- Adelic Rate-Distortion Theory: The p-Adic Distortion Measure and the Adelic Information-Rate Function
The Adelic Shannon Theory [1] generalised channel capacity to the adele ring $\mathbb{A}_{\mathbb{Q}}$. The companion bridge paper [2] established that the entropic number $(x, S)$ from Measurement Stratigraphy [3] is precisely the adelic information vector $\mathbf{I}(X) = (I_\i
- Adelic Entropic Numbers: When the Adelic Information Vector Becomes the Entropic Number
Two papers, written independently on the same day, converge on the same structure from opposite directions. *Adelic Shannon Theory* [1] generalises Shannon information theory to the adele ring $\mathbb{A}_{\mathbb{Q}}$, defining the *adelic information vector* $\mathbf{I}(X) = (I
- Adelic Shannon Theory: From Problem Statement to Constructive Foundations
Standard Shannon theory — channel capacity, entropy, source coding, and the Gaussian noise model — is archimedean: it measures information in bits over $\mathbb{R}$. The Adelic Physics Programme's central claim — $\mathbb{Q}$, not $\mathbb{R}$, is the physically accessible base f
- The Adelic Physics Programme: Open Problems and Future Directions
- FACTORING, Adelic Complexity, and the Silent-Radix Principle
- FACTORING, Adelic Complexity, and the Silent-Radix Principle
- Poisson Summation as the Adelic Bridge
- The Adelic Physics Program: Epistemological Foundations and Communications Framework
The QNFO Adelic Physics Program proposes that the physically accessible base field of physics is Q (the rational numbers), not R (the real numbers). Ostrowskis theorem demands all p-adic completions of Q be physically meaningful. This paper provides the epistemological and pedago
- P-adic Spin, Information, and Ultrametric Internal Quantum Numbers
P-adic completions of Q encode discrete quantum numbers structurally via Bruhat-Tits geometry: p=2 gives spin, p=3 gives color charge. The Z2 invariant distinguishes Dirac from Majorana.
- Biophoton Ultrametricity: Consilient Synthesis of Cellular Light Emission with p-adic Error-Confinement and Adelic Measurement Theory
Nature recently reported (Marchant, 2026, Nature 655, 1116-1119) that all living organisms emit ultra-weak biophotons with evidence of cellular signalling. We propose a consilient synthesis: biophoton emission forms a biological instantiation of ultrametric measurement theory fro
- 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