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728 papers from the QNFO program, filed on nine shelves by the reader each one is written for: energy per answer, error correction, physics, numbers and p-adics, logic and formalism, AI and knowledge, autonomous systems, assessments, and cross-cutting essays. Every page renders its mathematics and can be questioned in place. How a living paper works.
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Results for “foundations” 6 papers
Error correction. Codes, fault tolerance, logical qubits Tagged papers: 97.
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…
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…
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…
Extending v_p^max Code Classification: Testing the Mahler Spectral Conjecture on Additional Stabilizer Code Families
The Number-Theoretic Ultrametric Foundations paper (the QNFO archive https://papers.qnfo.org/papers/number-theoretic-ultrametric-foundations/) conjectured that the 2-adic valuation spectrum (v_p^max) of a code's Mahler expansion discriminates optimal codes (v_p^max=28) from random codes (v_p^max=4)…
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…
Phase Transitions of Logic
The realization of fault-tolerant universal quantum computation is currently hindered by a fundamental dichotomy between substrate controllability and intrinsic robustness. This paper introduces the “Universal Hamiltonian Computational Substrate” (UHCS) framework to quantitatively compare two…
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