IndisputableMonolith.Information.Compression_Ratio_RS
Defines RS-native domain cost and a canonical compression threshold, then packages a certificate that the compression ratio stays above that threshold. Information theorists working in the Recognition stack cite it when bounding how much structure can be discarded without leaving the admissible cost regime. The module is mostly definitions plus elementary positivity and evaluation lemmas.
claimIntroduce a domain cost $C(D)$ built from the RS $J$-cost, a canonical threshold $\theta>0$, and a certificate type asserting that a compression ratio $R$ satisfies $R \ge \theta$ (with inhabitation of a default certificate).
background
Recognition Science measures mismatch with the unique cost $J(x)=(x+x^{-1})/2-1$ forced by the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS tick and related units. In the information layer one needs a domain-level cost that aggregates $J$ over admissible configurations, not just a pointwise score.
This module sits in that layer. It defines domainCost as the cost assigned to a domain (with an evaluation identity and a nonnegativity lemma), and a positive canonicalThreshold used as the cutoff for acceptable compression. The certificate bundle CompressionRatioCert packages the inequality that a stated compression ratio meets or exceeds that threshold.
No forcing-chain step (T5–T8) is proved here; the module only specializes cost and threshold data already fixed upstream so later information results can quote a single named bound.
proof idea
Definition-heavy module. Domain cost is introduced and checked at a reference point (domainCost_at_eq); nonnegativity follows from the underlying $J$-cost. The canonical threshold is defined and proved positive. CompressionRatioCert is a structure (or Prop bundle) whose default inhabitant cert is constructed from those facts; cert_inhabited records that the type is nonempty. No deep tactic proof: algebraic identities and positivity inherited from Cost/Constants.
why it matters in Recognition Science
Gives the Information domain a single named compression-ratio certificate tied to RS cost rather than an ad hoc bit-count. Downstream pages can assume a uniform threshold instead of re-deriving positivity of $J$ and the cutoff each time. With no recorded used_by edges yet, it is infrastructure for later compression, coding, or channel lemmas in the same folder. It does not itself close a forcing-chain obligation; it only exports cost-consistent bounds those results will need.
scope and limits
- Does not derive $J$ uniqueness or the Recognition Composition Law.
- Does not prove an optimal coding theorem or Shannon-style rate bound.
- Does not fix numerical compression ratios for concrete physical channels.
- Does not connect the threshold to eight-tick, $D=3$, or mass-ladder results.
- Does not supply used_by consumers; it is leaf infrastructure until wired.