Pith Number

pith:DHCUZEJW

pith:2001:DHCUZEJWQOOWH47EVMRETU5UVT

not attested not anchored not stored refs pending

Attaching handlebodies to 3-manifolds

Marc Lackenby

arxiv:math/0109059 v2 · 2001-09-09 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DHCUZEJWQOOWH47EVMRETU5UVT}

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	2026-05-18T02:38:00.754612Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19c54c9136839d63f3e4ab2249d3b4aceea95330954cb6346a2da126d4e7503f

Aliases

arxiv: math/0109059 · arxiv_version: math/0109059v2 · doi: 10.48550/arxiv.math/0109059 · pith_short_12: DHCUZEJWQOOW · pith_short_16: DHCUZEJWQOOWH47E · pith_short_8: DHCUZEJW

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/DHCUZEJWQOOWH47EVMRETU5UVT \
  | 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: 19c54c9136839d63f3e4ab2249d3b4aceea95330954cb6346a2da126d4e7503f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c4b99fbd28d48ec58b13cbab7eabe6abac2cfc68e1b49114ed8ad6b08cb9417",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2001-09-09T21:57:57Z",
    "title_canon_sha256": "8319a72e4e827f4f6801cf4601654399719f5766b06691158fd28898eb91746d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0109059",
    "kind": "arxiv",
    "version": 2
  }
}