Pith Number

pith:CB7HE4FI

pith:2012:CB7HE4FICTFX5EUJOXMR7IXZ6Z

not attested not anchored not stored refs pending

Dualities in Koszul graded AS Gorenstein algebras

Roberto Martinez-Villa

arxiv:1211.0945 v1 · 2012-11-05 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CB7HE4FICTFX5EUJOXMR7IXZ6Z}

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	2026-05-18T03:41:31.217032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

107e7270a814cb7e928975d91fa2f9f65f4ed6680d694417ee14396084a05556

Aliases

arxiv: 1211.0945 · arxiv_version: 1211.0945v1 · doi: 10.48550/arxiv.1211.0945 · pith_short_12: CB7HE4FICTFX · pith_short_16: CB7HE4FICTFX5EUJ · pith_short_8: CB7HE4FI

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/CB7HE4FICTFX5EUJOXMR7IXZ6Z \
  | 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: 107e7270a814cb7e928975d91fa2f9f65f4ed6680d694417ee14396084a05556

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82a8a2711ba3fc8e92b14a475c188758a63eb5e49d24c798c7ef448793f88b04",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-11-05T17:45:03Z",
    "title_canon_sha256": "a6564347122cf1c85a5e7940b3bbe259d137076ada1027a9c4670b348e608546"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0945",
    "kind": "arxiv",
    "version": 1
  }
}