{
  "schema_version": "26.0-internal",
  "paper_id": "PFT:PHASE_ALIGNMENT_LOCK_METHODS_AND_REPLICATION_PATTERN_FIELD_THEORY_PAPERS",
  "entity_type": "paper",
  "slug": "phase-alignment-lock-methods-and-replication-pattern-field-theory-papers",
  "title": "Phase Alignment Lock: Methods and Replication - Pattern Field Theory Papers",
  "visibility": {
    "approved_public": false,
    "scope": "internal",
    "approval_state": "unreviewed"
  },
  "publication": {
    "published": null,
    "verification_status": "unchecked",
    "last_checked": null,
    "locations": [
      {
        "provider": "patternfieldtheory",
        "url": "https://patternfieldtheory.com/papers/phase-alignment-lock-methods-and-replication-pattern-field-theory-papers/",
        "verification_status": "discovered-unverified"
      },
      {
        "provider": "zenodo",
        "url": "https://zenodo.org/communities/pft",
        "verification_status": "discovered-unverified"
      },
      {
        "provider": "academia",
        "url": "https://independent.academia.edu/JamesAllen375",
        "verification_status": "discovered-unverified"
      }
    ]
  },
  "representations": {
    "html": {
      "available": true,
      "path": "index.html",
      "canonical": true
    },
    "json": {
      "available": true,
      "path": "paper.json"
    },
    "pdf": {
      "available": true,
      "path": "paper.pdf"
    },
    "latex": {
      "available": false,
      "path": null,
      "original_filename": "phase_alignment_lock.tex"
    },
    "timestamp": {
      "available": true,
      "path": "timestamp.ots"
    }
  },
  "sections": [
    {
      "level": 1,
      "title": "Phase Alignment Lock: Methods and Replication - Pattern Field Theory Papers",
      "anchor": null
    },
    {
      "level": 2,
      "title": "Repository Files",
      "anchor": null
    },
    {
      "level": 1,
      "title": "Phase Alignment Lock: Methods and Replication - Pattern Field Theory Papers",
      "anchor": null
    },
    {
      "level": 1,
      "title": "Introduction",
      "anchor": "#introduction"
    },
    {
      "level": 1,
      "title": "Allen Orbital Lattice: Minimal Recap",
      "anchor": "#allen-orbital-lattice-minimal-recap"
    },
    {
      "level": 2,
      "title": "Geometric substrate",
      "anchor": "#geometric-substrate"
    },
    {
      "level": 2,
      "title": "Prime indexing",
      "anchor": "#prime-indexing"
    },
    {
      "level": 2,
      "title": "Phase labels and active sets",
      "anchor": "#phase-labels-and-active-sets"
    },
    {
      "level": 1,
      "title": "Phase Alignment Lock: Definition and Geometry",
      "anchor": "#phase-alignment-lock-definition-and-geometry"
    },
    {
      "level": 2,
      "title": "PAL-coherent configurations",
      "anchor": "#pal-coherent-configurations"
    },
    {
      "level": 2,
      "title": "Angular radius approximation",
      "anchor": "#angular-radius-approximation"
    },
    {
      "level": 2,
      "title": "PAL balls and coherence capacity",
      "anchor": "#pal-balls-and-coherence-capacity"
    },
    {
      "level": 1,
      "title": "Algorithmic PAL Checking",
      "anchor": "#algorithmic-pal-checking"
    },
    {
      "level": 2,
      "title": "Naive pairwise check",
      "anchor": "#naive-pairwise-check"
    },
    {
      "level": 2,
      "title": "Radius-based prefilter",
      "anchor": "#radius-based-prefilter"
    },
    {
      "level": 2,
      "title": "Incremental PAL maintenance",
      "anchor": "#incremental-pal-maintenance"
    },
    {
      "level": 1,
      "title": "PAL-Constrained Dynamics",
      "anchor": "#pal-constrained-dynamics"
    },
    {
      "level": 2,
      "title": "Local update rule",
      "anchor": "#local-update-rule"
    },
    {
      "level": 2,
      "title": "PAL-enforced update",
      "anchor": "#pal-enforced-update"
    },
    {
      "level": 2,
      "title": "Coherence time and PAL-lock convergence",
      "anchor": "#coherence-time-and-pal-lock-convergence"
    },
    {
      "level": 1,
      "title": "Replication Protocols",
      "anchor": "#replication-protocols"
    },
    {
      "level": 2,
      "title": "Replication 1: PAL inequality validation",
      "anchor": "#replication-1-pal-inequality-validation"
    },
    {
      "level": 2,
      "title": "Replication 2: Coherence capacity estimates",
      "anchor": "#replication-2-coherence-capacity-estimates"
    },
    {
      "level": 2,
      "title": "Replication 3: PAL-constrained computation toy model",
      "anchor": "#replication-3-pal-constrained-computation-toy-model"
    },
    {
      "level": 2,
      "title": "Replication 4: PAL in Bayesian Coherence Collapse",
      "anchor": "#replication-4-pal-in-bayesian-coherence-collapse"
    },
    {
      "level": 1,
      "title": "Physical and Analogue Approximations",
      "anchor": "#physical-and-analogue-approximations"
    },
    {
      "level": 2,
      "title": "Coupled oscillator arrays",
      "anchor": "#coupled-oscillator-arrays"
    },
    {
      "level": 2,
      "title": "Phase-locked loop architectures",
      "anchor": "#phase-locked-loop-architectures"
    },
    {
      "level": 2,
      "title": "Neural phase alignment",
      "anchor": "#neural-phase-alignment"
    },
    {
      "level": 1,
      "title": "Discussion",
      "anchor": "#discussion"
    },
    {
      "level": 1,
      "title": "Document Timestamp and Provenance",
      "anchor": "#document-timestamp-and-provenance"
    }
  ],
  "external_locations": [
    {
      "provider": "patternfieldtheory",
      "url": "https://patternfieldtheory.com/papers/phase-alignment-lock-methods-and-replication-pattern-field-theory-papers/",
      "verification_status": "discovered-unverified"
    },
    {
      "provider": "zenodo",
      "url": "https://zenodo.org/communities/pft",
      "verification_status": "discovered-unverified"
    },
    {
      "provider": "academia",
      "url": "https://independent.academia.edu/JamesAllen375",
      "verification_status": "discovered-unverified"
    }
  ],
  "software": [],
  "data_files": [],
  "legacy_metadata": {
    "title": "Phase Alignment Lock: Methods and Replication - Pattern Field Theory Papers",
    "slug": "phase-alignment-lock-methods-and-replication-pattern-field-theory-papers",
    "canonical_html": "https://patternfieldtheory.com/papers/phase-alignment-lock-methods-and-replication-pattern-field-theory-papers/",
    "pdf": "https://patternfieldtheory.com/papers/phase-alignment-lock-methods-and-replication-pattern-field-theory-papers/paper.pdf",
    "ots": "https://patternfieldtheory.com/papers/phase-alignment-lock-methods-and-replication-pattern-field-theory-papers/timestamp.ots",
    "ots_file_date": "2025-12-01",
    "original_folder": "phase_alignment_lock",
    "original_tex_filename": "phase_alignment_lock.tex",
    "original_pdf_filename": "phase_alignment_lock.pdf",
    "original_ots_filename": "phase_alignment_lock.pdf.ots",
    "images_folder_copied": [
      "images"
    ],
    "csv_files_copied": [],
    "pandoc_status": "success",
    "source_last_write_utc": "2025-12-01T16:34:26Z",
    "generated_utc": "2026-05-08T11:02:00Z",
    "status": "canonical_html_export"
  },
  "migration": {
    "source": "papers(1).zip",
    "content_policy": "existing scientific HTML preserved; v26 shell and resource controls injected",
    "formula_status": "not rewritten during structural migration",
    "requires_source_formula_audit": true,
    "source_html_sha256": "a889c541f23edfeb1224d656e16c57fd85e1dbdf05333f8085e40754a83027c1"
  }
}