Pith Number

pith:ZKXTCZD4

pith:2007:ZKXTCZD4O4FXQB35KVD462624F

not attested not anchored not stored refs pending

An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary

Marc Lackenby

arxiv:0709.0376 v2 · 2007-09-04 · 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{ZKXTCZD4O4FXQB35KVD462624F}

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	2026-05-18T01:22:31.197153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

caaf31647c770b78077d5547cf6bdae14bcd1c95477b2fcc4ddbbae2c7b84c26

Aliases

arxiv: 0709.0376 · arxiv_version: 0709.0376v2 · doi: 10.48550/arxiv.0709.0376 · pith_short_12: ZKXTCZD4O4FX · pith_short_16: ZKXTCZD4O4FXQB35 · pith_short_8: ZKXTCZD4

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/ZKXTCZD4O4FXQB35KVD462624F \
  | 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: caaf31647c770b78077d5547cf6bdae14bcd1c95477b2fcc4ddbbae2c7b84c26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c108c23e2f14ae1e16e61ba855a765a3d86ed703994574a4b94089bff3372c34",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2007-09-04T09:36:52Z",
    "title_canon_sha256": "cd0a90d0090f28fbf47c69dd71099da0f81a5c44449f3993667720600634109e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.0376",
    "kind": "arxiv",
    "version": 2
  }
}