Pith Number

pith:3GE67FJL

pith:2006:3GE67FJLD6LULP2BRL37V7EEXP

not attested not anchored not stored refs pending

Hamilton-Perelman's Proof of the Poincar\'e Conjecture and the Geometrization Conjecture

Huai-Dong Cao, Xi-Ping Zhu

arxiv:math/0612069 v1 · 2006-12-03 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3GE67FJLD6LULP2BRL37V7EEXP}

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.

Cited by

1 paper in Pith

Off-diagonal solutions in Einsteingravity modeling f(R) gravity and dynamical darkenergy vs Lambda CDM cosmology

Receipt and verification

First computed	2026-07-04T14:57:58.883861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d989ef952b1f9745bf418af7fafc84bbc7ae9ddb705502d488733b4a0d48f6ea

Aliases

arxiv: math/0612069 · arxiv_version: math/0612069v1 · doi: 10.48550/arxiv.math/0612069 · pith_short_12: 3GE67FJLD6LU · pith_short_16: 3GE67FJLD6LULP2B · pith_short_8: 3GE67FJL

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/3GE67FJLD6LULP2BRL37V7EEXP \
  | 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: d989ef952b1f9745bf418af7fafc84bbc7ae9ddb705502d488733b4a0d48f6ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c5c7bf6ec4873b460eeb551ee202acadf106b4cff92d36101ffb42d55274e19",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2006-12-03T18:35:08Z",
    "title_canon_sha256": "3f73af27352e45bdc367ab2f6e4921bb3a12cf2df5417c2e67597262ede1714f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612069",
    "kind": "arxiv",
    "version": 1
  }
}