Pith Number

pith:BEUT265J

pith:2007:BEUT265JPKHMNXRR6HLOLJ57SN

not attested not anchored not stored refs pending

Criteria for virtual fibering

Ian Agol

arxiv:0707.4522 v2 · 2007-07-31 · 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{BEUT265JPKHMNXRR6HLOLJ57SN}

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	2026-05-18T02:58:12.475511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09293d7ba97a8ec6de31f1d6e5a7bf93405f53958f0b333d23504612ec5276d7

Aliases

arxiv: 0707.4522 · arxiv_version: 0707.4522v2 · doi: 10.48550/arxiv.0707.4522 · pith_short_12: BEUT265JPKHM · pith_short_16: BEUT265JPKHMNXRR · pith_short_8: BEUT265J

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/BEUT265JPKHMNXRR6HLOLJ57SN \
  | 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: 09293d7ba97a8ec6de31f1d6e5a7bf93405f53958f0b333d23504612ec5276d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbdc1073f31334162199cb18119dbcb5cc6a6ae9db2a2e58a716f6881584aa35",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2007-07-31T02:09:53Z",
    "title_canon_sha256": "43fc0f3f5203ac3df849b67ab1dd2dc32a6da5c129099ef84d33c1954eeb5b45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.4522",
    "kind": "arxiv",
    "version": 2
  }
}