Open Research Index

Arthur742Ramos/TopologicalComputationalPaths

Arthur Freitas Ramos, Ruy J. G. B. de Queiroz, Anjolina Grisi de Oliveira, Tiago M. L. de Veras, David Barros Hulak

Palomar Registrypalomar/PALOMAR-2026-08-29-000005Aug 29, 2026math.ATscore 0

A Lean formalization of topological semantics for endpoint-varying computational paths. It constructs both the canonical final composable quotient and the ordinary pullback of quotient arrows. The selected result proves that the canonical comparison is a continuous bijection and characterizes exactly when it is quotient, a homeomorphism, and an induced topology agreement; under these equivalent conditions ordinary composition is continuous. It also records discontinuity as an obstruction and proves compact--Hausdorff and discrete sufficient cases. The selected certificate additionally…

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