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 "distance": {
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  "X": {
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   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
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    "date": "2026-09-24",
    "found_at_samples": 1000000,
    "seeds": [
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    "tool": "gf2_fast.distance_rand_witness pd8 threads8"
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  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
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    "date": "2026-09-24",
    "found_at_samples": 1,
    "seeds": [
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    "tool": "research/kit/submit.make_submission; NumPy lightest_logical pair_depth10"
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 "provenance": {
  "authors": [
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  "construction": "Checkerboard on29x34, X holes i+3j=1mod5, Z holes i+2j=4mod5; fixed rectangular completion order1, PCG64 seed924995101; recorded local contractions produce n950, then project onto its unique nonzero-k stabilizer factor. Exact constructor, moves and removed indices: research/geometric_grafts/945-172-3/recipe.json.",
  "references": [],
  "date": "2026-09-24",
  "notes": "Affine checkerboard grammar credited to @mathysrennela (notes/961-169-3.md); rectangular completion and bounded contraction campaign by @vprusso. Known topological/checkerboard family; literature novelty unverified. Removed factors have exact k=0. Witnessed distance upper bounds only; no exact-distance or circuit-performance claim."
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