Coherence and Gauge from Compression: Second-Tier Correction, Cocycle Constraint, and Coboundary FreedomCoherence and Gauge from Compression: Second-Tier Correction, Cocycle Constraint, and Coboundary Freedom

Compression of noncommuting updates forces cocycle coherence and gauge freedom. This paper continues the Searcy Forced Structure sequence. Building on (i) interaction as non-commutation and (ii) refinement-stable incremental composition with generator tiers, it derives the next representational residue required for compressible bookkeeping of non-Abelian composition. If first-tier summaries are to preserve represented products, a second-tier correction term is forced. Associativity then enforces a coherence identity on this correction (cocycle-type constraint). Finally, the correction is shown to admit a natural gauge freedom: shifting the second-tier reference offset transforms the correction by a coboundary while leaving the represented product invariant. The treatment remains pre-physical and discrete: no continuum limit, calculus, Hilbert space axioms, or dynamics equation are assumed.