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.