IndisputableMonolith.Cosmology.RS_COS_Structural_009
Structural certificate module for RS cosmology item 009: a nonnegative domain cost functional built from the RS J-cost, a positive canonical threshold, and an inhabited certificate packing those facts. Cosmology auditors cite it when a structural bound must sit above a fixed cost floor. The content is definitional plus elementary positivity lemmas, not a deep derivation.
claimDefine a domain cost $C$ on the RS cost side, prove $C \ge 0$ and an evaluation identity at a reference point, fix a canonical threshold $\theta > 0$, and package these into an inhabited structural certificate $\mathrm{RS\text{-}COS\text{-}Structural\text{-}009}$.
background
Recognition Science measures mismatch with the J-cost from the Cost module (the unique cost forced by the Recognition Composition Law and T5). Cosmology structural certificates record simple, reusable inequalities that later expansion or horizon arguments can invoke without reopening the cost calculus.
This module sits under Cosmology and imports Constants (RS-native units, including the tick $\tau_0$) and Cost. Sibling names indicate a domain-level cost functional, its nonnegativity, an evaluation identity, and a positive canonical threshold used as a comparison floor.
The certificate object is the usual RS pattern: a Prop-carrying structure plus an inhabited instance so downstream files can depend on a single named cert rather than a loose bundle of lemmas.
proof idea
Definition-and-certificate module. Domain cost is introduced as a Cost-side functional; nonnegativity and the pointwise evaluation identity are short lemmas. The canonical threshold is a positive constant (positivity proved directly). The structural cert bundles those facts; inhabitation is by constructing the record from the lemmas already proved. No multi-step forcing or analytic argument appears at module scope.
why it matters in Recognition Science
Supplies the named structural certificate RS-COS-Structural-009 for the cosmology layer of the monolith. Downstream cosmology developments that need a fixed positive cost threshold or a nonnegative domain cost can import this cert rather than rebuild Cost inequalities locally. It does not itself close a forcing-chain step (T0–T8) or fix a physical constant band; it is infrastructure for later cosmological bounds that sit on the J-cost and RS units. No used_by edges are recorded yet, so its consumers are still open in the graph.
scope and limits
- Does not derive domain cost from the full UnifiedForcingChain (T0–T8).
- Does not prove observational cosmology identities (Hubble law, FLRW metrics, etc.).
- Does not fix numerical values of c, G, hbar, or alpha beyond Cost/Constants imports.
- Does not claim the threshold is unique or dynamically selected by cosmology.
- Does not discharge any sorry outside this module’s own certificate packing.