Pith Number

pith:WFX3O73J

pith:2010:WFX3O73JCK6FNWPQAPJF3KGQPN

not attested not anchored not stored refs pending

On fibered commensurability

Danny Calegari, Hongbin Sun, Shicheng Wang

arxiv:1003.0411 v2 · 2010-03-01 · math.GT · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WFX3O73JCK6FNWPQAPJF3KGQPN}

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	2026-05-18T04:25:13.320654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b16fb77f6912bc56d9f003d25da8d07b5e0c955eecdfa66a869df3d8561f5ea1

Aliases

arxiv: 1003.0411 · arxiv_version: 1003.0411v2 · doi: 10.48550/arxiv.1003.0411 · pith_short_12: WFX3O73JCK6F · pith_short_16: WFX3O73JCK6FNWPQ · pith_short_8: WFX3O73J

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/WFX3O73JCK6FNWPQAPJF3KGQPN \
  | 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: b16fb77f6912bc56d9f003d25da8d07b5e0c955eecdfa66a869df3d8561f5ea1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14a747949799543136ea04891aebd7bf0ae4beb97cdcc086059ddff077ee3e84",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-03-01T17:51:32Z",
    "title_canon_sha256": "50f7af4af3d35a0364a3c27e1dd2a42bccb0dd482ec0182a32bdc1c87f620ed1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.0411",
    "kind": "arxiv",
    "version": 2
  }
}