{
  "schema_version": 1,
  "paper_id": "trn64znfNx",
  "target_space": "ProCreations/repro-formal-problem-solving",
  "generated_at": "2026-07-22T21:51:50.457390+00:00",
  "note": "Transparent mapping of the current organizer-anchored claims to pre-existing independent artifacts; limitations are explicit.",
  "claims": [
    {
      "number": 1,
      "claim": "WIRE applies rotary position encodings to graphs by using Laplacian spectral coordinates to define graph-dependent rotation angles (Figure 1, Section 3).",
      "evidence_class": "direct independent execution",
      "evidence": "Fifteen graph instances construct Laplacian eigenfeatures and WIRE rotations, with raw angles/attention outputs retained for path, grid, random, and symmetric graphs.",
      "primary_artifact": "outputs/wire/wire_results.json"
    },
    {
      "number": 2,
      "claim": "The WIRE transformation is equivariant to node-order permutations up to sign flips and rotations in degenerate eigenspaces (Lemma 1).",
      "evidence_class": "direct independent execution",
      "evidence": "Permutation tests, including degenerate-eigenspace rotations and sign changes, reproduce equivariant attention outputs to numerical precision; deliberately inconsistent basis handling is included as a negative control.",
      "primary_artifact": "outputs/wire/wire_results.json"
    },
    {
      "number": 3,
      "claim": "Regular RoPE is recovered as a special case of WIRE on grid graphs with appropriate learnable frequencies (Theorem 2, Figure 2).",
      "evidence_class": "direct independent execution",
      "evidence": "On path/grid graph families, the spectral WIRE angles and attention phases match the corresponding regular-RoPE construction under the prescribed learnable frequencies.",
      "primary_artifact": "outputs/wire/wire_results.json"
    },
    {
      "number": 4,
      "claim": "WIRE asymptotically depends on graph effective resistance under the paper's spectral-feature assumptions (Theorem 3).",
      "evidence_class": "direct independent execution",
      "evidence": "Across the graph suite the spectral kernel is compared against effective resistance and the predicted asymptotic relation is checked under the paper's stated spectral-feature assumptions.",
      "primary_artifact": "outputs/wire/wire_results.json"
    },
    {
      "number": 5,
      "claim": "Experiments report WIRE improvements on synthetic monochromatic-subgraph and shortest-path tasks, point-cloud transformers, and efficient graph transformer benchmarks (Table 1, Table 2, Table 3, Table 4).",
      "evidence_class": "source-backed only; benchmark training not reproduced",
      "evidence": "Tables 1-4 are mapped to the pinned source, but the synthetic-task, point-cloud, and efficient-transformer training suites were not rerun. Linear-attention associativity and spectral mechanics are executed; benchmark improvements are not claimed as new runs.",
      "primary_artifact": "outputs/wire/wire_results.json"
    }
  ]
}