Pith Number

pith:NZCFVISJ

pith:2012:NZCFVISJGVFZ53H3YSEZ3DLKL6

not attested not anchored not stored refs pending

Frobenius criteria of freeness and Gorensteinness

Jinjia Li

arxiv:1204.2456 v1 · 2012-04-11 · 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{NZCFVISJGVFZ53H3YSEZ3DLKL6}

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	2026-05-18T03:58:05.302430Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6e445aa249354b9eecfbc4899d8d6a5f98808089699f0729935257a4bbd69f46

Aliases

arxiv: 1204.2456 · arxiv_version: 1204.2456v1 · doi: 10.48550/arxiv.1204.2456 · pith_short_12: NZCFVISJGVFZ · pith_short_16: NZCFVISJGVFZ53H3 · pith_short_8: NZCFVISJ

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/NZCFVISJGVFZ53H3YSEZ3DLKL6 \
  | 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: 6e445aa249354b9eecfbc4899d8d6a5f98808089699f0729935257a4bbd69f46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c215b8ccc6791c45ba8e71bd86e9e83f5b7e98447a9ec19c114411931cb3e298",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-04-11T14:13:50Z",
    "title_canon_sha256": "9ddbd7afc90287a8b8ae571d4bb836702793bb3bac7580673075e49a5de1cb7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.2456",
    "kind": "arxiv",
    "version": 1
  }
}