Pith Number

pith:M3VCTHOA

pith:2011:M3VCTHOAGM3BEDAVCCJG7NMR7B

not attested not anchored not stored refs pending

Non-rational centers of log canonical singularities

Christopher D. Hacon, Valery Alexeev

arxiv:1109.4164 v2 · 2011-09-19 · 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{M3VCTHOAGM3BEDAVCCJG7NMR7B}

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	2026-05-18T03:52:26.298199Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66ea299dc03336120c1510926fb591f84c7f431c05dc242353ce5fd2194b4194

Aliases

arxiv: 1109.4164 · arxiv_version: 1109.4164v2 · doi: 10.48550/arxiv.1109.4164 · pith_short_12: M3VCTHOAGM3B · pith_short_16: M3VCTHOAGM3BEDAV · pith_short_8: M3VCTHOA

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/M3VCTHOAGM3BEDAVCCJG7NMR7B \
  | 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: 66ea299dc03336120c1510926fb591f84c7f431c05dc242353ce5fd2194b4194

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c03595dfa9d74231e4e2664969d71384b541f5535d2268a4585acd4a33ba2cb7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-09-19T20:22:06Z",
    "title_canon_sha256": "6d739723b24c1585996c74cabd3069808e9aa2ad738d48c0760439c6bce5f138"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4164",
    "kind": "arxiv",
    "version": 2
  }
}