Pith Number

pith:PN5MOKOB

pith:2012:PN5MOKOBUGV4IL3TVNUMNBFZZH

not attested not anchored not stored refs pending

Smoothable locally Cohen--Macaulay and non Cohen--Macaulay multiple structures on curves

Bangere P. Purnaprajna, Francisco Javier Gallego, Miguel Gonz\'alez

arxiv:1211.5458 v1 · 2012-11-23 · math.AG · 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{PN5MOKOBUGV4IL3TVNUMNBFZZH}

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	2026-05-18T03:40:02.508850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b7ac729c1a1abc42f73ab68c684b9c9fb479dfe9c031e9baf0bc92de8463d49

Aliases

arxiv: 1211.5458 · arxiv_version: 1211.5458v1 · doi: 10.48550/arxiv.1211.5458 · pith_short_12: PN5MOKOBUGV4 · pith_short_16: PN5MOKOBUGV4IL3T · pith_short_8: PN5MOKOB

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/PN5MOKOBUGV4IL3TVNUMNBFZZH \
  | 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: 7b7ac729c1a1abc42f73ab68c684b9c9fb479dfe9c031e9baf0bc92de8463d49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29c8cd6454bfbb1b107368bd90e37caec3b606c5670676f0904725dfc08081c4",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-11-23T10:28:48Z",
    "title_canon_sha256": "7ca368f3359d2c0794aa74743c0f7a4325c9095df872725db524705baddbb252"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5458",
    "kind": "arxiv",
    "version": 1
  }
}