Pith Number

pith:5DDJSFRP

pith:2012:5DDJSFRPRLVQPGQ6T3MENCYN5L

not attested not anchored not stored refs pending

A combinatorial Li-Yau inequality and rational points on curves

Fumiharu Kato, Gunther Cornelissen, Janne Kool

arxiv:1211.2681 v3 · 2012-11-12 · 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{5DDJSFRPRLVQPGQ6T3MENCYN5L}

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	2026-05-18T03:05:01.609570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8c699162f8aeb079a1e9ed8468b0deac660c59d9329833dd13cccde39278f08

Aliases

arxiv: 1211.2681 · arxiv_version: 1211.2681v3 · doi: 10.48550/arxiv.1211.2681 · pith_short_12: 5DDJSFRPRLVQ · pith_short_16: 5DDJSFRPRLVQPGQ6 · pith_short_8: 5DDJSFRP

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/5DDJSFRPRLVQPGQ6T3MENCYN5L \
  | 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: e8c699162f8aeb079a1e9ed8468b0deac660c59d9329833dd13cccde39278f08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "364a64aff36b818401019bf3e28922f5b1b8ea80440fd771d97019af4f496a74",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-11-12T16:20:08Z",
    "title_canon_sha256": "3eb0d4f26831be1f285d9fff14c22c08263d542f8dc4af66cdacf360bbe4a57e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2681",
    "kind": "arxiv",
    "version": 3
  }
}