IndisputableMonolith.Foundation.RecognitionScienceSummary3
Foundation summary module that packages a domain-level cost functional, a positive canonical threshold, and an inhabited certificate bundle (RSSummary3Cert). Physicists citing the RS cost layer or threshold comparisons use it as a compact interface. The module is definitional: it wires Constants and Cost into named lemmas and a cert record, with no deep proof burden.
claimDefines a domain cost $C$ with $C\ge 0$ and evaluation-at-equality identities, a canonical threshold $\theta>0$, and an inhabited certificate record packaging these facts for Recognition Science summary layer 3.
background
Recognition Science builds physics from a single cost functional forced by the Recognition Composition Law. Upstream, Constants supplies the RS-native time quantum $\tau_0=1$ tick; Cost supplies the J-cost family (classically $J(x)=(x+x^{-1})/2-1$) used throughout the forcing chain T5 onward.
This module sits in the Foundation domain as a thin summary layer. It introduces a domain-scoped cost (nonnegative, with an equality-evaluation identity) and a strictly positive canonical threshold against which recognition events or defects can be compared. The certificate record RSSummary3Cert bundles those facts so downstream code can assume a single inhabited package rather than re-importing scattered lemmas.
No new forcing step (T0–T8) is proved here; the module only re-exports and names the cost/threshold interface needed by later summary or certification code.
proof idea
Definition-and-certificate module, not a theorem development. Nonnegativity and positivity facts are short lemmas over the imported Cost/Constants layer; the certificate is an inhabited structure assembling those lemmas. No multi-step tactic argument.
why it matters in Recognition Science
Gives Foundation a single named cert surface for domain cost and the canonical threshold, so later RS summary or audit code can depend on one inhabited record instead of ad-hoc imports. It does not itself advance the UnifiedForcingChain (T5 J-uniqueness, T6 $\phi$, T7 eight-tick, T8 $D=3$), but it stabilizes the cost/threshold vocabulary those steps rely on. No downstream used_by edges are recorded in the graph yet; the module is an interface hub rather than a parent theorem feeder.
scope and limits
- Does not prove J-uniqueness, RCL, or any T0–T8 forcing step.
- Does not derive numerical constants ($c$, $\hbar$, $G$, $\alpha$) or mass-ladder formulae.
- Does not assert physical units beyond RS-native ticks from Constants.
- Does not supply exploit-style or computational search procedures; pure interface math.
- Certificate inhabitedness is structural, not a global uniqueness claim.