Pith Number

pith:XEWV6DGH

pith:2012:XEWV6DGHQQ5TXGUVOQWVDEEGV3

not attested not anchored not stored refs pending

Rank of divisors on graphs: an algebro-geometric analysis

Lucia Caporaso

arxiv:1204.3487 v2 · 2012-04-16 · math.AG · 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{XEWV6DGHQQ5TXGUVOQWVDEEGV3}

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	2026-05-18T03:45:00.512094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b92d5f0cc7843b3b9a95742d519086aef61d0c71cd129e52bbb5c46852e8a9af

Aliases

arxiv: 1204.3487 · arxiv_version: 1204.3487v2 · doi: 10.48550/arxiv.1204.3487 · pith_short_12: XEWV6DGHQQ5T · pith_short_16: XEWV6DGHQQ5TXGUV · pith_short_8: XEWV6DGH

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/XEWV6DGHQQ5TXGUVOQWVDEEGV3 \
  | 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: b92d5f0cc7843b3b9a95742d519086aef61d0c71cd129e52bbb5c46852e8a9af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c988a483f2c77b36644d02331d60bbd30aa2053314c2b21fcea7a74d4a3744ef",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-04-16T13:58:48Z",
    "title_canon_sha256": "b69390b96a603b9bd68f6d3101aad9f69b7d3a8aeb8462e1ec73a64e3be809dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.3487",
    "kind": "arxiv",
    "version": 2
  }
}