module module high

`IndisputableMonolith.Mathematics.HodgeConjecture`

Mathematics.HodgeConjecture introduces DefectBoundedSubLedger as the RS model of a smooth projective algebraic variety: a finite collection of recognition events whose total J-cost remains finite. Researchers translating algebraic geometry statements into ledger forcing would cite the module when linking cohomology to minimal cycles. It supplies the object definitions that HodgeHardDirection and HodgeHarmonicForms import directly.

claimA DefectBoundedSubLedger is a finite set of recognition events with bounded total J-cost (the RS counterpart to a smooth projective algebraic variety).

background

The module imports Constants (where the RS time quantum satisfies τ₀ = 1 tick), LedgerForcing (which shows J-symmetry forces double-entry ledger structure), and HodgeConjectureStructure (which supplies the structural scaffold for Hodge-type algebraicity statements). It defines DefectBoundedSubLedger together with sibling notions such as CohomologyClass, CoarseGrainingStableClass, and JCostMinimalCycle. These objects sit inside the Recognition Science ledger framework whose forcing chain runs from J-uniqueness through the eight-tick octave to D = 3.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the core objects for the RS Hodge Conjecture and feeds the hard-direction assembly in HodgeHardDirection (every CoarseGrainingStableClass generated by JCostMinimalCycles) together with the harmonic-forms translation in HodgeHarmonicForms. It completes the structural scaffold step labeled M-006 in HodgeConjectureStructure.

scope and limits

Does not prove the classical Hodge conjecture over ℂ.
Does not supply explicit J-cost bounds for concrete varieties.
Does not equate the RS formulation to the standard statement.
Does not contain numerical checks against known Hodge classes.

used by (2)

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

IndisputableMonolith.Mathematics.HodgeHardDirection module_import
IndisputableMonolith.Mathematics.HodgeHarmonicForms module_import

depends on (3)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Foundation.LedgerForcing module_import
IndisputableMonolith.Mathematics.HodgeConjectureStructure module_import

declarations in this module (19)

structure DefectBoundedSubLedger L56
structure CohomologyClass L68
structure CoarseGrainingStableClass L78
structure JCostMinimalCycle L84
theorem j_cost_minimal_is_cgstable L100
theorem j_cost_minimal_is_cgstable' L119
def RSHodgeConjecture L145
theorem hodge_implies_zero_charge L154
theorem rs_pp_condition L167
theorem sub_ledger_exists L172
structure CoarseGrainingFlow L188
def trivialFlow L199
def flowLimit L206
theorem flowLimit_nonneg L211
def IsFlowStable L216
theorem flow_stable_at_zero L221
theorem defect_budget_theorem L229
structure HodgeCert L260
theorem hodgeCert L272