Pith Number

pith:QZ53QJ3J

pith:2008:QZ53QJ3JIRYZVOFZEW55X7XXK7

not attested not anchored not stored refs pending

Stabilization of Heegaard splittings

Abigail Thompson, Joel Hass, William Thurston

arxiv:0802.2145 v2 · 2008-02-15 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QZ53QJ3JIRYZVOFZEW55X7XXK7}

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	2026-05-18T02:38:19.216070Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

867bb8276944719ab8b925bbdbfef757e564c1aab8f2efcc99fecd541cddb431

Aliases

arxiv: 0802.2145 · arxiv_version: 0802.2145v2 · doi: 10.48550/arxiv.0802.2145 · pith_short_12: QZ53QJ3JIRYZ · pith_short_16: QZ53QJ3JIRYZVOFZ · pith_short_8: QZ53QJ3J

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/QZ53QJ3JIRYZVOFZEW55X7XXK7 \
  | 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: 867bb8276944719ab8b925bbdbfef757e564c1aab8f2efcc99fecd541cddb431

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9241109921c56d93868019493ea2e70d7051602502fd827021ecc00a20e30af2",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-02-15T07:20:06Z",
    "title_canon_sha256": "6780f6699555ef35d2060ce03f510989bd1e2aeb09c92454cf787b5bea39c3bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.2145",
    "kind": "arxiv",
    "version": 2
  }
}