- 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* $\mathbf{I}(X) = (I
- The History and Future of Measurement Stratigraphy, Number Theory, and Valuation Theory
[We propose a unified framework — the Stratigraphy of Measurement — that reinterprets the history of number systems as a sequence of expanding distinction operations. Each era adds a new enclosure: marking ($\\mathbb{N}$), comparing ratios ($\\mathbb{Q}$), convergent sequences ($
- p-Adic QEC Classifier Verification: A Computational Methodology
- 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
- A Falsifiability Protocol for the Q-Fundamental Hypothesis
- FACTORING, Adelic Complexity, and the Silent-Radix Principle
- FACTORING, Adelic Complexity, and the Silent-Radix Principle
- The Continuum Critique Trilogy
- Poisson Summation as the Adelic Bridge
- Alpha as Bifurcation Parameter: The Helical Electron Stability Problem
- The Notation Problem: Category-Theoretic Scaffold-Stripping of Six Marginalised Formal Systems
Six formal systems share a common fate: despite containing mathematical insights, they remain intellectually marginalised. We propose the scaffold-stripping hypothesis.
- 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
- Depth, Breadth, and Valuation: A Unified Ontology of the Physical Continuum
Three-axis framework: Depth (computable reals), Breadth (non-computable reals — physically vacuous), Valuation (p-adic completions as information carriers). Falsifiable predications for QEC, gauge structure.
- 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.
- The Computable Continuum: Depth Without Breadth
The uncountability of the real numbers conflates Archimedean completeness (depth) and set-theoretic cardinality explosion (breadth). All physically relevant properties are preserved by computable reals.
- A Consilient Gap Synthesis of the QNFO/QWAV Research Portfolio
The QNFO/QWAV research ecosystem has grown to 95 projects, 3,109 Knowledge Graph nodes, 1,502 edges, 917 papers in D1 living-paper, and 25 tracked OpenItems. At this scale, the set of unresolved gaps — deferred publications, stalled phases, missing cross-references, unregistered
- The ℚ-vs-ℝ Question: Why Physical Law Requires Only the Rational Numbers
- The Computable Real Boundary: Where Physics Ends and Cognitive Fiction Begins
Every experiment reduces to a finite act of distinction: this reading, not that; this frequency range, not that; this bit string, not its negation. Physics is, at its operational core, a discipline of finite distinguishability. Yet the mathematical architecture physics inherited
- 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
- Finite Specification, Ontological Indeterminism: The Gisin–Del Santo Program Converges with Autaxys Ontological Closure
We examine the Gisin--Del Santo program on finite-precision physics and its convergence with the Autaxys Ontological Closure (OC) framework. The Gisin--Del Santo program argues that (1) physical quantities contain only finite information, (2) real numbers are physically unreal --
- QWAV Commercial Platform: Strategic Architecture Whitepaper
Comprehensive strategic architecture whitepaper for the QWAV next-generation computing platform. Defines the formal boundary between QNFO and QWAV, articulates the commercial value proposition centered on the Joules-per-Solution (JPCUB) benchmark metric, and provides an 18-month
- 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
- Adelic Quantum Error Correction: A Synthesis Across All Primes v1.0.0
- Adelic Quantum Error Correction: Code Constructions Beyond the Stabilizer Formalism
Adelic generalization of Heydeman holographic QEC. v0.1.1 adds professionally rendered PDF.
- 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
- HM-LWE v3.0
Hidden-modulus LWE: novel hardness assumption
- The Joules-per-Solution Metric: Definition, Measurement Protocol, and Anti-Gaming Provisions for Honest Computational Benchmarking
We define and formalize the joules-per-solution (J/S) metric as a universal, cross-domain measure of computational energy efficiency. The metric accounts for six energy components: computation, memory, I/O, cooling, power conversion, and amortized manufacturing. We provide a clos
- The BQNN Classical Baseline: Constructive Falsification of Near-Term Quantum Advantage at a Fifteen-Million-to-One Energy Disadvantage
Classical BinaryConnect ensemble achieves 92.73% accuracy vs BQNN quantum inference (~82-85%) at 0.0365 J vs 550,000 J (ratio 1.5x10^7). CAL-BQNN-05 confirmed one year early.
- 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
- Consilience Between Physics and Number Theory: Convergent Theses from Ostrowski's Theorem to Adelic Quantum Mechanics
We synthesize convergent evidence from physics (quantum mechanics, quantum field theory, zitterbewegung, quantum error correction, the Standard Model mass spectrum) and number theory (Ostrowski's theorem, Tate's thesis, the Riemann zeta function, Bruhat-Tits buildings, the adele
- 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
- Vanishing ZBW Signal: The ZBW-Majorana Hypothesis as a Unified Framework for Topological Fermion Distinction
The ZBW-Majorana hypothesis establishes that Zitterbewegung is a Z2 topological observable distinguishing Dirac from Majorana fermions. This capstone paper synthesises six central claims including vanishing ZBW signal, Z2 invariant, topological protection, Bruhat-Tits geometry, e
- Consilience Between Physics and Number Theory: Convergent Theses from Ostrowski's Theorem to Adelic Quantum Mechanics
We synthesize convergent evidence from physics (quantum mechanics, quantum field theory, zitterbewegung, quantum error correction, the Standard Model mass spectrum) and number theory (Ostrowski's theorem, Tate's thesis, the Riemann zeta function, Bruhat-Tits buildings, the adele
- 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
- Vanishing ZBW Signal: The ZBW-Majorana Hypothesis as a Unified Framework for Topological Fermion Distinction
The ZBW-Majorana hypothesis, developed across four companion papers (P1--P4), establishes that Zitterbewegung (ZBW) --- the rapid trembling motion of Dirac fermions at the Compton scale --- is a $\mathbb{Z}_2$ topological observable that distinguishes Dirac from Majorana fermions
- Auditing the BQNN: Does a Tunable Quantum Neural Network on Trapped-Ion and Superconducting Hardware Demonstrate a Route to Near-Term Quantum Advantage?
We audit the BQNN paper by Lakhdar-Hamina et al. (2025, PRL / arXiv:2507.21222v2) which implements a tunable quantum neural network on three quantum computing platforms. Through a complete Phase 1-4 research pipeline including due diligence, external literature search across 32 p
- 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
- Holographic QEC as AdS/CFT RG Flow on Bruhat–Tits Trees
Tasks X3.1 and X3.2 established bosonic QEC as RG fixed-point subspaces on Bruhat–Tits trees. Task X3.3 completes the trilogy by showing that this structure is holographic: the Bruhat–Tits tree $\mathcal{T}_p$ is the $p$-adic analog of anti-de Sitter space, tensor networks on $\m
- PQS AI-Evaluation Audit: Post-Quantum Synthesis Investigation and AI Gate-Check Analysis
Archive of the complete research record investigating the Post-Quantum Synthesis (PQS) framework: a neutral investigation of PQS's four sub-pillars mapped against external literature, plus an earlier-iteration analysis of AI gate-check convergence between Claude and Gemini evalua