structure
definition
def or abbrev
DefectBoundedSubLedger
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formal statement (Lean)
56structure DefectBoundedSubLedger where
57 /-- Recognition events in the sub-ledger -/
58 events : List RecognitionEvent
59 /-- Defect = total J-cost of all recognition events -/
60 defect : ℝ
61 /-- Defect is bounded (the variety is non-singular) -/
62 defect_bounded : defect < phi ^ 44
63 /-- Defect is nonneg (J-cost is always nonneg) -/
64 defect_nonneg : 0 ≤ defect
65
66/-- A cohomology class on a DefectBoundedSubLedger is a real number
67 (encoding the "charge" of the class in the Z-complexity sense). -/
used by (33)
-
CoarseGrainingFlow -
CoarseGrainingStableClass -
CohomologyClass -
defect_budget_theorem -
flow_stable_at_zero -
HodgeCert -
hodge_implies_zero_charge -
IsFlowStable -
JCostMinimalCycle -
j_cost_minimal_is_cgstable -
j_cost_minimal_is_cgstable' -
RSHodgeConjecture -
rs_pp_condition -
sub_ledger_exists -
trivialFlow -
HodgeHardCert -
hodge_hard_direction_case_A -
hodge_hard_direction_case_B -
hodge_hard_direction_summary -
rs_hodge_holds_for_trivial_ledgers -
rs_hodge_holds_for_unit_defect -
all_ledgers_are_jcost_critical -
globally_minimal_gives_cycle -
hard_direction_for_zero_limit_ledger -
hard_direction_via_defect_budget -
HarmonicFormsCert -
harmonic_form_theorem_minimal_ledger -
harmonic_form_theorem_zero_charge -
HodgeDecomposition -
hodge_decomposition_exists