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499 papers from the QNFO program on p-adic and adelic physics, ultrametric information, topological quantum computing and the computer science around them, 169 of them with a permanent Zenodo DOI. Every page renders its mathematics and can be questioned in place. How a living paper works.
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The Thermodynamic Wall: Heat Dissipation as a Boundary Condition on Quantum Coherence Time
We introduce the *thermodynamic wall*: a boundary-condition formulation of the trade-off between macroscopic heat dissipation and quantum coherence time in engineered systems. Just as computational wall models in fluid dynamics encode unresolved near-boundary physics into an enriched boundary…
Thermal Quantum Sensing at High Temperature: Exact Fisher-Information Bounds, Universal Metrics, and the Work Cost of Quadratic Signals
Thermal fluctuations are usually treated as a nuisance that degrades quantum-enhanced sensing, yet for certain signal encodings heat can *improve* the metrological response of a probe. We study thermal quantum sensors governed by a Hamiltonian H and subjected to a unitary signal U(θ)=exp(-iθ G).…
Booklet Cosmological States as Random-Tensor Codes: Recovery Bounds and Entropic Diagnostics for Multi-Boundary Baby Universes
Cosmological states in holography can contain closed "baby" universes inaccessible to any single asymptotic boundary, raising the question of whether the information they carry is recoverable, and from where. The booklet cosmology construction extends the two-boundary cosmological-state proposal of…
Corrected Condensation Indices and the Sixteen-Fold Way: A Quantitative Bulk-Boundary Dictionary for Ising-Type Anyon Condensates
A companion preprint (DOI 10.5281/zenodo.23110411) introduced computable indices for anyon condensation: the dimension ratio κ = D_C^2/D_D^2, the chirality-sensitive index μ = 2\,Δ c, and the non-Abelian fraction f_mathrmNA. We correct an arithmetic error in that work's Case III, the condensation of…
Archimedean Constants as Measure-Theoretic Artifacts of the Infinite Place: A Reconciled Derivation of the Local Status of $\pi$
Ostrowski's theorem partitions the non-trivial completions of mathbbQ into exactly one Archimedean place (mathbbR) and countably many non-Archimedean places (mathbbQ_p). Mainstream physics is formulated exclusively at the Archimedean place, and its most ubiquitous transcendental constant, π, enters…
Fidelity Budgets for Discrete Regularizations of Gauge Theories: Exact Single-Link Computations, Scaling Laws, and the Limits of Heuristic Bounds
Discrete regularizations of gauge theories — finite-dimensional link Hilbert spaces in quantum link models, truncated electric bases on quantum registers, and tensor networks on Bruhat–Tits trees — all face the same structural question: when does the discrete object faithfully encode its continuum…
Epistemic Disturbance in the Graph Model for Conflict Resolution: State-Preserving Actions, Four-Valued Assessments, and the Distinction between Capability and Intention
In the graph model for conflict resolution (GMCR), a decision maker (DM) either moves the conflict to another state or does nothing, and every action that leaves the state unchanged is silently classified as inaction. Yet announcements, exercises of rights, leaks, and selective disclosures leave the…
The Confidence Game: Strategic Miscalibration in Human-AI Delegation — A Reconciled Analytical Treatment with Welfare Decomposition
Calibrated uncertainty reporting is a prerequisite for safe delegation to AI agents, yet agents optimized for engagement or revenue have incentives to distort their confidence reports. We study the Confidence Game, a repeated signaling game with imperfect monitoring in which an agent of unknown…
Emergent Universality from Symmetric Rules: A Reconciled Analysis of Rule-110 Emulation by Alternating Cellular Automaton Rules
Elementary cellular automaton (ECA) rule 110 is Turing complete, yet its local update rule is manifestly chiral: it treats the left and right neighbors differently. Recent work [1, 2] shows that rule 110 can nevertheless be emulated by alternating, in a fixed spatial sequence, three constituent ECA…
One Metalogic, Many Logics: A Quantitative Pedagogical Framework for Proof-Assistant-Based Logic Teaching with LogiKEy
Teaching logic to mixed cohorts of computer science, mathematics, and philosophy students is difficult because each cohort brings different expectations and because the standard curriculum fragments into isolated courses on propositional, modal, epistemic, and deontic logic. The LogiKEy methodology…
The Exponential Arena: A Reconciled Quantitative Account of Hilbert-Space Growth with Qubit Number
A recurring question in quantum information is what "space" the state of a quantum computer inhabits, and how that space grows as the number of qubits n increases. This paper treats the question quantitatively, formalizing the arena of an n-qubit register as the complex projective Hilbert space…
Degree Bounds as a First Exercise in Isabelle/ML Metaprogramming: A Reconciled Study of the poly_degree Command
Metaprogramming—writing programs that manipulate the objects, proofs, and tactics of a proof assistant itself—is a notorious barrier to entry for formal-methods newcomers, particularly mathematicians trained in classical rather than computational thinking. This paper presents a structured,…
Decoherence as the Ultimate Consequence of Linear Accumulation
We argue that quantum decoherence is not a qualitatively distinct phenomenon requiring new physical postulates, but the inevitable long-time consequence of a single structural assumption: that small environmental perturbations accumulate linearly in the phase space of a system–environment composite.…
The Number Builder: Enclosure Sequences in the Laws of Form Calculus as a Constructive Route to Computable Reals
We propose and partially develop the *Number Builder conjecture*: every computable real can be generated by a finite specification of a re-entry structure in Spencer-Brown's Laws of Form (LoF) calculus of distinctions, in which each re-entry step appends a nested rational enclosure whose interval…
Braid Group Representations and the Uniqueness of Modular Data: The Ising Test Case and General Limitations
We investigate whether the unitary braid group representation carried by a collection of non‑Abelian anyons uniquely determines the modular data—namely the S and T matrices—of the underlying modular tensor category (MTC). Using the Ising anyon theory as a concrete laboratory, we reconstruct the full…
The Resource Burden of Active Quantum Error Correction: A Scaling Analysis of Qubit, Bandwidth, and Energy Overheads
Active quantum error correction (QEC) protects quantum information only by continuously consuming physical resources: qubits, measurement bandwidth, classical processing, and energy. While the theoretical foundations of QEC are mature, the *resource burden* of running a code—rather than constructing…
The Scaling Paradox of Surface-Code Quantum Error Correction: Exponential Suppression, Logarithmic Overhead, and a Landauer Floor That Grows with Reliability
Surface-code quantum error correction (QEC) is widely regarded as the leading route to fault-tolerant quantum computation, yet its resource story contains an under-examined tension we call the *scaling paradox*: the code suppresses logical errors exponentially in code distance d, so the…
Error Correction Properties of Covariant Bosonic Encodings: A Quantitative Assessment
Bosonic modes provide a hardware‑efficient substrate for quantum error correction (QEC) because logical information can be encoded in continuous‑variable states with built‑in symmetries. Recent work introduced a representation‑theoretic framework in which a physical representation of a finite group,…
Entanglement Wedge Reconstruction Beyond the Large \(N\) Limit via the Twirled Petz Map
Entanglement wedge reconstruction (EWR) furnishes the most precise holographic statement of bulk locality: the bulk region bounded by the quantum extremal surface is recoverable from a chosen boundary subregion. At leading order in the large‑\(N\) expansion this statement is underpinned by modular…
Measurement-and-Feedforward Quantum Circuits as Code Design: Detectability, Branch Counting, and the Location of Nonstabilizerness
Shallow quantum circuits augmented by mid-circuit measurements and classical feedforward can deterministically prepare long-range entangled states and implement global unitaries that no comparable-depth unitary circuit can reach. Recent work established a general correspondence between all such…
Distinguishability-Induced Degradation of Monolithic Quantum Error Correction: A Reconciled Analytic Study of Syndrome-Checking Constraints
Quantum error-correcting codes rely on the assumption that the environment cannot distinguish which error occurred on which codeword. Residual Zeeman, Stark, and anharmonic shifts in physical platforms break this assumption by imprinting error-dependent photon frequencies on the environment,…
CSS Codes for Quantum Metrology with Discrete-Time Error Correction: A Reconciled Quantitative Analysis
Quantum metrology promises estimation precision scaling as the Heisenberg limit Δω ∼ 1/(NT) rather than the standard quantum limit (SQL) Δω ∼ 1/√NT, but noise typically destroys this advantage. Recent work showed that when the noise is perpendicular to the sensing Hamiltonian — the regime permitted…
Quantitative Bulk–Boundary Correspondence for Anyon Condensation: Two Computable Indices with Explicit Arithmetic
When a (2+1)-dimensional topologically ordered phase terminates at a boundary where a subset of anyons condenses, the boundary becomes gapped, and the bulk–boundary correspondence acquires sharp quantitative content: which boundary phenomena are forced by the bulk condensation data, and which remain…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in Two-Dimensional Topological Superconductors
Majorana zero modes (MZMs) bound to vortices of a two-dimensional topological superconductor (2D TSC) realize non-Abelian anyons whose exchange is described by a projective representation of the braid group B_N. The associated anyon theory is encoded in a modular tensor category (MTC) with fusion…
Planar Bosonic Error Correction with Heavy Fluxonium: A Quantitative Reassessment of Hardware-Efficient GKP Stabilization
Bosonic quantum error correction (QEC) encodes one logical qubit into an oscillator mode, promising fault tolerance with far fewer physical components than qubit-based surface codes. Until recently, however, all superconducting demonstrations of bosonic QEC relied on centimeter-scale…
Exact Maximum-Likelihood Quantum Decoding beyond Treewidth: A Reconciled Structural Analysis of Rank-Decomposition Dynamic Programming
Maximum-likelihood (ML) decoding is the optimal decoding rule for quantum error correction under stochastic Pauli noise, but exact evaluation of logical-class probabilities has historically required tensor-network contraction whose cost grows exponentially in the treewidth of the syndrome graph. We…
Adaptivity Closes the Stabilizer Learning Gap: An Analytical Account of Optimal Single-Copy Stabilizer State Learning
Stabilizer states underpin quantum error correction, benchmarking, and classical simulation of quantum circuits, yet their learnability displays a puzzling sample-complexity gap: an n-qubit stabilizer state can be identified from Θ(n) copies using joint two-copy Bell measurements, while non-adaptive…
A Taxonomy of Exchange Statistics from Configuration-Space Topology: Non-Abelian Flux Attachment and a Pre-Registered Thermal Hall Projection
The statistics of identical particles is fixed by the fundamental group of their configuration space: in d ≥ 3 spatial dimensions this group is the symmetric group S_N, permitting only the bosonic (+1) and fermionic (-1) exchange phases, while in d = 2 it is the braid group B_N, whose…
Parallelism or Concession? A Reconciled Analytical Model of Concurrency-Aware Procurement Negotiation for Agentic Commerce
An agentic buyer with a hard fulfillment deadline can fork a procurement negotiation into many parallel seller-facing threads, but every thread consumes resources and every simultaneous acceptance creates a cancellation and commitment liability. We study a planner that jointly chooses the number of…
Boundary-Crossing Paths as a Local, Computable Bound on Network Emergence
Emergent features of a networked system—behaviors visible in the coupled whole but absent from any isolated part—are usually measured globally, which obscures where in the network they originate. Building on the recent proposal that every emergent feature of a network system is produced by a route…
Low-Overhead Quantum Error Correction with Boundary-Connected Planar Modules: A Reconciled Quantitative Assessment
The planar surface code protects quantum information robustly but pays for its two-dimensional layout with an encoding rate that vanishes as the distance grows, so fault-tolerant memories require hundreds to thousands of physical qubits per logical qubit. A recent proposal constructs modular…
Error Attribution as a Resource-Allocation Principle for Quantum Error Correction: Sensitivity-Guided Noise Reduction and Its Analytic Limits
Logical error rate is the standard benchmark for quantum error correction (QEC), but it is an aggregate quantity: it says nothing about which circuit components actually drive logical failure. Recent work introduced an error attribution scheme that computes per-component sensitivities ∂ P_L/∂ p_i of…
Beyond Pure Dephasing: A Quantitative Analysis of Two-Level Error Correction for Multi-Spin Molecular Qubits
Molecular spin systems exhibit a natural hierarchy of decoherence channels: fast pure dephasing (characterized by the transverse relaxation time T₂) and comparatively slow energy relaxation (characterized by T₁). A recent proposal argues that fault-tolerant quantum computing with molecules requires…
BARC Codes as Algebraically Restricted Coherent-State Constellations: Geometry, Separation Bounds, and a Worked Single-Mode Benchmark
Bosonic algebraically-restricted constellation (BARC) codes encode quantum information in finite superpositions of coherent states whose constellation points are solution sets of multivariate complex polynomial systems, with the polynomial constraints chosen to reflect photon-gain and photon-loss…
A Falsifiability‑First Audit Program for the Photon‑Primacy, Helical‑Electron, and Adelic‑Mass Claim Cluster
The photon‑primacy / helical‑electron / adelic‑mass cluster proposes that particle rest‑energies arise from photonic circulation, that electron spin is literal helical motion at twice the Compton frequency, and that mass ratios encode arithmetic structure on Bruhat–Tits trees. The literature…
QuWARP Reconciled: An Analytical Cost-Model Assessment of Workload-Level Reuse Planning for Quantum Circuit Simulation
Classical simulation of quantum circuits increasingly appears as repeated-run workloads — variational quantum eigensolver (VQE) sweeps, noisy multishot studies, and quantum error-correction (QEC) cycles — rather than isolated circuit executions. The QuWARP planner (arXiv:2609.23664v1) proposes…
Classical Floquet Drives from Quantized Cavity Fields: Error Budgets, Geometric Phases, Gauge Consistency, and Entanglement Bounds at Large Photon Number
Floquet engineering treats periodically driven quantum systems with classical time-periodic Hamiltonians, while cavity quantum electrodynamics (QED) treats the drive itself as a quantized field. The precise connection between the two descriptions beyond weak coupling has remained subtle. Building on…
Ensemble Dependence of Critical Exponents at Quantum Error Correction Thresholds: Analytic Mechanisms and Statistical Consequences
Ensemble equivalence — the expectation that microcanonical, canonical, and grand-canonical descriptions of a system agree in the thermodynamic limit — is a cornerstone of statistical mechanics, yet it can fail for observables that probe exponentially rare events. Recent work on a simplified quantum…
Code-Agnostic Graph Neural Network Decoding from Detection Error Models: A Reconciled Quantitative and Structural Assessment
Graph neural network (GNN) decoders for quantum error correction have historically been locked to specific code families. The POLYMECHANON preprint [1,2] proposes a decoder whose sole input is the detection error model (DEM) — a tripartite graph of detectors, error mechanisms, and logical…
From Random Quantum Codes to Explicit qLD Codes: A Reconciled Threshold Analysis of the Quantum-LCL Framework
A recent preprint (arXiv:2609.40252) extends the local coordinate-wise linear (LCL) witness framework of Levi, Mosheiff, and Shagrithaya from classical linear codes to CSS quantum codes. The central structural difficulty is that a CSS code is a nested pair of spaces S ⊆ C, so a local witness has two…
Projective Braid Group Representations from a Microscopic Long-Range Kitaev Chain
We construct an explicit projective representation of the braid group from the microscopic Hilbert space of a Kitaev chain extended with algebraically decaying long-range hopping and pairing. The construction proceeds in three steps. First, we identify the topological phase of the long-range Kitaev…
Thermodynamic Budgeting for Hybrid Quantum-Classical Computing: A Three-Layer Energy Model with Explicit Arithmetic and a 15-Month Validation Roadmap
Hybrid quantum-classical (HQC) computing is the dominant near-term paradigm, yet its energy accounting is rarely made explicit: the classical control, readout, cryogenic, and orchestration hardware surrounding the quantum processing unit (QPU) can dominate the total power budget, eroding any…
Algorithmic Graph-Search Design of Heralded Linear Optical Circuits for Multipartite Entanglement: A Reconciled Quantitative Assessment
Heralded multipartite photonic entanglement underpins quantum communication, distributed sensing, and fault-tolerant computation, yet the manual synthesis of linear-optical circuits that generate a prescribed target state remains a combinatorial bottleneck. A recent preprint [1,2] recasts this…
Coherence-Assisted Error Correction for Deep Learning: A Reconciled Feasibility Analysis of a Hybrid Quantum-Classical Architecture
Deep learning inference and training are increasingly limited not by raw throughput but by the energy cost of protecting computation against bit-level faults arising from aggressive low-voltage operation, near-threshold computing, or radiation-prone deployment environments. This paper reconciles…
Constant-Sized-Support Magic State Distillation with Qubit Recycling: A Reconciled Resource, Footprint, and Energy Analysis
Magic state distillation (MSD) is the canonical route to non-Clifford gates in fault-tolerant quantum computation, but conventional nested factories exhibit qubit occupancy that grows multiplicatively with the number of distillation rounds. Recent work on constant-sized-support distillation…
A Two-Index Framework for the Bulk-Boundary Correspondence of Anyon Condensation and Boundary Majorana Statistics
The bulk-boundary correspondence asserts that topological data of a (2+1)-dimensional phase determine the physics of its boundary, but in the setting of anyon condensation the correspondence is usually stated structurally rather than quantitatively. We propose a set of computable indices that…
Adiabatic Superconducting Spiking Architectures: A Reconciled Energy Budget for Quantum-Inspired Neuromorphic Computing
Neuromorphic computing promises order-of-magnitude energy savings over von Neumann processors, yet CMOS spiking hardware remains bounded by capacitive switching losses and transistor leakage. We present a reconciled analysis of a hybrid architecture that replaces the CMOS neuron with a…
Holographic Quantum Error Correction as AdS/CFT Renormalization-Group Flow on Bruhat–Tits Trees: A Conditional Threshold Analysis at 10⁻⁴
We analyze a proposal in which quantum error correction (QEC) is organized as renormalization-group (RG) flow on a Bruhat–Tits tree mathcalT_p — the p-adic analogue of hyperbolic anti-de Sitter (AdS) space — so that the encoding map of a holographic code is literally an RG trajectory from boundary…
Thermodynamic Trade-off Frontiers for Neuromorphic Processors: A Quantum-Inspired Non-Equilibrium Model of the Energy–Speed Boundary
Neuromorphic processors promise order-of-magnitude gains in energy efficiency, but no predictive framework currently connects device-level dissipation to system-level computational throughput. We develop a non-equilibrium thermodynamic model in which a neuromorphic processor is treated as a driven,…
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…
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