Pith Number

pith:X72QXE4K

pith:2012:X72QXE4KCPEYAOH3NGWWKTPWKI

not attested not anchored not stored refs pending

Moduli of surfaces with an anti-canonical cycle

Mark Gross, Paul Hacking, Sean Keel

arxiv:1211.6367 v5 · 2012-11-27 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X72QXE4KCPEYAOH3NGWWKTPWKI}

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	2026-05-17T23:53:18.239132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bff50b938a13c98038fb69ad654df65220a8a16fb57c524a22d67da511767ec4

Aliases

arxiv: 1211.6367 · arxiv_version: 1211.6367v5 · doi: 10.48550/arxiv.1211.6367 · pith_short_12: X72QXE4KCPEY · pith_short_16: X72QXE4KCPEYAOH3 · pith_short_8: X72QXE4K

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/X72QXE4KCPEYAOH3NGWWKTPWKI \
  | 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: bff50b938a13c98038fb69ad654df65220a8a16fb57c524a22d67da511767ec4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f5a8671ce103d17f705cd08d0036b42d1250b53ca99eb02e58b95e4ee3826d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-11-27T17:34:35Z",
    "title_canon_sha256": "454c7d000df237dcc95242bd0f68df315d99523bcf69ae9d33ee960e93c706f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.6367",
    "kind": "arxiv",
    "version": 5
  }
}