-
The Harmonic Paradigm Under Ostrowski’s Theorem: A p-Adic/Adélic Re-Evaluation with Helical Compton Vortex Synthesis
Systematic Ostrowski-completion-theoretic audit of the Harmonic Paradigm V1.0-V4.0. Five findings: (1) Beta-function mechanism is infinity-place-specific -- Missarov (1989) confirms different universality class. (2) Q_p not ordered -- eliminates S-matrix, Noether, measurement. (3...
-
Ultrametric Quantum Computation and the Langlands Program
A unified thesis establishing ultrametric quantum computation on Bruhat-Tits trees as the physical substrate for the Langlands program, with Hecke operators as quantum gates and the adele ring as the natural spacetime.
-
Adelic Constraints on Quantum Field Theory—Phase 2 Synthesis
<p>Phase 2 subjected the Phase 1 findings to deeper epistemic scrutiny, guided by the “constants critique”: that no physical quantity can be natively transcendental, and that true physical observables must be rational cross-ratios. This critique proved correct. The Ph...
-
The Morita p-Adic Gamma Function: Computation, Adelic Structure, and the Factoring Question
<p>The Morita p-adic Gamma function $\Gamma_p(n) = (-1)^n \prod_{k=1,\,p \nmid k}^{n-1} k$ is a p-adic analytic object that interpolates factorials while explicitly skipping multiples of $p$. This document provides a self-contained exposition: the definition and functional equati...
-
Harmonic Analysis is Langlands — The Fast Fourier Transform as the Computational Langlands Correspondence for GL(1)
We identify the Fast Fourier Transform (FFT) as the computational Langlands correspondence for the general linear group GL(1). Harmonic analysis on the finite cyclic group Z/nZ decomposes functions into irreducible characters -- the FFT -- and this structure generalises directly ...
-
Noise-Augmented Silent Radix Encryption v2.3
We present Noise-Augmented Silent Radix Encryption (N-SRE), a key encapsulation mechanism that injects small p-adic errors into publicly transmitted envelope digits, formalizing the underlying hard problem as Hidden-Modulus Learning With Errors (HM-LWE).
-
Vanishing ZBW Signal: The ZBW-Majorana Hypothesis as a Unified Framework for Topological Fermion Distinction
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-theoret...
-
Adelic Langlands Physics — A Unified Framework Across All Completions of Q
The Adelic Langlands Physics (ALP) program establishes that **the Langlands Program is adelic physics without the physics**. Over five phases and 11 papers, we have shown: (1) At every completion $v$ of $\mathbb{Q}$, the fusion ring of a quantum group $C(\mathrm{SU}(n_v))_{k_v}$ ...
-
Hidden-Radix Cryptography and Post-Quantum Cryptography: A Comparative Analysis
A systematic comparison between hidden-radix cryptography (schemes where the numerical base or completion is kept secret) and modern post-quantum cryptography (PQC). Traces the evolution from naive base-change cipher through Silent Radix Encryption to p-adic/idèlic constructions....
-
Measure-Theoretic Artifacts of the Archimedean Place — v2.0: The Completion Problem, the Langlands Connection, and the Adelic Restructuring of Fundamental Physics
Ostrowski's theorem partitions all non-trivial completions of $\mathbb{Q}$ into exactly one Archimedean completion ($\mathbb{R}$, the $\infty$-place) and infinitely many non-Archimedean completions ($\mathbb{Q}_p$ for each prime $p$). These topologies are mutually singular — no s...
-
Tate's Thesis as a Template for Adelic Quantum Mechanics: Local-Global Structure and the Emergence of Archimedean Artifacts
We propose that Tates 1950 thesis provides an explicit structural template for constructing adelic quantum mechanics. The Dragovich programme has realized this template for free theories; Huang, Stoica, and Zhong (2022) provide an independent proof-of-concept in CFT. We interpret...
-
Zitterbewegung: From Archimedean Puzzle to Adelic Observable
The structural underdetermination of the position operator in relativistic quantum mechanics arises from a single representation-theoretic origin: the Silent Parameter Principle. SU(2) and Z2^x share identical fusion rules at matching levels. The 2-adic ZBW frequency deviates fro...
-
Measure-Theoretic Artifacts of the Archimedean Place: A Complete Taxonomy and the Adelic Restructuring of Fundamental Science
Ostrowski theorem partitions all non-trivial completions of Q into exactly one Archimedean completion and infinitely many non-Archimedean completions. Physics operates exclusively at the Archimedean place. Catalogues measure-theoretic artifacts across 5 categories with 16 complet...
-
Five Pillars, One Structure: Consilient Convergence in QNFO Research
Five independent QNFO research programs converge on a single structural insight: ultrametric (non-Archimedean) mathematics provides the correct state-space geometry for fundamental physics, quantum computation, and optimization.
-
The Adelic Cross-Domain Program: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat-Tits Trees
-
The Adelic Physics Program: A Grand Synthesis
2026-07-24
Number Theory
The Adelic Physics Program: A Grand Synthesis
-
Number-Theoretic Ultrametric Foundations: A Unified p-adic Framework for Error-Correcting Code Classification
2026-07-24
Number Theory
License: QNFO Unified License Agreement (QNFO-ULA)
-
Adelic Particle Spectrum: Alpha pi Mass as Projections
Extension of adelic harmonic oscillator to particle mass spectrum.
-
α-π-Helix: Geometric Unification of Fundamental Constants
Geometric unification of fundamental constants using α (fine-structure) and π (geometric) helix structures, classifying Standard Model particles as topological vortex/helicon states. v2.1 — Phase 10 complete with 6-domain synthesis including experimental roadmap, cosmology, mathe...
-
The Adelic Completion of the Harmonic Paradigm: A Five-Pillar Red-Team Assessment
The Harmonic Paradigm (V1.0-V4.0, 2026) proposed the harmonic oscillator as the universal IR attractor of quantum theory, with an 8-rung ladder spanning from transmon anharmonicity to quantum gravity. Its bibliography invoked Ostrowski's theorem and p-adic structures, yet its cor...
-
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.
-
Master Work Plan v2.0 — Cross-Domain Phase X1-X6
Cross-domain phase of the Master Research Work Plan v2.0, defining 6 avenues (X1-X6) bridging Adelic, Compton, and Harmonic domains. Informed by RG-Harmonic synthesis. 16 total calibration entries (10 from synthesis + 6 new).
-
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 app...
-
Compton Frequency Cross-Ratios on Bruhat-Tits Trees: Pre-Registered Search for Adelic Structure (Version 2.2, Corrected)
Corrected analysis with physically-constrained anharmonic oscillator model. Prior v2.1 phantom claim retracted (degenerate tautology: omega_0=1, alpha=0). v2.2 constrains anharmonicity to transmon regime (alpha_r in [0.01,0.05]) with surrogate-data null model. Result: anharmonic-...
-
Compton Frequency Cross-Ratios on Bruhat-Tits Trees: A Pre-Registered Search for Adelic Structure in the Standard Model Mass Spectrum (Version 2.0)
Pre-registered analysis of Compton-frequency cross-ratios on Bruhat-Tits trees. Five cross-ratios tested at three primes (p=2,3,5) for p-adic valuation structure. Two approximate rationals found (976/919 and 430/419) at precision marginally better than Dirichlet guarantee. Honest...