IndisputableMonolith.Information.Compression_Ratio_RS
Defines domain-level cost, a positive canonical threshold, and a compression-ratio certificate in Recognition Science units. Information theorists in the RS stack cite the certificate when bounding how much structure a domain can pack relative to the J-cost yardstick. The module is mostly definitional: nonnegativity of domain cost, positivity of the threshold, and an inhabited cert record.
claimIn RS units the module supplies a domain cost $C(D)\ge 0$, a canonical threshold $\theta>0$, and a compression-ratio certificate asserting that the ratio of domain cost to the reference scale lies at or below $\theta$.
background
Recognition Science measures mismatch with the unique J-cost $J(x)=(x+x^{-1})/2-1$ fixed by the Recognition Composition Law. The Cost import exposes that functional; Constants supplies the RS tick $\tau_0=1$ and the golden ratio $\varphi$ that sets native scales ($\hbar=\varphi^{-5}$, etc.).
This Information module lifts pointwise cost to a domain-level aggregate domainCost and fixes a positive canonicalThreshold against which compression is judged. The certificate type packages the numerical claim that a domain's cost-to-scale ratio does not exceed that threshold.
Sibling lemmas record equality at evaluation points, nonnegativity of domain cost, and positivity of the threshold, so downstream arguments can treat the ratio bound as a closed Prop rather than an ad-hoc inequality.
proof idea
Definition module with thin supporting lemmas. Domain cost is introduced as a nonnegative real functional; a one-line evaluation lemma ties it to pointwise cost. The canonical threshold is a positive constant in RS units. CompressionRatioCert is a structure (or Prop bundle) whose inhabitant cert is constructed from those facts; cert_inhabited records that the type is nonempty. No deep tactic proof: algebraic nonnegativity and positivity close the certificate.
why it matters in Recognition Science
Places a reusable compression-ratio certificate inside the Information domain of the monolith. Downstream work that needs a uniform bound on how much recognisable structure a domain can carry relative to the J-cost yardstick can import the inhabited cert rather than re-derive the inequality. The construction sits downstream of Cost (J-uniqueness, T5) and Constants ($\varphi$-native units), and is the natural information-side counterpart to the forcing-chain scales (eight-tick octave, $\varphi$-ladder). No used_by edges are recorded yet; the module is a leaf certificate ready for later information or complexity theorems.
scope and limits
- Does not derive J-uniqueness or the RCL; those live in Cost and the forcing chain.
- Does not compute numerical compression ratios for concrete physical domains.
- Does not prove optimality of the canonical threshold among all possible cutoffs.
- Does not connect the certificate to mass-ladder or alpha-band claims.
- Does not supply an algorithmic compressor; only a cost-ratio bound.