- The Compton-Counting Ontology and the Bruhat-Tits Tree
The Compton frequency of a particle, normalized by the Planck frequency, yields a dimensionless rational number --- the Compton count. We argue that this count subsumes every other physical quantity as a rational function, that the physical number system is therefore [\\(\\mathbb
- The Ostrowski Dimensionless Reformulation: A Systematic Compilation of Fundamental Physics Equations in Planck Units
Systematic compilation and dimensionless reformulation of 53 fundamental physics equations across ten disciplines, motivated by the Ostrowski Dimensionless Mandate. Dimensional formulations implicitly privilege the Archimedean completion of the rationals per Ostrowski theorem (19
- The Valuation Reading of the Qubit Delusion: Is the Adelic Kernel Load-Bearing?
The Qubit Delusion (DOI 10.5281/zenodo.21254143) argues that the qubit-gate-circuit model of quantum computation imports a particle ontology inconsistent with quantum field theory, and that the field's failure to deliver commercially viable hardware after $35 billion of investmen
- Passive Error Resilience Through Ultrametric Geometry: A Proposal for p-Adic Quantum Metrology
- Autaxys Ontological Closure: When Is a Physical Quantity Computationally Real?
We propose an operational criterion for physical reality: a quantity is physically real only if there exists a finite Turing-machine protocol that approximates it with a computable modulus of convergence, yielding measurement-distinguishable predictions. This criterion is not a m
- When Will Non-Archimedean Geometry Displace the Real Numbers? A Structured Assessment of the Adelic Substrate Thesis
The real numbers are the default continuum for physical modeling — every quantum state lives in a Hilbert space over $\mathbb{C}$, every neural network optimizes over $\mathbb{R}^n$, every error-correcting code is designed with Euclidean distance. Yet Ostrowski's theorem (1916) d
- Information-theoretic Limits on Programmatic Specification of Biological Systems
Shows via information theory that an organism does not contain enough organism-specific information to specify its own microscopic organization. The genome is a generator specification (not trajectory program). Establishes coarse-graining threshold with dual Hartley/Shannon entro
- Extending v_p^max Code Classification: Testing the Mahler Spectral Conjecture on Additional Stabilizer Code Families
ACRP-06: Tests UF paper C7.3 on 8 additional codes. Golay CSS confirmed v_p^max=28; all other stabilizer codes cluster at random baseline (1-6). C7.3 bound to Golay-type self-dual codes.
- Composite-Radix Theory: Characterizing the Kernel Membership of Silent Radix Encryption
ACRP-03: Strong triangle SURVIVES composite b, multiplicativity FAILS. PUK vs OAK hierarchy.
- The Substrate Is the Algorithm: A Categorical Formalization of the Strongest Consilience Thread
ACRP-05: Thread 3 formalization. Capability(S) ~ End(X_S) conjecture; five-pillar verification; Church-Turing-scoped resource-level thesis (computability-level equivalence, resource-level difference).
- Boundary Ultrametricity: The Tree vs. ∂∞𝒯 Distinction, Applied to the ZBW Transition Graph
ACRP-02 formal note. Boundary Gromov metric on dT_p is ultrametric and recovers |.|_p; tree vertex metric is NOT ultrametric. ZBW P1 Claim C2 corrected: 0-hyperbolic core, not ultrametric core (147/500 violations per paper data).
- Statistical Audit of the 5-Smooth Semigroup Mass-Ratio Claim
ACRP-04 statistical audit. Verdict: CONSISTENT WITH LOOK-ELSEWHERE ARTIFACT. p_global=0.116; 2 claimed-fit arithmetic errors; 5 non-optimal triples; precise ratios deviate 4-9138 sigma; pre-registered neutrino prediction trivially passes.
- QNFO Consilient Synthesis v2.0: The Shared Adelic Kernel
QNFO Consilient Synthesis v2.0: the shared adelic kernel (valuation → tree boundary → Ostrowski → adeles). Applies all 7 corrections (C1–C7) from the 2026-07-25 red-team audit, restructured kernel-first with honest kernel-membership table and mandatory symmetry sections.
- 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
- Ultrametric Consilience Atlas: Cross-Domain Applications of p-Adic Mathematical Structure
- The QWAV Decade: Enterprise p-Adic Computing 2025-2035
- Counterfactual Physics: What If p-Adic Methods Had Won?
- Computing After Silicon: A History-Constrained Forecast of Computing Machine Evolution, 2026-2050
A history-constrained forecast of computing machine evolution 2026-2050. Seven post-silicon candidates assessed; heterogeneous convergence (AI accelerators, quantum co-processors, processing-in-memory) is the central thesis; twelve dated falsifiable predictions registered for 203
- Five Pillars, One Framework: A Cross-Domain Audit of the Ruliad, Autaxys QC, and Measurement Stratigraphy
A cross-domain synthesis examining the physical-adjacent information-theoretic programme through Measurement Stratigraphy v2.1 and the Ruliad framework.
- 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