{
  "schema_version": 1,
  "problem_number": "AIM-TOPOLOGY-0097",
  "title": "Higher A-Homotopy Vanishing for Coxeter Chamber Graphs",
  "author": {
    "name": "Alper Ferudun",
    "affiliation": "Mercury Software GmbH",
    "url": "https://github.com/AlperTheKing"
  },
  "abstract": "We prove that the standard Cayley graph of every finite-rank Coxeter system has trivial A-homotopy groups in all degrees at least two. The argument uses a right-angled Coxeter cover, short-walk lifting and based contractions of finite median graphs. For a finite real reflection group, this establishes the all-degree group comparison for the real 3-parabolic arrangement, using the known fundamental-group comparison and classical asphericity. The right-angled construction and degree-one kernel are credited to earlier work. The result concerns k=3 and does not settle the general comparison for k>3. This is an unrefereed manuscript; no absolute priority claim is made.",
  "result_type": "COMPLETE_COXETER_HIGHER_A_VANISHING_THEOREM",
  "categories": [
    "math.AT",
    "math.CO",
    "math.GR"
  ],
  "keywords": [
    "discrete homotopy",
    "A-homotopy",
    "Coxeter groups",
    "median graphs",
    "graph coverings",
    "3-parabolic arrangements"
  ],
  "manuscript_version_date": "2026-10-11",
  "publication_date": "2026-10-11",
  "publication_date_kind": "first public online release",
  "version": "1.0",
  "date_modified": "2026-10-11",
  "presentation_revision_only": false,
  "doi_archived_file_version": "1.0",
  "status": "unrefereed preprint",
  "canonical_url": "https://eulersolve.org/papers/aim-topology-0097/",
  "pdf_url": "https://eulersolve.org/papers/aim-topology-0097/paper.pdf?v=f0aa2fa99a97",
  "doi": "10.5281/zenodo.23291327",
  "zenodo_record_url": "https://zenodo.org/records/23291327",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "scope_caveat": "Complete higher-A vanishing theorem for finite-rank Coxeter systems and its all-finite-Coxeter k=3 consequence. The k>3 comparison and unspecified wider AIM-TOPOLOGY-0097 question remain unresolved. The classical right-angled construction, degree-one comparison and median-graph inputs are credited. Self-audited and unrefereed; no independent review, formal verification or certified priority.",
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    "source.zip": {
      "sha256": "20c5cdf70fcf177294bbe59a471010dbae75fdae0875ad407593ff9ffe37b3c3"
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  "ai_use_disclosure": "AI-assisted tools supported research, computation, proof development, and manuscript preparation. The author remains responsible for all claims and the final text."
}