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611 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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Numbers & p-adics papers 6 papers
Mathematicians. Valuation theory and the p-adic and adelic programme, Bruhat-Tits trees and ultrametric geometry as mathematics, Ostrowski's theorem, numeral and radix systems, primes, arithmetic and algebraic structures, zeta and gamma functions.
Teaching. Course and seminar material Tagged papers: 33.
Flag Structures and the Flagging Act: A Cross-Domain Survey with Explicit Counting Derivations and a Posed Re-Entry Problem
The word "flag" names a family of mathematically precise objects — chains of nested subspaces (flag varieties), nested set systems with exchange axioms (flag matroids), asymptotic-inequality certificates (flag algebras), and directional curvature invariants of Finsler spaces — and, in ordinary…
Emergent Universality from Symmetric Rules: Rule-110 Emulation by Alternating Trivial Cellular Automaton Rules
Elementary cellular automaton (ECA) rule 110 is Turing complete, yet its local rule is chiral: it treats its left and right neighbours differently, and this handedness underlies the glider dynamics that carry its computation. A recent construction shows that rule 110 can nevertheless be emulated by…
Geometric Ratios as Generators of Hierarchical Structure: An Arithmetic Audit of π, φ, and e
A recurring conjecture in the ultrametric-physics program holds that hierarchical—i.e., ultrametric—structure "emerges" when a scale ratio q is set equal to a fundamental geometric constant: π, the golden ratio φ = (1+√5)/2, or Euler's number e. This paper converts that conjecture into falsifiable…
Pillar 3: PBO/Autaxys — Pattern-Based Ontology as Intrinsic Self-Ordering
PBO/Autaxys: Pattern-Based Ontology as Intrinsic Self-Ordering
Embodied Mathematics After Lakoff & Nunez: A QNFO Perspective
This review examines Where Mathematics Comes From (Lakoff & Núñez, 2000) from the QNFO perspective, identifying convergence on anti-Platonism, the symbol-concept distinction, and critique of formalism. Extensions include ultrametric formalization of the four grounding metaphors and a cognitive…
Math is NOT the Universe
This report re-evaluates our Euclidean understanding of reality, showing its inadequacy for modern physics. It traces the shift from Newtonian absolute spacetime to Einstein’s curved spacetime and the scale-dependent complexities of fractal geometry and quantum theory. This analysis argues for a…
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