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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 21 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.
Bruhat–Tits trees. Bruhat-Tits trees used as the model space Tagged papers: 43.
Joint Bruhat–Tits Tree Product as a Candidate Universal Structure for Standard Model Mass Ratios, Quantum Error-Correction Lattices, and Efimov Scaling: Formalization, Arithmetic Consequences, and a Partial Falsification
The Standard Model (SM) treats particle masses as free parameters, quantum-error-correction (QEC) lattice designs are chosen by heuristic optimization, and the Efimov discrete scaling factor lacks a structural explanation; a single mathematical object generating all three would change how each…
Time as Bruhat-Tits Tree Depth: Discrete $p$-Adic Temporal Ordering and Tree-Geodesic Causality
We develop a conjectural but internally precise model in which physical time is not a continuous real parameter but a discrete depth coordinate on a Bruhat-Tits tree: an event is a vertex of a rooted $(p+1)$-regular tree, and its time is the integer depth $d\in\mathbb{N}$, identified conjecturally…
Zitterbewegung as a $p$-Adic Ultrametric Observable: A $\mathbb{Z}_2$ Invariant on the Bruhat–Tits Tree, Its Readout, and Its Non-Additivity Signature
Zitterbewegung (ZBW) — the Compton-frequency trembling of Dirac wave packets — is conventionally modeled as an Archimedean interference oscillation between positive- and negative-energy branches. We develop a conjectural alternative in which the ZBW readout is ultrametric: the observable lives on a…
Spectral Decomposition of the Bruhat–Tits Tree as a Candidate Origin of Particle Mass Hierarchies: Exact Radial Spectrum, Finite Truncations, Semigroup Tests, and a Falsification Analysis
The Bruhat–Tits tree $\mathcal{T}_p$ of $\mathbb{Q}_p$ is the infinite $(p+1)$-regular tree that serves as the bulk of $p$-adic AdS/CFT. We test the conjecture that a natural Laplacian on $\mathcal{T}_p$ — or the prime-indexed arithmetic of the tree — encodes Standard Model mass ratios. We compute,…
Why Vertices, Not Points? Vertex-Anchored Braiding, Stabilizer Arithmetic, and Displacement Gaps on Bruhat–Tits Buildings
Bruhat–Tits buildings are the canonical combinatorial-geometric objects attached to reductive groups over non-Archimedean local fields, and the recent QNFO constructions of p-adic braid groups [12], p-adic anyon models [13], and a p-adic Temperley–Lieb parameter [14] anchor their discrete braiding…
One Table, Two Regimes: Standard-Model Particles and Condensed-Matter Excitations as Patterns on the Bruhat-Tits Tree
Physics maintains two particle catalogs that never meet in one framework: the Standard Model's finite table of elementary fermions and bosons, and the open-ended zoo of quasiparticles and anyons discovered in condensed matter. This paper assembles both catalogs into a single pattern table on the…
The Adelic Cross-Domain Program: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat-Tits Trees
v3.2 corrections (2026-07-25): arithmetic errors in mass ratio triplets corrected (5 of 9 verified independently); Efimov lambda derivation replaced with honest structural correspondence; constraining literature section added per KIF-18 symmetry; semigroup density epistemological risk acknowledged;…
The Adelic ZBW Programme: ZBW-Majorana Hypothesis, Ostrowski-QEC Synthesis, and Cross-Programme Consilience
The structural underdetermination of the position operator in relativistic quantum mechanics -- manifested at the Archimedean place as zitterbewegung (the Newton-Wigner no-go) and at p-adic places as a discrete Bruhat-Tits observable -- arises from a single representation-theoretic origin: the…
The Adelic Cross-Domain Program v5.0: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat–Tits Trees
The Adelic Cross-Domain Program maps the architecture of the Standard Model onto the geometry of Bruhat–Tits trees — the p-adic analogues of hyperbolic space. The fine-structure constant α, the renormalization group, quantum error correction, the Efimov effect, and the Standard Model mass spectrum…
The Adelic Cross-Domain Program: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat-Tits Trees (Phase 3-4 Update)
Cross-Domain Phase 2 synthesis paper uniting six avenues (X1-X6). Key result: the Pythagorean semigroup P={2^a·3^b·5^c} is simultaneously the SM mass spectrum, GKP code lattice, Efimov discretuum, and diagonal embedding of T_{2,3,5}. Full calibration register with 15 entries.
Compton Frequency Cross-Ratios on Bruhat-Tits Trees: A Pre-Registered Search for Adelic Structure in the Standard Model Mass Spectrum (Version 2.3)
Version 1.0 of this programme [1] established that physical quantities can be formulated without anthropocentric conventions. Its extension into an "Adelic Theory of Everything" [2] attempted to match Standard Model particle masses to CM j-invariants via decimal PDG data — an approach we now…
Fine-Structure Constant as a Cross-Ratio: A Geometric Reframing of α
The fine-structure constant alpha is reframed as the cross-ratio of two measurable electron length scales (classical radius / Compton wavelength). Version 1.0 adds the adelically extended cross-ratio on Bruhat-Tits buildings, explicit falsifiability conditions, and synthesis with the QNFO adelic…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection
Formulates Zitterbewegung as a p-adic topological observable. Establishes that the ZBW current J_mu_ZBW carries a Z_2 invariant encoding the Dirac/Majorana distinction, and proposes ultrametric readout protocols via Bruhat-Tits buildings.
p-Adic Braid Groups on Bruhat-Tits Buildings
Constructs p-adic braid groups on Bruhat-Tits buildings, establishing the geometry of discrete braiding.
Bruhat-Tits Tree as a Unifying Geometric Object
Modern artificial intelligence, particularly in high-stakes domains, is hampered by a fundamental geometric mismatch: the reliance on continuous, “flat” Euclidean spaces to represent intrinsically hierarchical data. This incongruity leads to information loss and the proliferation of opaque “black…
Spectral Dynamics on Bruhat-Tits Trees
The probabilistic nature of prevalent primality tests, such as Miller-Rabin, presents a fundamental limitation where certainty is achieved only asymptotically. This study proposes a deterministic alternative rooted in the non-Archimedean geometry of p-adic numbers, specifically leveraging the…
Formal Derivation of Emergent Spacetime to the Bruhat-Tits Tree
The fundamental incompatibility between the continuous spacetime of general relativity and the background-dependent time of quantum mechanics suggests that time is not a fundamental constituent of reality. This paper addresses the ontological crisis of time by formally deriving macroscopic spacetime…
Adelic Cross‑Ratio
Every quantitative description of the physical world relies on a choice of coordinate system—a language with its own scales, units, origin, and orientation. The same underlying reality can be expressed in infinitely many such languages, each assigning different numerical coordinates to the same…
Universe as Self-Proving Theorem
This document establishes a Geometric Unification Framework positing that the universe is a self-proving theorem, where physical laws and fundamental constants emerge as necessary consequences of its inherent logical and geometric consistency. The framework employs category theory as its…
The Bridge Theorem: A Rigorous Mathematical Framework Connecting p-adic and Bruhat-Tits Geometries
A rigorous mathematical framework establishing bridge connections between p-adic ultrametric spaces and Bruhat-Tits buildings.
Radix to Ultrametrics to Page-Wootters to Wheeler-DeWitt to Bruhat-Tits: A Convergent Synthesis
Convergent synthesis bridging discrete p-adic ultrametrics with continuous quantum geometry via Page-Wootters, Wheeler-DeWitt, and Bruhat-Tits buildings.
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