net
plain-language theorem explainer
Net defines the per-state balance as the difference between debit and credit under a ledger constraint in the RRF strain module. Workers on ledger conservation and recognition cycles cite it when confirming zero net for closed systems. It is realized by direct subtraction of the two component maps from the constraint structure.
Claim. Let $L$ be a ledger constraint on a state space, consisting of debit and credit maps to integers. For any state $x$, the net balance is $L.debit(x) - L.credit(x)$.
background
The RRF Core Strain module defines strain as the measure of departure from equilibrium, with the governing law that strain tends to zero as the recognition functional J reaches zero. LedgerConstraint is the structure that encodes this balance requirement through two functions: debit and credit, each mapping a state to an integer value. The module supplies an abstract interface for strain functionals built on such constraints.
proof idea
One-line definition that subtracts the credit value from the debit value for the supplied state under the given ledger constraint.
why it matters
It supplies the per-state balance primitive used by GradedLedger to enforce inflow equals outflow at each vertex and by OctaveLoop to guarantee zero net flux over an eight-step recognition cycle. The definition supports strain minimization arguments in CPM models and cosmological balance conditions, consistent with the Recognition Science requirement that balanced ledgers exhibit vanishing net.
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