H_ThermodynamicsVerified
plain-language theorem explainer
Recognition cost satisfies the Landauer bound Jcost(m) ≥ (log m)^2 / 2 for each bond multiplier m in a thermodynamics ledger state. Physicists deriving information erasure limits from recognition axioms would cite this hypothesis. The declaration is introduced as a scaffold definition whose Taylor expansion justification remains to be completed in the Thermodynamics submodule.
Claim. For every thermodynamics ledger state $s$ and every active bond $b$, let $m$ be the bond multiplier and $u = $log$ m$. The recognition cost then obeys $J(m) ≥ u^2 / 2$.
background
The module aggregates the information-theoretic and thermodynamic foundations of Recognition Science. It incorporates CompressionPrior for minimum description length grounded in J-cost, EMLFromRecognition for oriented exp-log gates, FEPBridgeFromJCost for local free-energy contact, JCostNecessity for uniqueness from recognition axioms, and Thermodynamics for the Landauer limit together with 8-tick dissipation.
proof idea
This is a direct definition of the Prop as the universal quantification over ledger states and bonds of the inequality Cost.Jcost m ≥ (Real.log m)^2 / 2. No lemmas are invoked; the declaration functions as a one-line wrapper encoding the bound using the J-cost function from the RSNative measurement core.
why it matters
The hypothesis places the thermodynamic bound inside the information bridge aggregator, connecting recognition cost to the Landauer limit for information erasure. It aligns with the eight-tick octave dissipation (T7) and supports derivations of constants such as alpha inverse inside (137.030, 137.039). The doc-comment flags the open task of completing the Taylor expansion proof in Thermodynamics.lean to remove scaffold status.
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