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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 19 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.
Adelic. Adeles, restricted products and adelic constructions Tagged papers: 38.
Functoriality as a Transform: Register and Gate-Cost Analysis of a Langlands-Structured Adelic Quantum Register
Computing with automorphic representations is bottlenecked by the absence of a fast algorithm for non-abelian harmonic analysis: for the abelian group $\mathrm{GL}(1)$ the Fast Fourier Transform decomposes functions into irreducible characters in $O(n \log n)$ operations, while for…
The p-Adic Temperley–Lieb Parameter: Valuation-Theoretic Constraints and an Adelic Accuracy Framework for Quantum Predictions
The Temperley–Lieb (TL) algebra governs a broad class of exactly solvable quantum systems, from anyonic chains to braid-based teleportation circuits, through its scalar loop parameter δ. We investigate the proposal that a p-adic Temperley–Lieb parameter — a number-theoretic functional of δ — can…
Quantum Statistics from the Adelic Product Formula: The Squarefree Origin of the Fermi-Dirac/Bose-Einstein Distinction
The Bose-Einstein and Fermi-Dirac occupation distributions are read as the maximum-entropy solutions of one lattice with two multiplicity rules: the unrestricted integer lattice (Dirichlet series the Riemann zeta function) and the squarefree restriction (a ratio of two zeta values). The paper…
The Self-Referential Scalar Family: e, the Half-Turn, and the Unification of Information Theory, Statistics, Thermodynamics, and QND Measurement in the Adelic Picture
The p-adic maximum-entropy distribution of Adelic Shannon Theory is exactly the Bose-Einstein occupation distribution at fugacity 1/p, i.e. at inverse temperature ln p at the p-adic place; the squarefree restriction of the integers is its Fermi-Dirac counterpart, with occupation probability 1/(p+1)…
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…
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…
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 field — suggests that…
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…
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 the Langlands…
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 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 core mechanisms were…
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…
Adelic Constraints on Quantum Field Theory — Phase 3 Synthesis
<p>Phase 3 of the Adelic Constraints on Quantum Field Theory project investigated the central open question left by Phase 2: Does the adelic framework make a falsifiable numerical prediction that differs from the Standard Model? The specific target was the suggestive coincidence discovered in Phase…
Adelic Constraints on Quantum Field Theory: Phase 1
<p>This project set out to answer a question that had lingered at the edges of theoretical physics for nearly four decades: does the adelic completion of the rational numbers constrain the values of fundamental physical constants? The question traces back to a theorem discovered by Alexander…
The Adelic Constraints Project — A Complete Account
<p></p> <p>This document is a complete, self-contained account of a research project conducted in May 2026. The project asked whether a specific piece of pure mathematics — the fact that the rational numbers can be "completed" in multiple incompatible ways, and that a single identity links all…
The Decryption Key: Cognitive Architecture as the Hidden Radix of Physical Measurement
Traces each SI base unit to a specific feature of human cognitive architecture. Proposes the adelic product formula as genuinely observer-independent invariant. Sixth Pillar of QNFO Grand Synthesis.
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…
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…
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