Open research library
Papers you can read, cite and question
728 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.
Looking for an answer rather than a paper? Ask the whole corpus: answers cite the papers they come from.
Results for “p-adic” 37 papers
Geometric Ratios as Generators of Hierarchical Structure: An Arithmetic Audit of π, φ, and e
A recurring conjecture in the ultrametric-physics program holds that hierarchical—i.e., ultrametric—structure "emerges" when a scale ratio q is set equal to a fundamental geometric constant: π, the golden ratio φ = (1+√5)/2, or Euler's number e. This paper converts that conjecture into falsifiable…
Optimal Radix q under Resource Constraints: A Reconciled Derivation Framework for Ultrametric Hierarchies
Hierarchical (ultrametric) representations organize N items in a q-ary tree of depth n = ⌈ln N / ln q⌉, and the choice of branching factor q determines how storage, interconnection, and traversal resources scale. Prior ultrametric modeling has treated the radix as a fixed structural parameter…
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…
Why Vertices, Not Points? Vertex-Anchored Braiding, Stabilizer Arithmetic, and Displacement Gaps on Bruhat–Tits Buildings
Bruhat–Tits buildings are the canonical combinatorial-geometric objects attached to reductive groups over non-Archimedean local fields, and the recent QNFO constructions of p-adic braid groups [12], p-adic anyon models [13], and a p-adic Temperley–Lieb parameter [14] anchor their discrete braiding…
The Corrected Primon-Gas Dictionary: Zeta Partition Functions and the Discipline of Arithmetic Interpretations
The primon gas has connected quantum statistical mechanics with multiplicative number theory since the early 1990s and remains in active use. This paper consolidates the correspondence into a single audited reference: a corrected, verified dictionary; a five-level ladder separating mathematical…
Discriminating the Arithmetic Cut: Matched-Level-Density Null Models for the Primon-Gas Specific Heat and Spectral Correlations
The arithmetic-statistics program reads the two exchange statistics of identical particles as two multiplicity rules on one integer lattice, and its published observable is the specific heat of the primon gas: a computable deviation from the smooth ideal gas at every sampled temperature. The…
The Distinction-Based Ultrametric: A Hierarchy Distance Without Primes, and the Statistical Test of Arithmetic Structure in Physical Spectra
Quantum mechanics is written in one completion of the rational numbers, the real line, though Ostrowski's theorem gives one completion for every prime. A line of work reads physical structure through those other places, but its empirical tests of prime-specific geometry in physical systems have…
Adelic Quantum Arithmetic: Particles as Prime Factors
Standard quantum mechanics is written in the Archimedean completion of the rational numbers: Hilbert space over the complex numbers uses only the real place, one among all completions classified by Ostrowski's theorem. The primes are the other places, and their structure is multiplicative — unique…
Completeness Senses and the Levi-Civita Field: Ordered Non-Archimedean Number Systems Beyond Ostrowski's Classification
Ostrowski's theorem classifies every nontrivial rank-1 absolute value on the rationals: the Archimedean absolute value and, for each prime p, a p-adic absolute value. Their completions are the real numbers and the p-adic fields. This classification is often read as closing the question of what a…
The Ultrametric Program: One Structural Object Across Seven Research Domains, and Its Falsifiable Tests
Seven research domains — ultrametric physics, the laws of form, infomatics, paradigm engineering, consilience research, a cloud-native platform, and interactive demos — are claimed to be seven vocabularies for one structural object: a nested, hierarchical partition logic. The object is defined by…
The Self-Referential Scalar Family: e, the Half-Turn, and the Unification of Information Theory, Statistics, Thermodynamics, and QND Measurement in the Adelic Picture
Standard information theory measures uncertainty at the archimedean place; the adelic program extends it to all completions of the rationals, carrying a p-adic valuation entropy alongside Shannon entropy. This paper shows that the two most familiar distributions of statistical mechanics are already…
One Table, Two Regimes: Standard-Model Particles and Condensed-Matter Excitations as Patterns on the Bruhat-Tits Tree
Physics currently maintains two particle catalogs that never meet in one framework: the Standard Model's finite table of elementary fermions and bosons, and the open-ended zoo of quasiparticles and anyons that condensed matter discovers in every new material. This paper assembles both catalogs into…
The Trapped-Ion Ultrametric Testbed: A Falsifiability Register for Testing p-Adic Structure in Quantum Dynamics
Twenty-one published records from a single research program, spanning December 2025 to August 2026, are here organized into one testable claim: trapped-ion quantum simulators are the first near-term platform on which ultrametric (p-adic) structure in quantum dynamics can be accepted or rejected by…
Non-Archimedean Projective Perspective: The Monna Map as a Visual Rendering Interface
Things farther away appear smaller, and two-point linear perspective is taken to approximate the eye. That entire phenomenology is Archimedean geometry. This paper asks what changes if the metric of physical space were instead non-Archimedean and ultrametric — would we perceive the same thing, and…
Prime Valuation Depth: Multiplication as Branching, the Calculus of Indications, and the Structural No-Cloning Reading
This paper develops a structural reading of the p-adic valuation as a measure of depth along a prime branch of the integer factorization tree, rather than a measure of size. The reading, grounded in Ostrowski's classification of absolute values on the rationals, is proposed as a bridge between the…
Boundary Ultrametricity: The Tree vs. ∂∞𝒯 Distinction, Applied to the ZBW Transition Graph
The QNFO corpus frequently conflates two distinct mathematical properties of trees: 0-hyperbolicity (of the vertex/graph metric) and ultrametricity (of the boundary metric). This note formalizes the distinction, proves the boundary Gromov-product metric on…
Ultrametric Consilience Atlas: Cross-Domain Applications of p-Adic Mathematical Structure
A single mathematical structure — the p-adic ultrametric topology — appears in apparently unrelated domains: quantum error correction (stabilizer codes), protein folding (energy landscapes), neural coding (population activity clustering), financial markets (hierarchical correlation), climate…
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 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 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 ($\\mathbb{R}$_comp),…
P-adic Spin, Information, and Ultrametric Internal Quantum Numbers
Paper I established that the Archimedean continuum the real numbers_c suffices for all physical dynamics — depth without breadth. Here we complete the picture: what of the ultrametric completions of the rational numbers? We argue that the p-adic numbers the rational numbers_p are not "extra spatial…
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 equation, a computational…
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 sequence converges…
Measure-Theoretic Artifacts of the Archimedean Place: A Complete Taxonomy and the Adelic Restructuring of Fundamental Science
Ostrowski's theorem partitions all non-trivial completions of ℚ into exactly one Archimedean completion (ℝ, the ∞-place) and infinitely many non-Archimedean completions (ℚₚ for each prime p). These topologies are mutually singular — no sequence converges simultaneously in ℝ and any ℚₚ. Physics, as…
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…
Non-Anthropocentric Natural Units: From the Bekenstein Bound to Ostrowski's Theorem
The Bekenstein-Hawking entropy bound $S \leq A/4\ell_P^2$ is a pillar of quantum gravity, typically expressed in Planck units with entropy measured in bits or nats. We ask: what remains of this bound when ALL anthropocentric constructions are stripped away — unit choices, logarithmic bases, and even…
The p-Adic Temperley-Lieb Parameter: Cyclotomic Units, Markov Traces, and the p-Adic Jones Polynomial
In Phase 1, we defined the p-adic braid group $B_n(\mathbb{Q}_p)$ on the Bruhat-Tits tree $\mathcal{T}_p$ and showed it satisfies the standard braid relations. Here we complete the connection to the Temperley-Lieb algebra and the Jones polynomial at non-archimedean places. The TL algebra parameter…
p-Adic Braid Groups on Bruhat-Tits Buildings
The standard braid group $B_n$ is defined as the fundamental group of the configuration space of $n$ distinct points in $\mathbb{R}^2$, $\pi_1(\text{Conf}_n(\mathbb{R}^2))$. This construction is inherently archimedean: it relies on the continuous topology of $\mathbb{R}^2$ to define braiding as…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection
The Zitterbewegung (ZBW) of a Dirac fermion — the rapid oscillatory motion at the Compton frequency arising from interference between positive- and negative-energy states — has resisted direct experimental observation for nearly a century. The standard interpretation attributes this to the Compton…
Number-Theoretic Ultrametric Foundations: A Unified p-adic Framework for Error-Correcting Code Classification
We present a unified framework connecting deep number-theoretic structures — $p$-adic valuation theory, Mahler spectral expansions, Kodaira-Néron fiber classification, and the Amice transform — to the classification of quantum error-correcting codes. The framework is organized into seven…
The Bridge Theorem: A Rigorous Mathematical Framework Connecting p-adic and Bruhat-Tits Geometries
We prove that under a global constraint of the form $\hat{H}|\Psi\rangle = 0$ (the Wheeler-DeWitt equation), conditional quantum states produced by the Page-Wootters mechanism $|\psi(\tau)\rangle_R = \langle\tau|_C |\Psi\rangle_{CR}$ naturally organize into an ultrametric hierarchy. The proof…
Radix to Ultrametrics to Page-Wootters to Wheeler-DeWitt to Bruhat-Tits: A Convergent Synthesis
Convergent synthesis bridging discrete p-adic ultrametrics with continuous quantum geometry via Page-Wootters, Wheeler-DeWitt, and Bruhat-Tits buildings.
Bruhat-Tits Tree as a Unifying Geometric Object
Modern artificial intelligence, particularly in high-stakes domains, is hampered by a fundamental geometric mismatch: the reliance on continuous, “flat” Euclidean spaces to represent intrinsically hierarchical data. This incongruity leads to information loss and the proliferation of opaque “black…
Computational Toolkit for p-Adic Spacetime
The fundamental incompatibility between the continuous manifolds of general relativity and the discrete nature of quantum mechanics remains a central tension in theoretical physics. This manuscript develops and validates a computational toolkit designed to test theories of p-adic spacetime, which…
Functional Decoupling Framework for p-adic Hamiltonian Models of Granular Field Interactions
The reconciliation of continuous temporal evolution with discrete physical granularity remains a central challenge in theoretical physics, requiring novel mathematical approaches to model localized action within unbroken fields. This study introduces a functional decoupling framework that divides…
Spectral Analysis of Anomalous Diffusion on p-Adic Fractals
The reconcilement of continuous Riemannian geometry with the discrete arithmetic of the integers remains one of the most profound challenges in mathematical physics, particularly regarding the spectral interpretation of the Riemann zeros (Berry & Keating, 1999). While standard diffusion on…
Spectral Dynamics on Bruhat-Tits Trees
The probabilistic nature of prevalent primality tests, such as Miller-Rabin, presents a fundamental limitation where certainty is achieved only asymptotically. This study proposes a deterministic alternative rooted in the non-Archimedean geometry of p-adic numbers, specifically leveraging the…
New papers by email
One short weekly digest: titles and links. No tracking; unsubscribe any time.