Pith Number

pith:3WNSJWU3

pith:2012:3WNSJWU3NDMCZ25ZPKOYFEYV7R

not attested not anchored not stored refs pending

The dual complex of singularities

Chenyang Xu, J\'anos Koll\'ar, Tommaso de Fernex

arxiv:1212.1675 v3 · 2012-12-07 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3WNSJWU3NDMCZ25ZPKOYFEYV7R}

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	2026-05-18T02:56:19.298345Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd9b24da9b68d82cebb97a9d829315fc4c34b89e6320423cb3f6f65b9f6552b4

Aliases

arxiv: 1212.1675 · arxiv_version: 1212.1675v3 · doi: 10.48550/arxiv.1212.1675 · pith_short_12: 3WNSJWU3NDMC · pith_short_16: 3WNSJWU3NDMCZ25Z · pith_short_8: 3WNSJWU3

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/3WNSJWU3NDMCZ25ZPKOYFEYV7R \
  | 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: dd9b24da9b68d82cebb97a9d829315fc4c34b89e6320423cb3f6f65b9f6552b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d5a22d58f8f4d52bc554c89f740d2e06794deed40399be7a99232dd36df34b9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-12-07T18:38:25Z",
    "title_canon_sha256": "f3c0554ec5aaa66e20461aaf45b712b38bf653be6a7ffb1a153515dc8231d27c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1675",
    "kind": "arxiv",
    "version": 3
  }
}