Pith Number

pith:2AMKZ2ZZ

pith:2006:2AMKZ2ZZDU6YVDYCYF3V6QJ5KG

not attested not anchored not stored refs pending

Volume growth, curvature decay, and critical metrics

Gang Tian, Jeff Viaclovsky

arxiv:math/0612491 v1 · 2006-12-17 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2AMKZ2ZZDU6YVDYCYF3V6QJ5KG}

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

A Gap Theorem for Half-Conformally Flat Manifolds

Receipt and verification

First computed	2026-07-04T15:48:29.309369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d018aceb391d3d8a8f02c1775f413d51b0980866e32e7468682f0d2081f80b0e

Aliases

arxiv: math/0612491 · arxiv_version: math/0612491v1 · doi: 10.48550/arxiv.math/0612491 · pith_short_12: 2AMKZ2ZZDU6Y · pith_short_16: 2AMKZ2ZZDU6YVDYC · pith_short_8: 2AMKZ2ZZ

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/2AMKZ2ZZDU6YVDYCYF3V6QJ5KG \
  | 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: d018aceb391d3d8a8f02c1775f413d51b0980866e32e7468682f0d2081f80b0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6c687e91324cabb501f4460f9972e1d092188808b162e5e5e1f5d7e557e138c",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2006-12-17T17:59:16Z",
    "title_canon_sha256": "393c200234bac23009982f816c94a340a563997d324ed39c41f96a112e139bce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612491",
    "kind": "arxiv",
    "version": 1
  }
}