χTopic tag
#cohomology
5 documents indexed here. Mathematical objects, methods, systems, and recurring technical questions.
ℓNotes
2- Notes
Chapter 11 — Čech Cohomology Framework
Čech cohomology as the natural language of the theory — what holds exactly in the discrete setting, what requires additional topological hypotheses, and how the cocycle condition encodes the closure of relational transit.
- Notes
Chapter 12 — Three Computational Axes
The three computational axes of invariants: intrinsic cohomology, relative cohomology of the fruit–door pair, and persistence barcodes of the door set.
χONN documents
1¶Papers
2- Papers · 2026
Ontology Neural Network and ORTSF: A Framework for Topological Reasoning and Delay-Robust Control
Paper of record for the original ONN + ORTSF framing. A later audit found that the higher-order/cohomological thesis adds no information beyond pairwise data un
- Papers · 2025
An Axiomatic Framework for Understanding Relations via Gauge-Invariant Cohomology
What does it mean for something to exist within a web of relations? We answer this question by developing a rigorous mathematical framework in which existence e