Pith Number

pith:5G4JCLUU

pith:2012:5G4JCLUUBMSQUB5AK3EB3H7BZL

not attested not anchored not stored refs pending

Finding disjoint surfaces in 3-manifolds

Marc Lackenby

arxiv:1209.3130 v1 · 2012-09-14 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5G4JCLUUBMSQUB5AK3EB3H7BZL}

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	2026-05-18T03:45:32.744679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9b8912e940b250a07a056c81d9fe1cad321c113ec5f4e34cedcdaebce3560ba

Aliases

arxiv: 1209.3130 · arxiv_version: 1209.3130v1 · doi: 10.48550/arxiv.1209.3130 · pith_short_12: 5G4JCLUUBMSQ · pith_short_16: 5G4JCLUUBMSQUB5A · pith_short_8: 5G4JCLUU

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/5G4JCLUUBMSQUB5AK3EB3H7BZL \
  | 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: e9b8912e940b250a07a056c81d9fe1cad321c113ec5f4e34cedcdaebce3560ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26f60cc6eb9f489396b4c3e88eccb3a16d963d1280f79bb0f60b1ca5cd1a6372",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-14T08:59:50Z",
    "title_canon_sha256": "6ed5d61a2ef0aa9701b29add4c30decc21b5eb3af21f0e9c3a13611589bf6a3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3130",
    "kind": "arxiv",
    "version": 1
  }
}