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728 papers from the QNFO program, filed on nine shelves by the reader each one is written for: energy per answer, error correction, physics, numbers and p-adics, logic and formalism, AI and knowledge, autonomous systems, assessments, and cross-cutting essays. Every page renders its mathematics and can be questioned in place. How a living paper works.
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Results for “topological” 2 papers
Proof assistants. Machine-checked proofs (Lean, Isabelle, Coq) Tagged papers: 13.
Exchange Symmetry Is an Involution, Not an Idempotent: A Derivation‑Based Fact‑Check
The claim that particle exchange is idempotent, that the two‑particle configuration space is the three‑sphere $S^{3}$, that the spin‑statistics theorem holds without qualification, and that non‑Abelian anyons are idempotent appears in recent speculative notes. This paper addresses the gap between…
Proof-of-Concept for Auditable Attention using Ultrametric Tree Distances
The dominance of high-dimensional Euclidean vector spaces in contemporary transformer architectures has precipitated an interpretability crisis, as continuous geometric embeddings can obscure the causal mechanisms of semantic attention. This paper presents a formal proof-of-concept for a…
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