Pith Number

pith:LHJWUW2S

pith:2016:LHJWUW2SVRPE2ZLUKOO3OYZHM3

not attested not anchored not stored refs pending

The logical complexity of finitely generated commutative rings

Anatole Kh\'elif, Eudes Naziazeno, Matthias Aschenbrenner, Thomas Scanlon

arxiv:1610.04768 v1 · 2016-10-15 · math.LO · 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{LHJWUW2SVRPE2ZLUKOO3OYZHM3}

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	2026-05-18T01:02:07.132704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59d36a5b52ac5e4d6574539db7632766f527fb9fd1fd182cdc23388894716613

Aliases

arxiv: 1610.04768 · arxiv_version: 1610.04768v1 · doi: 10.48550/arxiv.1610.04768 · pith_short_12: LHJWUW2SVRPE · pith_short_16: LHJWUW2SVRPE2ZLU · pith_short_8: LHJWUW2S

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/LHJWUW2SVRPE2ZLUKOO3OYZHM3 \
  | 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: 59d36a5b52ac5e4d6574539db7632766f527fb9fd1fd182cdc23388894716613

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1aeff3b60b1b7efe9149d8a9ac87635c7ec5a0a917ffb7b1fb812433f94dad15",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2016-10-15T17:55:59Z",
    "title_canon_sha256": "3c977e5af6ed12ef3dabb8ccaebc72575b1e813255c2d6f54b921394513dd884"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.04768",
    "kind": "arxiv",
    "version": 1
  }
}