Pith Number

pith:SPPDKHCB

pith:2010:SPPDKHCB5Q7YZGLFNLS5ANYCJU

not attested not anchored not stored refs pending

Cohen-Macaulayness of bipartite graphs, revisited

Rashid Zaare-Nahandi

arxiv:1012.0457 v2 · 2010-12-02 · 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{SPPDKHCB5Q7YZGLFNLS5ANYCJU}

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	2026-05-18T04:33:28.746809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93de351c41ec3f8c99656ae5d037024d1dad14c1d37c413633cabb01490a41d2

Aliases

arxiv: 1012.0457 · arxiv_version: 1012.0457v2 · doi: 10.48550/arxiv.1012.0457 · pith_short_12: SPPDKHCB5Q7Y · pith_short_16: SPPDKHCB5Q7YZGLF · pith_short_8: SPPDKHCB

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/SPPDKHCB5Q7YZGLFNLS5ANYCJU \
  | 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: 93de351c41ec3f8c99656ae5d037024d1dad14c1d37c413633cabb01490a41d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81be244bcdb610f5cdec72724d2534eb513ffcb7123dbd8e478ee991a9b4cd7e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-12-02T15:38:19Z",
    "title_canon_sha256": "c63d150dc1768e3afe1b9bb67f6200547a7655b963f08a7060992dceb41e6635"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0457",
    "kind": "arxiv",
    "version": 2
  }
}