recognition /
Mathematics /
Mathematics.HodgeConjecture /
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formal statement (Lean)
221 theorem flow_stable_at_zero (L : DefectBoundedSubLedger) (cgf : CoarseGrainingFlow L)
222 (cls : CoarseGrainingStableClass L) (hstable : IsFlowStable L cgf cls)
223 (hlimit : flowLimit cgf = 0) : cls.z_charge = 0 := by
proof body
Term-mode proof.
224 have hle : cls.z_charge ≤ 0 := hlimit ▸ hstable
225 exact le_antisymm hle cls.symmetric
226
227 /-- **Defect Budget Theorem**: A class that is stable under ALL coarse-graining flows
228 (including those with limit 0) must have z_charge = 0. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (17)
Lean names referenced from this declaration's body.
Defect
in IndisputableMonolith.CPM.LNALBridge
decl_use
le_antisymm
in IndisputableMonolith.Foundation.ArithmeticFromLogic
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A
in IndisputableMonolith.Foundation.IntegrationGap
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
A
in IndisputableMonolith.Masses.Anchor
decl_use
CoarseGrainingFlow
in IndisputableMonolith.Mathematics.HodgeConjecture
decl_use
CoarseGrainingStableClass
in IndisputableMonolith.Mathematics.HodgeConjecture
decl_use
DefectBoundedSubLedger
in IndisputableMonolith.Mathematics.HodgeConjecture
decl_use
flowLimit
in IndisputableMonolith.Mathematics.HodgeConjecture
decl_use
IsFlowStable
in IndisputableMonolith.Mathematics.HodgeConjecture
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
A
in IndisputableMonolith.Modal.Actualization
decl_use
that
in IndisputableMonolith.NumberTheory.PhiLadderLattice
decl_use
L
in IndisputableMonolith.Recognition
decl_use
L
in IndisputableMonolith.Recognition.Cycle3
decl_use