module module high

`IndisputableMonolith.Algebra.LedgerAlgebra`

The LedgerAlgebra module establishes the integer group structure for modeling signed flows as ledger events in the Recognition Science framework. It would be cited by researchers constructing algebraic or categorical models that rely on debit-credit balance. The module consists of definitions and basic lemmas that verify group axioms and balance preservation through direct algebraic checks.

claimLedgerEvent is the additive group of integers, $L := (ℤ, +, 0)$, where a positive element represents a debit flow on an edge and a negative element represents a credit flow.

background

Recognition Science builds algebraic layers to support the Recognition Composition Law and the forcing chain from T0 to T8. This module imports the Cost definitions and introduces LedgerEvent as signed integer flows together with auxiliary notions such as paired events whose sum is zero and the predicate IsBalanced on ledger pages. The group operation is ordinary integer addition, which encodes net flow conservation on edges.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the group primitives imported by RecognitionCategory, which in turn supports the categorical formulation of recognition processes. It fills the algebraic base layer required for later statements of the Recognition Composition Law and the eight-tick octave structure.

scope and limits

Does not treat non-integer or continuous flows.
Does not prove the Recognition Composition Law itself.
Does not incorporate the phi-ladder or mass formulas.
Does not address spatial dimensions or Berry thresholds.

used by (1)

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

IndisputableMonolith.Algebra.RecognitionCategory module_import

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Cost module_import

declarations in this module (19)

structure LedgerEvent L55
theorem paired_event_sum_zero L68
theorem conj_involution L75
structure LedgerPage L82
def computeBalance L89
def IsBalanced L93
theorem empty_balanced L97
theorem paired_preserves_balance L101
structure Window8 L111
def neutralWindow L123
theorem neutralWindow_isNeutral L136
structure GradedLedger L145
structure Cycle L171
structure PotentialFunction L193
theorem potential_implies_exact L201
structure DoubleEntryAlgebra L215
theorem antisymmetric_implies_balance L224
structure MoralLedger L241
theorem ledger_algebra_certificate L260