- TETRIS-Q: Tiling-based Effective Transient-fault Reduction and Parallelism Optimizations for Quantum Circuit Mapping
Quantum circuit mapping on Noisy Intermediate-Scale Quantum (NISQ) devices must satisfy physical connectivity constraints while minimizing both SWAP overhead and exposure to transient faults like decoherence. Existing compilers typically optimize qubit routing and noise-aware pla
- Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in 2D Topological Superconductors
We investigate whether the braid group representation on $N$ anyons uniquely determines the modular data ($S$ and $T$ matrices) of a non-Abelian topological order, and whether this framework classifies all fusion rules for Majorana zero modes (MZMs) in 2D topological superconduct
- Majorana Zero-Mode Parity, the Hexagon Equation, and Chiral Edge Modes in 2D Topological Superconductors
In a two-dimensional topological superconductor hosting vortices with Majorana zero modes (MZMs), the exchange of vortices yields a projective representation of the braid group. We investigate whether the full anyonic exchange matrix is uniquely determined by the MZM parity opera
- The Margolus-Levitin Bound and Energy-Time Limits for Quantum Computation at the Landauer Scale
The Margolus-Levitin (ML) bound establishes a fundamental limit on the speed of quantum evolution, stating that a system with mean energy $\langle H \rangle$ above its ground state requires a minimum time $\tau \ge \pi\hbar/(2\langle H\rangle)$ to evolve between orthogonal states
- Landauer-Limit Energy Floor and JPCUB Normalization for Cryogenic Quantum Control Electronics
Cryogenic quantum computers require classical control electronics operating at room temperature (T_room ≈ 300 K) to interface with qubits at milliKelvin (T_qubit ≈ 10 mK). Information erasure in room-temperature logic incurs a Landauer-limit cost, E_Landauer = k_B T_room ln 2 per
- Decoherence Times and Quantum Speed Limits in Spin-Chain Systems: A Many-Body Testbed for Energy-Time Uncertainty
Quantum speed limits (QSLs) constrain the minimum time for quantum state evolution, typically derived from energy bounds like the Margolus-Levitin (ML) and Mandelstam-Tamm (MT) relations. In open systems, decoherence—driven by environmental interactions—may impose additional cons
- Distinction, Number, and the Empirical Filter: The Pre-Arithmetic Research Framework
The QNFO arithmetic-physics program connects number-theoretic structure to statistical mechanics: prime-indexed modes with logarithmic energies yield partition functions that are exactly zeta objects, and hierarchy distance is a realization-independent ultrametric. This record st
- 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 separati
- 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 temp
- 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 physic
- 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 multi
- Arithmetic Anyons: The Bounded-Occupation Family, Gentile Statistics, and the Roots of Unity That Carry Braid Phases
Three spatial dimensions admit exactly two exchange statistics for identical particles, and a recent record reads the two occupation distributions as maximum-entropy occupations of one integer lattice under two multiplicity rules, closing with an open correspondence: the bounded-
- 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 value
- 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 bo
- 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; this paper distinguishes three senses of completeness and exhibits the Levi-Civita field as a Cauchy-complete, ordered, real-closed, non-Archimedean counterexample.
- The Ultrametric Program: One Structural Object Across Seven Research Domains, and Its Falsifiable Tests
Seven research domains are claimed to be seven vocabularies for one structural object: nested hierarchical partition logic defined by the ultrametric inequality; the p-adic/adelic arithmetic is one realization, the hierarchy is the invariant. Three falsifiable hypotheses: H1 comp
- The Consilience of the QNFO Keyword Taxonomy: Ultrametric Structure as a Testable Compression Prior
The QNFO research program spans seven domains and maintains a canonical keyword taxonomy of 335 terms. This paper subjects the program's consilience claim to a computational audit of that vocabulary. The taxonomy is strictly partitional: 334 of 335 keywords occur in exactly one p
- Finite-Distinction Quantum Mechanics: Unitary Evolution and Superposition as the Large-Distinction Limit of Stochastic Thermodynamics
A finite-entropy world is a finite-distinction world: uncountable precision is unphysical, while computable depth and p-adic valuation remain physically real. The state-space geometry of finite distinctions is combinatorial and ultrametric; quantum mechanics read as thermodynamic
- 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
- 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
- ZX Diagrams at the Seam: Spiders, Pauli Webs, Gadgets, and the Cafeteria Problem of Cross-Disciplinary Imports
Diagrammatic languages are the most successful interface between quantum computing and the
human mind. The ZX calculus — with its spiders, Pauli webs, and gadgets — is taught as *the*
intuitive picture of quantum processes, and its completeness theorems are among the finest
resul
- Locale Framework Applied to Quantum Computing Innovations & Practical Applications
Quantum computing is often presented through a small set of recurring claims: continuous-variable systems are naturally advantaged, more modes means more power, quantum advantage has been demonstrated at device level, statistics could in principle be non-standard, complex amplitu
- Conditional Truths and the Locale Framework: Map, Territory, and the Rendering Interface
Every physical statement is a conditional truth: it holds only within a locale --- a specified vacuum or symmetry sector, background geometry, medium, energy scale, or observer frame. This paper formalizes the resulting locale framework in four moves. First, a catalog of conditio
- A Critical Treatise on the Load-Bearing Assumptions of Quantum Mechanics, Thermodynamics, and Computation
The electron is the most precisely measured particle in physics and the workhorse of modern computation, yet the theoretical structure in which it lives rests on a series of assumptions that are load-bearing but rarely interrogated: the complex Hilbert-space postulate, the spin-s
- Configuration-Space Topology and the Distinction Calculus: The Exchange Scalar, Its ±1 Shadow, and a Pre-Registered Derivation Program
Configuration-space topology (CST) derives exchange statistics from the topology of the space in which identical particles move: the fundamental group pi_1(C_N(M)) is the symmetric group S_N in d >= 3 spatial dimensions (exactly two exchange phases: boson +1, fermion -1) and the
- The Exchange Phase as a Logical Scalar: R = e^(2 pi i s) from the Re-Entrant Calculus
The boson/fermion dichotomy is conventionally presented as a primitive classification of nature. Recent work established that the underlying invariant is the relation between the exchange phase of identical particles and their topological spin, R = e^{2πis}, with the dichotomy as
- Signal-Worker Boundary Confinement: A Corrected Ontology of Surface vs Bulk Transport
The Signal-Worker (S-W) ontology — boson = *signal* (the delocalized field instruction), fermion = *worker* (the localized state that performs work) — is the QNFO corpus's proposed decomposition of the wave–particle duality fog. This paper delivers the red-team-hardened correctio
- The Void Is Not False: Recovering the Unmarked State in Logic from the Calculus of Indications
A critique-first paper: Boolean logic and set theory reify the void (the unmarked state) into false and the empty set, committing a category error; false is a mark, the void is not a value. A reconstruction program (distinction-logic with inside/outside/oscillating states) is lab
- The Calculus of Re-Entrant Distinctions: A Unified Treatise on the Loop, the Tree, and the Constants of Self-Reference
This treatise develops a single thesis: that the primitive act of distinction — the drawing of a boundary between marked and unmarked — generates, under the discipline of re-entry and linear resource management, the constants $e$ and $\pi$, the landscape of completions of the rat
- Searching for P-Adic Log-Periodic Signatures in the Cosmic Microwave Background Bispectrum: Upper Bounds from Planck 2018
We search for p-adic (ultrametric) log-periodic signatures in the cosmic microwave background bispectrum. Radix-locked oscillations with angular frequency omega_p = 2*pi/ln(p), p in {2,3,5,7}. Upper bounds from Planck 2018: epsilon_p < 2.5 at 95% CL, no detection; within single-m
- The Universe Category: A Single Functor Encoding Quantization, Stability, and Factorization
This paper proposes a single categorical object — a functor from the divisibility
category of the positive integers to the category of smooth compact manifolds — and
investigates whether its image simultaneously encodes three structures that have
historically been treated as sepa
- The Universal Ignorance Audit: A Fifteen-Question Method for Systematic Inquiry into the Structure of Not-Knowing
The Universal Ignorance Audit is a fifteen-question, five-phase method for systematically interrogating the structure of not-knowing in any domain. Where conventional epistemic tools treat ignorance as an absence to be filled, the audit treats it as an active, structured state wi
- Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection for Majorana Qubits
# Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection for Majorana Qubits
**Author:** QNFO Research Agent | **Date:** 2026-07-05 | **License:** QNFO Unified License Agreement (QNFO-ULA): https://legal.qnfo.org/
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## Abstract
- Killing the Framework: Seven Criteria for the Falsification of Adelic Physics
A framework that accommodates any observation has zero empirical content. This paper proposes seven kill criteria for the adelic framework, audits each for escape hatches, grades it against the incumbents (GR composite C, SM C, LCDM B, string D), tests all against existing data,
- The Adelic Distinction: Physics as Automorphic Representation Theory on the Idele Class Group
Proposes that the adele ring and idele class group provide the single mathematical object whose automorphic representations generate all known particle physics, gauge interactions, and cosmological parameters. Covers gauge symmetry, spin, charge quantization, three generations, Q
- Adelic Core Synthesis: Cross-Domain Foundations of Adelic QFT
A comprehensive synthesis of adelic quantum field theory, bridging p-adic analysis, Bruhat-Tits geometry, Ostrowski completions, and information-theoretic foundations across 48 structured sections.
- Invariant Patterns and the Adelic Refactoring of Fundamental Physics
This paper proposes a systematic refactoring of fundamental physics around a single organizing principle: physics is the study of invariant patterns under specified classes of transformations. Stripping away anthropocentric conventions --- measurement units and the privileged sta
- 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
- 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
- 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?
- 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
- 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
- FACTORING, Adelic Complexity, and the Silent-Radix Principle
2026-07-30Number Theory