IndisputableMonolith.Algebra.LedgerAlgebra
The LedgerAlgebra module supplies the group structure for signed integer flows that model debit and credit events on edges. Category builders in RecognitionCategory cite it to ground balanced ledger constructions. The module consists of type definitions and elementary group lemmas imported from Cost and Mathlib.
claimA ledger event is an element of the additive group $(\mathbb{Z}, +, 0)$, where a positive value denotes a debit and a negative value denotes a credit.
background
Recognition Science tracks physical flows through ledger events. The module imports Mathlib and the Cost module to equip the integers with their standard additive group structure. The supplied doc-comment states that a ledger event is a signed integer flow on an edge, positive for debit and negative for credit, forming the group $(\mathbb{Z}, +, 0)$.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the RecognitionCategory construction that assembles recognition structures from ledger primitives. It supplies the base group operations required before graded ledgers and windowed balance checks appear in downstream algebra.
scope and limits
- Does not perform numerical evaluation of balances or flows.
- Does not connect ledger events to physical constants or dimensions.
- Does not define multi-edge or higher-arity ledger compositions.
- Does not include time-indexed or probabilistic extensions.
used by (1)
depends on (1)
declarations in this module (19)
-
structure
LedgerEvent -
theorem
paired_event_sum_zero -
theorem
conj_involution -
structure
LedgerPage -
def
computeBalance -
def
IsBalanced -
theorem
empty_balanced -
theorem
paired_preserves_balance -
structure
Window8 -
def
neutralWindow -
theorem
neutralWindow_isNeutral -
structure
GradedLedger -
structure
Cycle -
structure
PotentialFunction -
theorem
potential_implies_exact -
structure
DoubleEntryAlgebra -
theorem
antisymmetric_implies_balance -
structure
MoralLedger -
theorem
ledger_algebra_certificate