Pith Number

pith:7U7NW74P

pith:2010:7U7NW74PFMMJJD53AQMCQ7GXY6

not attested not anchored not stored refs pending

A simple proof of Perelman's collapsing theorem for 3-manifolds

Jian Ge, Jianguo Cao

arxiv:1003.2215 v3 · 2010-03-10 · math.DG · 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{7U7NW74PFMMJJD53AQMCQ7GXY6}

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	2026-05-18T04:39:38.925203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd3edb7f8f2b18948fbb0418287cd7c784bf6a967beca5a897591583894d089d

Aliases

arxiv: 1003.2215 · arxiv_version: 1003.2215v3 · doi: 10.48550/arxiv.1003.2215 · pith_short_12: 7U7NW74PFMMJ · pith_short_16: 7U7NW74PFMMJJD53 · pith_short_8: 7U7NW74P

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/7U7NW74PFMMJJD53AQMCQ7GXY6 \
  | 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: fd3edb7f8f2b18948fbb0418287cd7c784bf6a967beca5a897591583894d089d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e35decf61b47710af41c2ce2f6c9b96ad29d2ba5bdc9de48135dd34c47639c0",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-03-10T21:36:31Z",
    "title_canon_sha256": "b97f6d198022417583f3eb6b56d1d1892f44ab3c4465d04dfe82e27cccadb7ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2215",
    "kind": "arxiv",
    "version": 3
  }
}