IndisputableMonolith.Foundation.RecognitionScience_Logo5
Foundation module packaging the Logo5 certificate for Recognition Science: a nonnegative domain cost, its evaluation identity, and a strictly positive canonical threshold. Anyone citing the Logo5 stamp or the inhabitation of the certificate bundle will land here. The module is mostly definitions plus short positivity and equality lemmas, closed by an inhabited certificate record.
claimDefine a domain cost $C$ with $C\ge 0$ and a matching evaluation identity, a canonical threshold $\theta>0$, and a Logo5 certificate record packing these facts; the certificate type is inhabited.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the Cost layer, forced uniquely by the Recognition Composition Law and the T5 step of the unified forcing chain. Constants supplies the RS-native tick $\tau_0=1$ and the golden ratio $\phi$ used as the self-similar scale.
This module sits in Foundation and introduces a domain-level cost functional together with a canonical numerical threshold. The cost is required to be nonnegative and to agree with a pointwise evaluation rule; the threshold is required to be strictly positive. Those three facts are the payload of the Logo5 certificate.
Upstream material is thin: only Constants and Cost are imported. No forcing-chain theorems are re-proved here; the module assumes the ambient RS cost calculus and packages a small, checkable stamp around domain cost and threshold.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity lemmas; domainCost_at_eq records the evaluation identity. RSLogo5Cert is a structure bundling those properties; cert is a concrete instance; cert_inhabited is the one-line inhabitation witness. No deep tactic scripts or multi-step algebraic reductions.
why it matters in Recognition Science
Supplies the Logo5 certificate object used as a Foundation stamp that domain cost and the canonical threshold are well-formed and positive. Downstream use edges are empty in the current graph, so this module is a leaf packaging layer rather than a lemma feeding T5–T8 or the mass ladder. It keeps the cost-threshold interface explicit and inhabitable so later recognition or certification developments can depend on a single named record instead of ad-hoc inequalities. It does not itself advance the forcing chain, RCL uniqueness, or the eight-tick octave.
scope and limits
- Does not derive J-uniqueness, RCL, or any T0–T8 forcing step.
- Does not fix numerical values of c, hbar, G, or alpha.
- Does not prove mass-ladder or Berry-threshold claims.
- Does not connect domain cost to defectDist or phi-ladder rungs.
- Does not supply downstream consumers in the current dependency graph.