IndisputableMonolith.LedgerUniqueness
LedgerUniqueness supplies uniqueness results for reachability structures and affine maps on discrete sets within the Recognition Science ledger. Workers on the T4 forcing step cite it to confirm that functions on reach sets are determined up to additive constants. The argument proceeds by importing reach-set lemmas from Potential and Causality, then layering component-wise uniqueness on top of the base Recognition principle that nothing recognizes itself.
claimIf two affine maps $f,g$ agree on the discrete reach set $ ext{Reach}_N$ or the ball $ ext{inBall}$, then $f-g$ is constant on each connected component.
background
The module sits inside the T4 uniqueness layer of the forcing chain. It imports Recognition (T1: nothing cannot recognize itself), Potential (dependency-light uniqueness lemmas on discrete reach sets), and Causality.Basic (reachability primitives). Local objects include ReachN (the N-step reachable set), inBall (the closed ball under the reach metric), Reaches (the reachability relation), IsAffine (the affine property), and the component-wise uniqueness statements built from them.
proof idea
The module first assembles kinematics and reach-set definitions, then applies the imported T4 lemmas from Potential to obtain uniqueness on ReachN and inBall, and finally lifts to uniqueness up to constant on each connected component via the IsAffine predicate.
why it matters in Recognition Science
The results close the discrete uniqueness step required before the J-uniqueness and phi-ladder constructions in the main forcing chain. They feed the ledger-level consistency arguments that rest on T4, ensuring that reachability data determine potentials uniquely up to the constants allowed by the Recognition axioms.
scope and limits
- Does not establish uniqueness outside the discrete reach-set setting.
- Does not treat continuous or infinite-dimensional cases.
- Does not derive the value of the constant from first principles.
- Does not connect directly to the mass formula or alpha band.