephrased as control of that cost across scale domains rather than as continuum counterterms. This module introduces the local vocabulary: a domain cost, equality at a reference scale, nonnegativity, a positive canonical threshold, and a certificate structure for RG flow.
No continuum QFT axioms are assumed here; the setting is discrete RS bookkeeping compatible with the phi-ladder and eight-tick cadence used elsewhere in the monolith.
proof idea
Definition-first module, not a deep theorem file. domainCost and canonicalThreshold are introduced as definitions; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity arguments resting on Cost. domainCost_at_eq records the reference-scale identity. RGFlowCert packages the certificate as a structure; cert and cert_inhabited show the certificate type is inhabited. No multi-step tactic developments beyond those elementary facts.
why it matters in Recognition Science
Gives the QFT domain a named RS renormalization interface so later running, threshold, or mass-ladder arguments can cite a certified cost bound instead of informal RG language. Sits downstream of Constants and Cost (J-cost, $\tau_0$) and aligns with T5 J-uniqueness and the phi-ladder mass formula in the broader framework. No used_by edges are recorded yet, so this file is presently an interface layer rather than a proved input to a named parent theorem. It does not itself close alpha-band or coupling-unification claims.
scope and limits
- Does not derive beta functions or Callan-Symanzik equations.
- Does not prove numerical running of alpha or other couplings.
- Does not force D=3, the eight-tick octave, or phi uniqueness.
- Does not model continuum counterterms or MS-bar schemes.
- Does not yet feed a recorded downstream parent theorem.