Pith Number

pith:XCLQGMUH

pith:2010:XCLQGMUHP7LBGUEZQ654OUQEYA

not attested not anchored not stored refs pending

Lyubeznik numbers of projective schemes

Wenliang Zhang

arxiv:1001.3662 v4 · 2010-01-20 · math.AC · 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{XCLQGMUHP7LBGUEZQ654OUQEYA}

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	2026-05-18T04:16:42.363444Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8970332877fd613509987bbc75204c03f4fdf9cbd0380d91457741864286bc3

Aliases

arxiv: 1001.3662 · arxiv_version: 1001.3662v4 · doi: 10.48550/arxiv.1001.3662 · pith_short_12: XCLQGMUHP7LB · pith_short_16: XCLQGMUHP7LBGUEZ · pith_short_8: XCLQGMUH

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/XCLQGMUHP7LBGUEZQ654OUQEYA \
  | 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: b8970332877fd613509987bbc75204c03f4fdf9cbd0380d91457741864286bc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a98f52a8ed6277bf2dccadd84e06f8282ad74bd6c501149607c951e39f696dfd",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-01-20T20:16:28Z",
    "title_canon_sha256": "1ac0007c4b084fef0b3610746aacbbc077dcedbb0bc07a427712f00dc189fe17"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.3662",
    "kind": "arxiv",
    "version": 4
  }
}