Pith Number

pith:2PM3ZFC7

pith:2013:2PM3ZFC7P3ADWJILZVDPW55M6T

not attested not anchored not stored refs pending

Representing finite distributive lattices as congruence lattices of lattices

George Gr\"atzer

arxiv:1309.7511 v1 · 2013-09-28 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2PM3ZFC7P3ADWJILZVDPW55M6T}

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	2026-05-18T03:11:56.776732Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3d9bc945f7ec03b250bcd46fb77acf4c830fb102618b747fbe29af4b5e4f539

Aliases

arxiv: 1309.7511 · arxiv_version: 1309.7511v1 · doi: 10.48550/arxiv.1309.7511 · pith_short_12: 2PM3ZFC7P3AD · pith_short_16: 2PM3ZFC7P3ADWJIL · pith_short_8: 2PM3ZFC7

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/2PM3ZFC7P3ADWJILZVDPW55M6T \
  | 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: d3d9bc945f7ec03b250bcd46fb77acf4c830fb102618b747fbe29af4b5e4f539

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b93ca51588485ee620c8f5c97452f1e40087521b0e7525481d1f4ff17abd0664",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-09-28T23:32:01Z",
    "title_canon_sha256": "2233a402f01f57a8aac903749db532257073e86def19e96ae5760b2fa0674eaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7511",
    "kind": "arxiv",
    "version": 1
  }
}