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IndisputableMonolith.Mathematics.HodgeConjecture

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The module introduces the Recognition Science reformulation of the Hodge conjecture by defining DefectBoundedSubLedger as finite collections of recognition events with bounded total J-cost. It serves as the structural proxy for smooth projective algebraic varieties. Researchers working on RS algebraic geometry and cohomology would cite it when assembling the full conjecture. The module is purely definitional and organizes imports from LedgerForcing and HodgeConjectureStructure to prepare the scaffold.

claimA defect-bounded sub-ledger is a finite set of recognition events with finite total J-cost, the RS analog of a smooth projective algebraic variety.

background

Recognition Science derives ledger structures from J-symmetry via the LedgerForcing module, which establishes that J-symmetry forces double-entry bookkeeping. The HodgeConjectureStructure import supplies the formal scaffold for algebraicity statements in this setting. Constants provide the base time quantum τ₀ = 1 tick. The central object is the DefectBoundedSubLedger: a finite collection of recognition events whose total J-cost remains finite, serving as the variety proxy for the RS Hodge conjecture.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the core definitions that feed the hard-direction assembly in HodgeHardDirection, where every CoarseGrainingStableClass is generated by JCostMinimalCycles, and supports the harmonic-forms translation in HodgeHarmonicForms. It fills the structural scaffold for the RS Hodge Conjecture by linking J-cost boundedness to cohomology classes.

scope and limits

used by (2)

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 (19)