Pith Number

pith:PI7KUJO6

pith:2010:PI7KUJO6CMCS6H4XYQM72SSA5R

not attested not anchored not stored refs pending

The classification of minimal product-quotient surfaces with $p_g=0$

Ingrid Bauer, Roberto Pignatelli

arxiv:1006.3209 v2 · 2010-06-16 · math.AG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PI7KUJO6CMCS6H4XYQM72SSA5R}

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	2026-05-18T04:25:03.112841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a3eaa25de13052f1f97c419fd4a40ec5869ac2c5ea7f1b2c74b4ed59fee0bb6

Aliases

arxiv: 1006.3209 · arxiv_version: 1006.3209v2 · doi: 10.48550/arxiv.1006.3209 · pith_short_12: PI7KUJO6CMCS · pith_short_16: PI7KUJO6CMCS6H4X · pith_short_8: PI7KUJO6

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/PI7KUJO6CMCS6H4XYQM72SSA5R \
  | 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: 7a3eaa25de13052f1f97c419fd4a40ec5869ac2c5ea7f1b2c74b4ed59fee0bb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29b9a97b0ed309493da515ab6bdea4f47dfbee6a580251a5b37a0179878cd3f6",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-06-16T13:34:39Z",
    "title_canon_sha256": "d74f3e5db42999150227fb2e750c361b419011d777db94ee4c36b3d8ab946b2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.3209",
    "kind": "arxiv",
    "version": 2
  }
}