Pith Number

pith:LQLUYPDW

pith:2010:LQLUYPDWQE6P65VGEIGZL6P644

not attested not anchored not stored refs pending

Two interesting examples of $\mathcal{D}$-modules in characteristic $p>0$

Gennady Lyubeznik, Mordechai Katzman, Wenliang Zhang

arxiv:1010.2525 v1 · 2010-10-12 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LQLUYPDWQE6P65VGEIGZL6P644}

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	2026-05-18T02:58:01.663769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c174c3c76813cff76a6220d95f9fee7110854735144af6b9a4a96056c4e4b80

Aliases

arxiv: 1010.2525 · arxiv_version: 1010.2525v1 · doi: 10.48550/arxiv.1010.2525 · pith_short_12: LQLUYPDWQE6P · pith_short_16: LQLUYPDWQE6P65VG · pith_short_8: LQLUYPDW

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/LQLUYPDWQE6P65VGEIGZL6P644 \
  | 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: 5c174c3c76813cff76a6220d95f9fee7110854735144af6b9a4a96056c4e4b80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eefe5ca577d3dce25a98241bdacf972ded8b0bbf6c0750423c2b093e68136afa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-10-12T22:05:47Z",
    "title_canon_sha256": "c8cae5514409124f4eea6a76d9a5b189ab706ee5bb69b1c66bfd8831743aa6ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2525",
    "kind": "arxiv",
    "version": 1
  }
}