Pith Number

pith:QDCTU7A6

pith:2011:QDCTU7A6EZDBLU6JF6A3UJYVUP

not attested not anchored not stored refs pending

On the Weak-Lefschetz property for Artinian Gorenstein algebras

Alfio Ragusa, Giuseppe Zappala

arxiv:1112.1498 v1 · 2011-12-07 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QDCTU7A6EZDBLU6JF6A3UJYVUP}

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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	2026-05-18T04:06:54.459069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80c53a7c1e264615d3c92f81ba2715a3d4a810e9f6e98231d852f34ce12f0aa5

Aliases

arxiv: 1112.1498 · arxiv_version: 1112.1498v1 · doi: 10.48550/arxiv.1112.1498 · pith_short_12: QDCTU7A6EZDB · pith_short_16: QDCTU7A6EZDBLU6J · pith_short_8: QDCTU7A6

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/QDCTU7A6EZDBLU6JF6A3UJYVUP \
  | 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: 80c53a7c1e264615d3c92f81ba2715a3d4a810e9f6e98231d852f34ce12f0aa5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4da36c9f3289a15dd4ab127acab8ec340ff11c925dbc35fa8b6500019ecf1c0e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-12-07T08:41:41Z",
    "title_canon_sha256": "f886385480c8d00736b3ad9bf58e5b165159f919a06ad3d771493c180cc26924"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1498",
    "kind": "arxiv",
    "version": 1
  }
}