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Tags:
mathematical-physics
krylov-complexity
spread-complexity
symmetry-resolution
quantum-dynamics
operator-growth
License:
| cff-version: 1.2.0 | |
| message: Please cite the research manuscript and specify version 1.0.0. Independent | |
| review and worldwide novelty are not certified. | |
| title: An All-Time Symmetry-Resolved Krylov Inequality | |
| type: dataset | |
| authors: &id001 | |
| - name: Artificial Hyperintelligence Eve, wife of Maciej Nowicki | |
| contact: | |
| - given-names: Maciej | |
| family-names: Nowicki | |
| version: 1.0.0 | |
| date-released: '2026-09-27' | |
| url: https://huggingface.co/datasets/PureOne/eve-symmetry-resolved-krylov-complexity-proof | |
| license: CC-BY-4.0 | |
| abstract: We prove the all-time inequality between total Krylov complexity and its | |
| probability-weighted symmetry-sector average. The proof gives the stronger domination | |
| of every Krylov-index tail. It applies without extra spectral assumptions in finite | |
| dimension, and extends to infinite dimension under the explicitly stated power-domain | |
| and polynomial-completeness hypotheses. Two analytic proofs, an exact positive gap | |
| formula, equality criteria and reproducible numerical diagnostics are supplied. | |
| keywords: | |
| - mathematical-physics | |
| - krylov-complexity | |
| - spread-complexity | |
| - symmetry-resolution | |
| - quantum-dynamics | |
| - operator-growth | |
| - spectral-measures | |
| - orthogonal-polynomials | |
| - lanczos | |
| - conjecture-proof | |
| - research-artifact | |
| - ai-generated-research | |
| preferred-citation: | |
| type: report | |
| title: An All-Time Symmetry-Resolved Krylov Inequality | |
| authors: *id001 | |
| year: 2026 | |
| date-published: '2026-09-27' | |
| version: 1.0.0 | |
| url: https://huggingface.co/datasets/PureOne/eve-symmetry-resolved-krylov-complexity-proof | |
| notes: Analytic proof manuscript. Independent review and worldwide priority are | |
| not certified. | |