LedgerPage
plain-language theorem explainer
A ledger page is a finite list of signed integer flows equipped with their aggregate sum. Algebraists working on the Recognition ledger cite this structure when introducing balance predicates and pairing lemmas. The definition is a direct record construction that initializes the balance field by folding addition over the flows in the event list.
Claim. A ledger page consists of a list of events $(e_i)$ with each $e_i$ an element of the additive group of integers, together with the integer balance $b = e_1 + e_2 + ... + e_n$.
background
In the LedgerAlgebra module a ledger event is a signed integer flow on an edge, positive for debit and negative for credit, carrying the additive group structure on the integers. A ledger page aggregates such events into a list and records their total sum as the balance field. The module imports Mathlib and Cost; its upstream dependencies include the seven-element list of plot families, the eight kinship systems, and the nuclear-density tiers, but the immediate prerequisite is the LedgerEvent structure whose flow component supplies the integer group.
proof idea
The declaration is a structure definition. It directly names the events field as a List LedgerEvent and sets the balance field to the result of folding addition over the flow values of those events. No lemmas or tactics are invoked; the construction is a pure record initializer.
why it matters
LedgerPage supplies the basic object for the ledger algebra and is the direct input to the IsBalanced predicate that checks whether the computed sum equals zero. It is also the starting point for the theorem that adjoining a pair of conjugate events preserves balance. The structure therefore anchors the algebraic layer that supports conservation statements in the Recognition framework.
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