Pith Number

pith:PFFZOWAF

pith:2019:PFFZOWAFMTFQ2ZDC24ZYA4HCPW

not attested not anchored not stored refs pending

Cohen Macaulay Hybrid Graphs

Fazal Abbas, Imran Anwar, Safyan Ahmad

arxiv:1904.03824 v1 · 2019-04-08 · math.AC · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PFFZOWAFMTFQ2ZDC24ZYA4HCPW}

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	2026-05-17T23:49:08.027564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

794b97580564cb0d6462d7338070e27d91d4bd9ff402e6bb7a67e703fa82f678

Aliases

arxiv: 1904.03824 · arxiv_version: 1904.03824v1 · doi: 10.48550/arxiv.1904.03824 · pith_short_12: PFFZOWAFMTFQ · pith_short_16: PFFZOWAFMTFQ2ZDC · pith_short_8: PFFZOWAF

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/PFFZOWAFMTFQ2ZDC24ZYA4HCPW \
  | 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: 794b97580564cb0d6462d7338070e27d91d4bd9ff402e6bb7a67e703fa82f678

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3562860f96ea9692567d336dbbd638b1534f0aa754fd5dd6d66d90b8422d32ca",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2019-04-08T03:58:02Z",
    "title_canon_sha256": "91f13f22c3eab23ede567d155a483db7a183fb429e7b6841dc6faf31254a2f2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.03824",
    "kind": "arxiv",
    "version": 1
  }
}