Pith Number

pith:D7FHKR4Z

pith:2011:D7FHKR4ZFDQBXA4KHCCUJ535DS

not attested not anchored not stored refs pending

The possible extremal Betti numbers of a homogeneous ideal

J\"urgen Herzog, Leila Sharifan, Matteo Varbaro

arxiv:1111.0442 v4 · 2011-11-02 · 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{D7FHKR4ZFDQBXA4KHCCUJ535DS}

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	2026-05-18T03:14:50.400353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fca75479928e01b838a388544f77d1cb464615595932f4bb299e0cc271774a1

Aliases

arxiv: 1111.0442 · arxiv_version: 1111.0442v4 · doi: 10.48550/arxiv.1111.0442 · pith_short_12: D7FHKR4ZFDQB · pith_short_16: D7FHKR4ZFDQBXA4K · pith_short_8: D7FHKR4Z

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/D7FHKR4ZFDQBXA4KHCCUJ535DS \
  | 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: 1fca75479928e01b838a388544f77d1cb464615595932f4bb299e0cc271774a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa96d75c1254a2b07786dc712213526851d1c07bb91d211674752fc06b7d8b31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-11-02T09:46:55Z",
    "title_canon_sha256": "bb0d19aefed7b6912b8448874d7cb88d91df1d7ff4a2b7db2667224ba2e42ce7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0442",
    "kind": "arxiv",
    "version": 4
  }
}