{
  "schema": "theoremdb-agent-record-v1",
  "ref": "R670",
  "content_hash": null,
  "slug": "rr8gc-artifact-1282-move-replay",
  "type": "artifact",
  "title": "Exact replay of the 1,282-move initial state",
  "summary": "Standard-library Python fixes every ordering convention, validates the rotor vector, and replays all 1,282 moves.",
  "relevance": "For Longest rotor-router cover time on the eight by eight grid, record rr8gc-artifact-1282-move-replay (“Exact replay of the 1,282-move initial state”) supplies evidence or a replay used to check the packet. The record states: Standard-library Python fixes every ordering convention, validates the rotor vector, and replays all 1,282 moves.",
  "relevance_source": "recorded",
  "body": "Vertices are numbered row-major from 0 through 63. At each vertex, form its local neighbor list by taking north, east, south, west in that order and deleting directions that leave the grid. A rotor index points into this shortened list. On each move the index is incremented modulo the local degree, then the walker follows the selected edge.\n\nStart at vertex 56 with rotor indices\n```\n[1,0,0,0,0,0,0,0,\n 0,1,1,1,1,1,1,0,\n 0,1,1,1,1,1,3,0,\n 0,1,1,1,1,1,0,0,\n 0,1,1,1,1,1,0,0,\n 1,2,1,1,1,1,0,0,\n 1,1,1,1,1,0,0,0,\n 0,1,1,1,1,0,0,0]\n```\nThe walk reaches 63 vertices by move 1,063. Vertex 7 remains unseen until move 1,282. The trajectory uses 221 of the 224 directed arcs. The canonical report has SHA-256 digest `b070c0e29fe515ae5ccd7d3a2e2eb159b6b819efd0b35737c073e5736211ab8d`.",
  "status": "available",
  "evidence_grade": "executable",
  "scope": {
    "kind": "bounded",
    "statement": "the stated start vertex and one complete 64-rotor initial state on the 8 by 8 grid",
    "bounds": {
      "rows": {
        "min": 8,
        "max": 8
      },
      "columns": {
        "min": 8,
        "max": 8
      },
      "configurations": {
        "min": 1,
        "max": 1
      },
      "moves_replayed": {
        "min": 1282,
        "max": 1282
      }
    },
    "exhaustive": true
  },
  "reproduction": {
    "schema": "theoremdb-reproduction-v1",
    "readiness": "partial",
    "kind": "inline_python_computation",
    "entrypoint": "join source_lines with newline and run with python3",
    "runtime": "CPython 3, standard library only",
    "citation": {
      "url": "https://doi.org/10.4169/amer.math.monthly.123.7.627",
      "locator": "Self-contained Python standard-library replay performed on 2026-07-25"
    },
    "inline_source": [
      "from collections import Counter",
      "from hashlib import sha256",
      "from json import dumps",
      "N=8",
      "START=56",
      "INITIAL=[1,0,0,0,0,0,0,0,0,1,1,1,1,1,1,0,0,1,1,1,1,1,3,0,0,1,1,1,1,1,0,0,0,1,1,1,1,1,0,0,1,2,1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0]",
      "DIRECTIONS=[(-1,0),(0,1),(1,0),(0,-1)]",
      "neighbors=[]",
      "for vertex in range(N*N):",
      "    row,column=divmod(vertex,N)",
      "    neighbors.append([N*(row+dr)+column+dc for dr,dc in DIRECTIONS if 0<=row+dr<N and 0<=column+dc<N])",
      "degrees=[len(x) for x in neighbors]",
      "assert degrees.count(2)==4 and degrees.count(3)==24 and degrees.count(4)==36",
      "assert all(0<=INITIAL[v]<degrees[v] for v in range(N*N))",
      "directed_arcs=sum(degrees)",
      "diameter=2*(N-1)",
      "assert directed_arcs==224 and diameter==14",
      "rotors=INITIAL.copy()",
      "at=START",
      "first_visit=[-1]*(N*N)",
      "first_visit[at]=0",
      "visited=1",
      "trajectory=[at]",
      "edge_counts=Counter()",
      "for move in range(1,3137):",
      "    rotors[at]=(rotors[at]+1)%degrees[at]",
      "    nxt=neighbors[at][rotors[at]]",
      "    edge_counts[(at,nxt)]+=1",
      "    at=nxt",
      "    trajectory.append(at)",
      "    if first_visit[at]<0:",
      "        first_visit[at]=move",
      "        visited+=1",
      "        if visited==N*N:",
      "            cover_time=move",
      "            break",
      "assert cover_time==1282 and max(first_visit)==1282",
      "report={'certified_upper_bound':diameter*directed_arcs,'cover_time':cover_time,'diameter':diameter,'directed_arcs':directed_arcs,'directed_arcs_used':len(edge_counts),'final_vertex':at,'first_visit_times':first_visit,'initial_rotors_sha256':sha256(bytes(INITIAL)).hexdigest(),'last_new_vertex':first_visit.index(cover_time),'max_directed_arc_traversals':max(edge_counts.values()),'start':START,'trajectory_sha256':sha256(','.join(map(str,trajectory)).encode()).hexdigest(),'undirected_edges':directed_arcs//2}",
      "payload=dumps(report,sort_keys=True,separators=(',',':'))",
      "assert sha256(payload.encode()).hexdigest()=='b070c0e29fe515ae5ccd7d3a2e2eb159b6b819efd0b35737c073e5736211ab8d'",
      "print(payload)"
    ],
    "missing": [
      "command",
      "expected_output"
    ]
  },
  "formal_statement": null,
  "source": {
    "url": "https://doi.org/10.4169/amer.math.monthly.123.7.627",
    "locator": "Self-contained Python standard-library replay performed on 2026-07-25"
  },
  "models": [],
  "continuation": null,
  "relations": [
    {
      "slug": "R673",
      "title": "The worst cover time lies between 1,282 and 3,136 moves",
      "object_type": "claim",
      "relation": "supports",
      "direction": "outgoing"
    },
    {
      "slug": "R672",
      "title": "Seeded local search raises the incumbent from 807 to 1,282",
      "object_type": "attempt",
      "relation": "produces",
      "direction": "incoming"
    },
    {
      "slug": "rotor-router-eight-grid-cover",
      "title": "rotor router eight grid cover",
      "object_type": "problem",
      "relation": "recorded_for",
      "direction": "outgoing"
    }
  ]
}