{
  "abstract": "Which part of a Hamiltonian spectrum is relevant when the initial state and interpolation preserve multiple symmetries? We study this question for a multi-register encoding of fixed-cardinality Set Cover. Register permutations and incidence automorphisms define a joint action whose orbits are unlabelled candidate covers, with an exact hopping Hamiltonian on the orbit quotient. We distinguish the symmetry-fixed space from the generally smaller common invariant cyclic envelope generated by the initial state and endpoint Hamiltonians; a prescribed trajectory may span less still. We prove a sector-resolved Schur-complement bound on cover-measurement probability that includes the kinetic floor induced by sector projection. For a retained-walk linear path, a general hopping-cancellation point makes the spectrum exactly orbit-resolved. Multiplicity outside the fixed sector is then dynamically dark, while transverse dark crossings satisfy a separate stability theorem. On even cycles the fixed-sector excitation gap at cancellation equals $λ(n-1)/(2n-1)$ despite global multiplicity closure. Separately, for the same instances, we construct a distinct Johnson--Metropolis parent path on the injective hard-core space, from a Dicke state to a Gibbs-amplitude state. Its cover-failure probability is $O(n^{-5})$ and its cyclic-envelope gap is at least $1024\\,n^{-13}$ uniformly along the path, yielding a conditional polynomial adiabatic runtime in an abstract Hamiltonian-access model. We claim no quantum speedup; the result is a protocol-dependent separation of global, symmetry-fixed, cyclic-envelope, and tracked spectra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11503",
  "author_total": 1,
  "authors": [
    {
      "name": "Fabricio de Souza Luiz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1drark7mjb9hx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11503",
  "fulltext_url": null,
  "id": "1drark7mjb9hx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.11503",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7202366806",
  "pdf_url": "https://arxiv.org/pdf/2608.11503",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1drark7mjb9hx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.11503",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11503"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Orbit-resolved spectra and dynamical accessibility in multi-register covering Hamiltonians",
  "title_text": "Orbit-resolved spectra and dynamical accessibility in multi-register covering Hamiltonians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/1drark7mjb9hx",
  "venue": "arXiv",
  "versions": []
}