IndisputableMonolith.Cosmology.RS_COS_Structural_002
Structural cosmology module packaging a non-negative domain cost and a strictly positive canonical threshold into an inhabited certificate. Cosmologists citing RS structural claims use it as a typed witness that the cost/threshold pair is well-posed. The module is mostly definitions plus elementary positivity and evaluation lemmas, closed by an inhabited cert record.
claimDefine a domain cost $C$ on the RS cost structure, prove $C \ge 0$ and an evaluation identity at equality cases, introduce a canonical threshold $\theta > 0$, and package these facts as an inhabited structural certificate $\mathrm{RS\_COS\_Structural\_002}$.
background
Recognition Science measures mismatch with the J-cost from the Cost module (the unique cost forced by the Recognition Composition Law). Cosmology modules lift that cost to domain-scale quantities: a domain cost assigns a non-negative real to cosmological domains, and a canonical threshold marks the scale at which a structural transition is recognized.
The Constants import supplies the RS-native tick $\tau_0 = 1$. This module sits in the Cosmology domain and does not re-derive J-uniqueness or the forcing chain; it only assembles the cost/threshold interface needed by later structural claims.
Sibling definitions introduce domainCost, its non-negativity and on-equality evaluation, canonicalThreshold with positivity, and the certificate record that bundles them.
proof idea
Definition-heavy module. Domain cost and canonical threshold are introduced as defs; non-negativity and positivity are short lemmas from the Cost/Constants infrastructure; evaluation-at-equality is an algebraic identity. The certificate type and its inhabited instance simply package those lemmas, so downstream code can require one cert rather than several separate hypotheses.
why it matters in Recognition Science
Gives Cosmology a reusable structural witness (cost non-negative, threshold positive) without reopening the T5 J-uniqueness or RCL arguments. No downstream edges are recorded yet, so the module is a leaf certificate: later RS cosmology structural theorems are expected to take the inhabited cert as a hypothesis rather than reproving positivity. It does not touch mass ladders, alpha, or the eight-tick octave; it only stabilizes the cost/threshold interface for structural cosmology claims labeled 002.
scope and limits
- Does not derive J-cost uniqueness or the Recognition Composition Law.
- Does not prove dynamical cosmology equations or expansion histories.
- Does not fix numerical values of thresholds beyond positivity.
- Does not connect to mass ladders, alpha, or eight-tick timing.
- Does not supply downstream consumers; used_by is currently empty.