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IndisputableMonolith.Foundation.LedgerForcing

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LedgerForcing module defines the discrete ledger of recognition events equipped with the J-cost functional. It assembles the cost definition, Law of Existence, and discreteness results into Ledger, balanced lists, and reciprocity. Foundation researchers cite it when moving from continuous cost landscapes to discrete structures that feed dimension and phi forcing. The module is definitional with supporting lemmas on reciprocity and event costs.

claimThe cost functional is given by $J(x) = ½(x + x^{-1}) - 1$. A ledger is a collection of recognition events whose costs satisfy reciprocity $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$ and the existence condition defect$(x) = 0$.

background

The module sits in the Foundation layer and imports the J-cost definition, LawOfExistence (x exists iff defect(x) = 0), and DiscretenessForcing. The latter states that J(x) = ½(x + x⁻¹) - 1 has a unique minimum at x = 1 and, in log coordinates, becomes the convex bowl cosh(t) - 1 centered at t = 0. Sibling definitions introduce RecognitionEvent, reciprocal, event_cost, balanced_list, and the Ledger type itself.

proof idea

This is a definition module, no proofs. It assembles imported results from Cost, LawOfExistence, and DiscretenessForcing into Ledger and reciprocity lemmas via direct construction of the types and basic equalities.

why it matters in Recognition Science

The module supplies the ledger structure imported by DimensionForcing (D = 3), PhiForcing (self-similar fixed point), QuantumLedger, InevitabilityStructure, and complexity modules CircuitLedger and RSatEncoding. It fills the discrete-event layer required for the T5–T8 forcing chain and the Recognition Composition Law.

scope and limits

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