IndisputableMonolith.LedgerParityAdjacency
LedgerParityAdjacency represents parity states as boolean vectors over d coordinates, extending GrayCycle patterns to ledger debit-credit balances. Ledger modelers cite it to guarantee that each tick flips exactly one parity bit in the phi vector. The module supplies targeted definitions and adjacency lemmas that compose directly with the imported hypercube cycle facts.
claimA parity pattern is a map $p : [d] → {0,1}$ such that two patterns are adjacent precisely when they differ in one coordinate; this equips the $d$-dimensional hypercube with an odd/even labeling for ledger updates.
background
The module operates inside the Recognition Science ledger framework, where a state tracks debit and credit entries and each tick posts a single unit to one account. It imports GrayCycle, whose doc-comment states: state space Pattern d := Fin d → Bool, adjacency when patterns differ in exactly one coordinate, and a length-2^d closed walk visiting every pattern once. Local definitions such as parityPattern, coordAtomicStep, and ledgerVecParity translate this hypercube structure into explicit parity (odd/even) assignments at each coordinate.
proof idea
This is a definition module, no proofs. It introduces parityPattern as the boolean vector representation, then records one-line facts such as coordAtomicStep_oneBitDiff and ledgerVecStep_oneBitDiff that restate GrayCycle adjacency for the ledger vector setting.
why it matters in Recognition Science
The module supplies the parity adjacency layer required by LedgerPostingAdjacency, whose doc-comment records that a single post changes phi = debit-credit by ±1 at exactly one coordinate. It therefore bridges GrayCycle's Hamiltonian cycle on the hypercube to the explicit ledger-shaped model used in the Recognition forcing chain and the eight-tick octave construction.
scope and limits
- Does not prove existence or uniqueness of the Gray cycle.
- Does not model sequences of multiple ledger posts.
- Does not connect parity patterns to mass formulas or the phi-ladder.
- Does not address continuous limits or Berry creation thresholds.