Pith Number

pith:ZMZ54J4Y

pith:2011:ZMZ54J4Y4GQG5SXEHPF33I4IL6

not attested not anchored not stored refs pending

Rational surfaces with a large group of automorphisms

Igor Dolgachev, Serge Cantat

arxiv:1106.0930 v2 · 2011-06-05 · math.AG · math.DS · 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{ZMZ54J4Y4GQG5SXEHPF33I4IL6}

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	2026-05-18T04:03:55.875535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb33de2798e1a06ecae43bcbbda3885fa67ef1917e3be50faf5c10d2b9484c82

Aliases

arxiv: 1106.0930 · arxiv_version: 1106.0930v2 · doi: 10.48550/arxiv.1106.0930 · pith_short_12: ZMZ54J4Y4GQG · pith_short_16: ZMZ54J4Y4GQG5SXE · pith_short_8: ZMZ54J4Y

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/ZMZ54J4Y4GQG5SXEHPF33I4IL6 \
  | 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: cb33de2798e1a06ecae43bcbbda3885fa67ef1917e3be50faf5c10d2b9484c82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75e0491e9a8decf11014c15d93d2afdaf76c1a3b98fc08f331e8f0e0ffe5aaa9",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-06-05T20:35:13Z",
    "title_canon_sha256": "f71686b039dbd34b3675f5dd933c13b8c7ac881f0583debc4c7008ec12e584eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0930",
    "kind": "arxiv",
    "version": 2
  }
}