Pith Number

pith:2IUBLWUI

pith:2002:2IUBLWUI47QQNE4L4EZGKQ5KHA

not attested not anchored not stored refs pending

Every orientable 3-manifold is a B\Gamma

Danny Calegari

arxiv:math/0206066 v2 · 2002-06-07 · 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{2IUBLWUI47QQNE4L4EZGKQ5KHA}

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	2026-05-18T02:41:33.011339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d22815da88e7e106938be1326543aa381cff419d9e0f1111cb1923ac33a1a3c5

Aliases

arxiv: math/0206066 · arxiv_version: math/0206066v2 · doi: 10.48550/arxiv.math/0206066 · pith_short_12: 2IUBLWUI47QQ · pith_short_16: 2IUBLWUI47QQNE4L · pith_short_8: 2IUBLWUI

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/2IUBLWUI47QQNE4L4EZGKQ5KHA \
  | 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: d22815da88e7e106938be1326543aa381cff419d9e0f1111cb1923ac33a1a3c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "295b68a09f6541c9a875e788069d557cfedeec54c6dfbffb06dd7313d5ed6422",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2002-06-07T11:15:10Z",
    "title_canon_sha256": "293d8221863eb83d2a45efacbf9f0684540495890e6d86277bd9b667c951837a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0206066",
    "kind": "arxiv",
    "version": 2
  }
}