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IndisputableMonolith.Foundation.LedgerForcing

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The LedgerForcing module assembles the discrete ledger as a structure of recognition events under the J-cost functional. Foundation researchers cite it when extending to dimension or quantum structures. The module imports Cost, LawOfExistence, and DiscretenessForcing to supply the required definitions and relations.

claimThe cost functional satisfies $J(x) = ½(x + x^{-1}) - 1$, with recognition events obeying $x$ exists if and only if defect$(x) = 0$, and the ledger is the resulting balanced collection of such events.

background

This module resides in the Foundation domain and supplies the ledger layer between cost and higher forcing results. The Cost import defines the functional $J(x) = ½(x + x^{-1}) - 1$. DiscretenessForcing states that $J(x)$ has a unique minimum at $x=1$ and, in log coordinates, $J(e^t) = cosh(t) - 1$, a convex bowl centered at $t=0$. LawOfExistence supplies the equivalence $x$ exists ⟺ defect$(x) = 0$. Sibling definitions include RecognitionEvent, event_cost, reciprocal, and Ledger.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module feeds DimensionForcing (D=3), PhiForcing (self-similar discrete ledger to golden ratio), QuantumLedger, InevitabilityStructure, and the complexity modules CircuitLedger and RSatEncoding. It supplies the ledger object required after J-uniqueness (T5) and before the eight-tick octave and spatial dimension steps in the forcing chain.

scope and limits

used by (10)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (3)

Lean names referenced from this declaration's body.

declarations in this module (29)