Pith Number

pith:VGA2Q7FN

pith:2009:VGA2Q7FNR5RFHEDAVVMHR2PCMS

not attested not anchored not stored refs pending

Classifying birationally commutative projective surfaces

Susan J. Sierra

arxiv:0910.5018 v1 · 2009-10-27 · 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{VGA2Q7FNR5RFHEDAVVMHR2PCMS}

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	2026-05-18T04:27:47.830476Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a981a87cad8f62539060ad5878e9e2649ce283e0e892f92ab2f75e06764a74c6

Aliases

arxiv: 0910.5018 · arxiv_version: 0910.5018v1 · doi: 10.48550/arxiv.0910.5018 · pith_short_12: VGA2Q7FNR5RF · pith_short_16: VGA2Q7FNR5RFHEDA · pith_short_8: VGA2Q7FN

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/VGA2Q7FNR5RFHEDAVVMHR2PCMS \
  | 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: a981a87cad8f62539060ad5878e9e2649ce283e0e892f92ab2f75e06764a74c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77a46ee1c816f75784de3f1b2b60154d577ebef0e2cba69e93c4592c129b3f8a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2009-10-27T01:00:03Z",
    "title_canon_sha256": "b6fe7e5a01831f1401baba4a6fd8d90322abd0003fc27c30aedc0a98ad3c80a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.5018",
    "kind": "arxiv",
    "version": 1
  }
}