Pith Number

pith:C4P7YY7M

pith:2011:C4P7YY7MC7IAYLIMOES7IBHLXJ

not attested not anchored not stored refs pending

Weakly-exceptional singularities in higher dimensions

Constantin Shramov, Ivan Cheltsov

arxiv:1111.1920 v4 · 2011-11-08 · math.AG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C4P7YY7MC7IAYLIMOES7IBHLXJ}

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	2026-05-18T03:55:01.608711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

171ffc63ec17d00c2d0c7125f404ebba629c7e230543966da88b13fa7bba84fa

Aliases

arxiv: 1111.1920 · arxiv_version: 1111.1920v4 · doi: 10.48550/arxiv.1111.1920 · pith_short_12: C4P7YY7MC7IA · pith_short_16: C4P7YY7MC7IAYLIM · pith_short_8: C4P7YY7M

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/C4P7YY7MC7IAYLIMOES7IBHLXJ \
  | 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: 171ffc63ec17d00c2d0c7125f404ebba629c7e230543966da88b13fa7bba84fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1635463ad6240244f1033f6a15260c8a640215b3165e654556a4a6249f0e466c",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-11-08T14:38:32Z",
    "title_canon_sha256": "d3d293ab983bfc3ed8e19a8ccbde7a161a3cc7ef8e44ae6e8f8e751d710c7fbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1920",
    "kind": "arxiv",
    "version": 4
  }
}