- 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
- Quantum Computation Latency-Energy Tradeoff and the JPCUB Metric
Quantum computation faces a critical tradeoff between wall-clock latency and energy consumption, with faster gates and parallel syndrome extraction often increasing power demands. This work investigates whether minimizing latency necessarily raises energy costs, leveraging the Ma
- Revising the Joules-per-Compute (JPCUB) Benchmark: Normalizing Energy Efficiency by Logical-Qubit Operations
Current joules-per-compute (JPCUB) benchmarks normalize energy consumption per physical gate, conflating logical operations with error-correction overhead. This obscures trade-offs between qubit connectivity, gate fidelity, and fault-tolerant design, hindering equitable compariso
- 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
- A Lower Bound on Energy Cost per Logical-Qubit Operation in Surface-Code Quantum Error Correction
Surface-code quantum error correction (QEC) is pivotal for fault-tolerant quantum computing, but its energy efficiency remains underexplored. This work derives a practical lower bound on the energy cost per logical-qubit operation, accounting for gate-fidelity decay’s impact on c
- 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.
- Error Correction Is a Landauer Machine: The Thermodynamic Floor of Quantum Error-Correction Overhead
Every cycle of active (measurement-based) quantum error correction is an erasure process priced by Landauer's principle at no less than kT ln 2 per erased bit; correction overhead therefore converges to a positive thermodynamic floor, (n-k)/k * kT ln 2 per logical qubit per round
- Terminology Silos and the Consilience Gap: A Quantitative Audit of Cross-Domain Vocabulary
Interdisciplinary consilience is claimed everywhere and measured almost nowhere. This paper measures one of its basic preconditions: whether scientific domains share vocabulary. 97.2% of external technical vocabulary occurs in exactly one discipline; bridge terms are massively en
- 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 $1,032 Research Program: What Fifty Billion Tokens Taught Me About AI-Accelerated Science
A primary-source ledger of a 263-day solo AI-accelerated research program: $1,032.08 API costs, 323,381 requests, 50.11B tokens (96.4% cache-hit), 911 Zenodo records; measured ~60-110x cost ratio vs a US postdoc; pre-registered kill criterion Aug 2028.
- Visual Graphs vs Matrices: Epistemic Limits, Cognitive Preference, and the Design of Understandable Computation
The ZX calculus and the matrices of linear algebra denote exactly the same maps. A field that knows this has, nonetheless, converged on the pictures. This paper argues that the convergence is not a matter of taste and not a matter of mathematics: it is a fact about bounded cognit
- 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
- A Pre-Registered Falsification of Deterministic Measurement-Triggered Relaxation
- Epistemic Legibility in AI-Assisted Science: Ignorance Auditing as a Governance Instrument for the Peer-Review and Evaluation Bottleneck
As AI systems take on hypothesis generation, experiment planning, analysis, and writing, the scientific ecosystem faces a new bottleneck: not production, but evaluation, verification, and governance. This position paper contributes a documented case and an instrument to that prob
- One Table, Two Regimes: Standard-Model Particles and Condensed-Matter Excitations as Patterns on the Bruhat-Tits Tree
Physics 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 discovered in condensed matter. This paper assembles both catalogs into a single patt
- 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
- Five Objections, One Standard: An Evidence-Graded Adjudication of a Critique of Post-Quantum Synthesis
- Spiral Number Line: Prime Nodes and Geometry
- Generative Spiral: A Geometric Foundation for Physical and Mathematical Understanding
- 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
- 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 phenomenology is Archimedean geometry. This paper asks what changes if the metric of physical space were instead non-Archimedean and ultrametric. Four moves: (1) the Archime
- The Purpose Principle: Grounding Research in Reality, Utility, and Premise-Depth
**Why a reader should care (SO-WHAT-GATE-1):** Most research effort today is allocated by disciplinary prestige and publication counts, neither of which measures whether the work has any traceable connection to a human problem. As AI pipelines make it possible to generate silo-fo
- 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
- Joules-per-Solution for Stochastic and Agentic Inference: Benchmarking Frontier and Agentic LLMs Against the Human Brain
The joules-per-solution (J/S) metric, introduced in JPCUB P0 as a universal, physics-grounded measure of computational efficiency, assumed deterministic solvers: one run yields one solution. Large language models (LLMs) violate that assumption twice over: they are stochasti
- 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
- Invariant Structural Value: Fundamental Constants and Formulas as Invariant Relations
- The Boson/Fermion Distinction: Spin-Statistics as Structural Invariant
The textbook dichotomy between bosons and fermions is commonly presented as a primitive classification of nature. This paper argues that the dichotomy is a derived, dimension-dependent shadow of a single structural relation: the exchange phase of identical particles equals their
- 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
- Formal Self-Reference Limits: Objectification, Anthropocentric Conventions, and the Partial Self-Knowledge of Formal Systems
This paper answers the seed question: *why are our formal quantitative systems uncomfortable with self-reference when they are also inherently anthropocentric — from base-10 pentadactylity to the heartbeat-Hertz second and the body-scaled meter — and can we not truly see ourselve
- Implications for Computing and Quantum Error Correction
- QNFO Funding Strategy — Verified Funder Landscape & Shortlist
This paper presents a verified funder landscape and fit-score shortlist for sustaining QNFO, a two-year-old, solo-run, AI-assisted research platform that has produced an open corpus of approximately 1,000 method papers across seven program areas. Every funder fact was verified by
- Prioritizing Large Language Models for Scientific Research and Agentic AI: A LiveBench-Grounded Audit (August 2026)
An audit of the frontier large-language-model landscape (August 2026) for mathematics-heavy scientific research and agentic AI, grounded in the LiveBench 2026-06-25 contamination-free benchmark. Findings: no Llama model ranks in the top 42; DeepSeek V4 Pro 0813 is the mathematics
- Prime Valuation Depth: Multiplication as Branching, the Calculus of Indications, and the Structural No-Cloning Reading