IndisputableMonolith.Foundation.RecognitionScience_Logo5
Foundation module packaging the Logo-5 certificate for Recognition Science: a nonnegative domain cost compared against a positive canonical threshold. It exposes the cost functional, its evaluation identity, nonnegativity, the threshold, and an inhabited certificate record. Downstream work cites the certificate rather than rebuilding the inequalities. The content is definitional packaging plus short positivity proofs over the Cost import.
claimDefine a domain cost $C$ (from the RS cost layer), prove $C \ge 0$, fix a canonical threshold $\theta > 0$, and package an inhabited Logo-5 certificate asserting the cost/threshold relation used by the foundation layer.
background
Recognition Science measures mismatch with a nonnegative cost built from the unique $J$-functional forced by the Recognition Composition Law. The Cost import supplies that cost layer; Constants supplies RS-native units (including the tick $\tau_0$).
This module sits in Foundation and introduces a domain-level cost wrapper, its pointwise evaluation identity, nonnegativity, and a positive canonical threshold. Those pieces are bundled into an RSLogo5 certificate record so later modules can assume a single inhabited cert instead of re-proving the elementary inequalities.
No forcing-chain step (T5–T8) is re-derived here; the module only packages cost positivity and a threshold for Logo-5 bookkeeping.
proof idea
Definition module with thin lemmas. Domain cost is introduced as a wrapper over the imported Cost layer; an evaluation identity records how the wrapper sits on points. Nonnegativity and threshold positivity are short arguments from the Cost/Constants facts already in scope. The certificate type collects those propositions; inhabitation is a constructor application assembling the proved fields. No deep tactic script or new analytic estimate.
why it matters in Recognition Science
Gives Foundation a single named Logo-5 certificate (cost nonnegativity plus canonical threshold) so later RS modules can depend on one inhabited record rather than ad-hoc inequalities. It does not itself appear in the supplied used-by list; it is a leaf packaging node over Constants and Cost. Landmark contact is only indirect: the cost layer ultimately rests on $J$-uniqueness (T5) and the RCL, which this module does not re-prove. Closes local scaffolding around the Logo-5 cert interface.
scope and limits
- Does not derive $J$-uniqueness, RCL, or any T0–T8 forcing step.
- Does not compute particle masses, $\alpha$, or dimension $D=3$.
- Does not define the global RS cost from scratch; wraps the Cost import.
- Does not supply numerical bounds beyond threshold positivity.
- Does not claim downstream consumers; used-by list is empty.