Pith Number

pith:X6ODZN52

pith:2010:X6ODZN52ZPQ2BC3Q6GWTO2CJPB

not attested not anchored not stored refs pending

The Pachner graph and the simplification of 3-sphere triangulations

Benjamin A. Burton

arxiv:1011.4169 v2 · 2010-11-18 · math.GT · cs.CG · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X6ODZN52ZPQ2BC3Q6GWTO2CJPB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:20:03.741237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf9c3cb7bacbe1a08b70f1ad376849786161dea98a381c362f17ad050d4755fe

Aliases

arxiv: 1011.4169 · arxiv_version: 1011.4169v2 · doi: 10.48550/arxiv.1011.4169 · pith_short_12: X6ODZN52ZPQ2 · pith_short_16: X6ODZN52ZPQ2BC3Q · pith_short_8: X6ODZN52

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/X6ODZN52ZPQ2BC3Q6GWTO2CJPB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: bf9c3cb7bacbe1a08b70f1ad376849786161dea98a381c362f17ad050d4755fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65e2d1d5e34c4b6cf18f70a5d8d33df48f5f117d163ebb0744334ce95c7bd09f",
    "cross_cats_sorted": [
      "cs.CG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-11-18T11:00:46Z",
    "title_canon_sha256": "ba043b8f2bc5645cffbf47a911175b9ebb61c9b1c7b163a13f801ebd0ef14014"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4169",
    "kind": "arxiv",
    "version": 2
  }
}