Homological Calculations for Finite Toy Models of Rewriting Systems
Year: 2026
Type: article
Abstract: This paper studies two explicitly defined finite chain complexes intended as toy models for rewriting systems. For a four-cycle complex, we prove that its first homology group is isomorphic to Z. For a three-cycle complex equipped with a specified two-cell, we prove that its first homology group vanishes. We also compute the first integral cohomology group of the four-cycle complex using the universal coefficient theorem. The paper distinguishes these proven algebraic results from possible categorical, sheaftheoretic, and operational extensions. In particular, it does not claim to construct a general epistemic category, a complete Squier resolution, a Verdier duality theorem, or an operational self-healing mechanism. The vanishing of first homology in the three-cycle model is an algebraic statement about cycles and boundaries; it does not by itself imply termination, confluence, or algorithmic recovery
Author: Naing, Myo Sett
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225784591
FWCI:
Cites:
Cited by:
Related to: