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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” 5 papers
Tree geometry. Trees, depth, hierarchies and dendrograms Tagged papers: 34.
Born Rule as Haar Measure on $p$‑Adic Tree Balls: A Structural Derivation and Its Implications for Quantum Statistics
Quantum theory postulates the Born rule without a deeper structural justification, and Bell‑type correlations are usually interpreted as non‑local. This gap hinders deterministic reconstructions of quantum mechanics and inflates the engineering overhead of quantum‑information technologies that must…
Cocycle Solving in Cognition: Ultrametric Reaction Times and Analogy Depth
Cognitive consistency and analogical difficulty are pervasive challenges for psychologists, educators, and artificial‑intelligence designers. Existing Euclidean models cannot capture the hierarchical constraints that appear in belief networks and analogy spaces. We therefore propose a formalism in…
Convergence, Consilience, and the Hierarchical Architecture of Reality: A Corrected Meta-Analysis with Worked Examples from Interdisciplinary Physics
Scientists in disconnected fields repeatedly rediscover the same mathematical structures — gauge symmetry, effective field theory, universal critical exponents — and each rediscovery costs duplicated effort while suggesting that the space of viable theories is tightly constrained. Whether that…
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…
Topological Signal Processing
The inherent limitations of conventional digital signal processing—specifically the latency and energy bottlenecks imposed by analog-to-digital conversion—represent a critical barrier for next-generation systems like 6G networks. This paper introduces a novel physical computing paradigm that…
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