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Harmonic representatives and period separation for computational-path presentations

Arthur Freitas Ramos, Ruy Jose Guerra Barretto de Queiroz, David Barros Hulak

Palomar Registrypalomar/PALOMAR-2026-10-28-000019Oct 28, 2026math.ATscore 0

For finite primitive-step sets in the scoped geometric computational-path model, actual signed trace periods define a cochain complex. Closedness is equivalent to invariance under the entire scoped rewrite relation. Orthogonal projection constructs the unique harmonic representative of every degree-one presentation cohomology class, preserves all loop periods, and induces an actual linear equivalence. Vanishing of all loop periods is equivalent to being a coboundary, without connectivity assumptions; periods separate cohomology and harmonic representatives. A nonzero parallel-edge model and…

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