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Results for “foundations” 9 papers
p-adic. p-adic numbers and valuation-driven models Tagged papers: 82.
Non‑Archimedean Statistical Foundations for a Fully Connected Reality
Standard parametric statistics assume independent, identically distributed (i.i.d.) observations, an assumption that fails when all events share a common causal ancestry encoded by an ultrametric (p‑adic) structure. This paper addresses the gap between classical significance testing and a fully…
Ultrametric Foundations for Quantum Dynamics: A $p$-Adic Calculus Approach
Fault-tolerant quantum processors demand error-correction overheads estimated at $10^{3}$–$10^{6}$ physical qubits per logical qubit, and each correction round dissipates energy through irreversible syndrome erasure. A proposed alternative models quantum dynamics over the $p$-adic fields…
Reformulating Quantum Mechanics on Bruhat–Tits Trees: A Deterministic Boundary‑Measure Framework
Quantum foundations confront the measurement problem and the postulated Born rule $P_i=|c_i|^2$. Existing platforms—type‑I parametric‑down‑conversion sources delivering $10\;\text{kHz}$ coincidences at $200\;\text{mW}$ pump power [1] and superconducting processors achieving $99.90\%$ single‑qubit…
Implications for Computing and Quantum Error Correction
The anchor paper introduced the branch-depth reading: the p-adic valuation $v_p(n)$ is a measure of depth along a prime branch of the integer factorization tree (not a measure of size), and because the tensor product multiplies Hilbert-space dimensions, $v_2(\dim H) = n$ counts tensor-branch depth…
Counterfactual Physics: What If p-Adic Methods Had Won?
The p-adic approach to physics was nearly mainstream. Vladimirov and Volovich developed p-adic quantum mechanics in the 1980s. Freund and Witten connected p-adic string amplitudes to the adelic product formula in 1987. Dragovich extended p-adic methods to cosmology and the Standard Model. Yet by…
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…
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). Ostrowski's theorem — a proven result in number theory — then demands that all p-adic completions of ℚ be physically meaningful, transforming the…
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…
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