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Numbers & p-adics papers 23 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.
p-adic. p-adic numbers and valuation-driven models Tagged papers: 53.
Time as Bruhat-Tits Tree Depth: Discrete $p$-Adic Temporal Ordering and Tree-Geodesic Causality
We develop a conjectural but internally precise model in which physical time is not a continuous real parameter but a discrete depth coordinate on a Bruhat-Tits tree: an event is a vertex of a rooted $(p+1)$-regular tree, and its time is the integer depth $d\in\mathbb{N}$, identified conjecturally…
Zitterbewegung as a $p$-Adic Ultrametric Observable: A $\mathbb{Z}_2$ Invariant on the Bruhat–Tits Tree, Its Readout, and Its Non-Additivity Signature
Zitterbewegung (ZBW) — the Compton-frequency trembling of Dirac wave packets — is conventionally modeled as an Archimedean interference oscillation between positive- and negative-energy branches. We develop a conjectural alternative in which the ZBW readout is ultrametric: the observable lives on a…
Is There a $p$-Adic $\pi$? Haar-Measure Circle Constants over $\mathbb{Q}_p$ and an Adelic Product Formula
The real number $\pi \approx 3.14159$ is defined as the ratio of a circle's circumference to its diameter. Since Ostrowski's theorem embeds $\mathbb{Q}$ diagonally into every completion $\mathbb{R}$ and $\mathbb{Q}_p$, one may ask whether this ratio admits a well-defined analogue $\pi_p$ at each…
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…
Post-Positional Numeracy: Finite-Adele Encoding and Product-Formula-Verified Exact Rational Arithmetic
Exact computation on the rationals today inhabits a single completion. Digital arithmetic runs in the real numbers and accepts rounding; exact alternatives run in a single $p$-adic completion through Hensel codes and reconstruct through the Chinese remainder theorem with Farey bounds. This paper…
The Trapped-Ion Ultrametric Testbed: A Falsifiability Register for Testing p-Adic Structure in Quantum Dynamics
Sixteen 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…
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…
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…
FACTORING, Adelic Complexity, and the Silent-Radix Principle
The silent radix -- the observation that no positional numeral internally specifies its own base -- was previously explored as a cryptographic primitive through Silent Radix Encryption (SRE), a key encapsulation mechanism whose security rests on the hardness of recovering a secret base from public…
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 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…
Infomatics: An Axiomatic Framework for Information as Fundamental Substrate
Axiomatic framework treating information as fundamental substrate. 4 axioms, 4 theorems. QED from information action. Fine-structure constant alpha=1/137. p-adic correction c1=5 matches 0.0014%. Falsifiable prediction: small-integer p-adic expansion of 1/alpha.…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection
Formulates Zitterbewegung as a p-adic topological observable. Establishes that the ZBW current J_mu_ZBW carries a Z_2 invariant encoding the Dirac/Majorana distinction, and proposes ultrametric readout protocols via Bruhat-Tits buildings.
p-Adic Braid Groups on Bruhat-Tits Buildings
Constructs p-adic braid groups on Bruhat-Tits buildings, establishing the geometry of discrete braiding.
The p-Adic Temperley-Lieb Parameter: Cyclotomic Units, Markov Traces, and the p-Adic Jones Polynomial
Establishes the Temperley-Lieb parameter as p-adic cyclotomic units and constructs the p-adic Jones polynomial.
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…
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…
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…
Unified Theory of Non-Archimedean Ontology
URL: https://papers.qnfo.org/papers/unified-theory-of-non-archimedean-ontology/ Date: 2026-03-15 Version: 1.0 The foundational premise of this framework is that the universe is constructed not from matter or energy, but from pure information. In this view, physical objects and phenomena are emergent…
Number-Theoretic Ultrametric Foundations: A Unified p-adic Framework for Error-Correcting Code Classification
A unified framework connecting p-adic valuation theory, Mahler spectral expansions, Kodaira-Neron fiber classification, and the Amice transform to the classification of quantum error-correcting codes. Three conjectures with 14 lemmas, computational verification across 4 code families at 83%…
The Bridge Theorem: A Rigorous Mathematical Framework Connecting p-adic and Bruhat-Tits Geometries
A rigorous mathematical framework establishing bridge connections between p-adic ultrametric spaces and Bruhat-Tits buildings.
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