Pith Number

pith:K7D63IP3

pith:2013:K7D63IP3TS525UDUYQ7ZUWGTPM

not attested not anchored not stored refs pending

An analogue of Liouville's Theorem and an application to cubic surfaces

David McKinnon, Michael Roth

arxiv:1306.2977 v1 · 2013-06-12 · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K7D63IP3TS525UDUYQ7ZUWGTPM}

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	2026-05-18T03:20:59.947409Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57c7eda1fb9cbbaed074c43f9a58d37b202f1ceff05a1017d893f069b886f37f

Aliases

arxiv: 1306.2977 · arxiv_version: 1306.2977v1 · doi: 10.48550/arxiv.1306.2977 · pith_short_12: K7D63IP3TS52 · pith_short_16: K7D63IP3TS525UDU · pith_short_8: K7D63IP3

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/K7D63IP3TS525UDUYQ7ZUWGTPM \
  | 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: 57c7eda1fb9cbbaed074c43f9a58d37b202f1ceff05a1017d893f069b886f37f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72622950102892f1b1c8594ef48e355b8c1743754eced9e6947861e8f80feb6f",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-06-12T21:10:44Z",
    "title_canon_sha256": "a2c842b92104c12064fbb4d004bf4b27ca31c999c078a3bd144944ec2b1933f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2977",
    "kind": "arxiv",
    "version": 1
  }
}