Pith Number

pith:2K6F6AIX

pith:2014:2K6F6AIXCWWO77RDE2WLGPDNM2

not attested not anchored not stored refs pending

A positive proportion of plane cubics fail the Hasse principle

Manjul Bhargava

arxiv:1402.1131 v1 · 2014-02-05 · math.NT · 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{2K6F6AIXCWWO77RDE2WLGPDNM2}

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	2026-05-18T03:00:01.606642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2bc5f011715aceffe2326acb33c6d66aaa60102b55a320d46f2d83c06e1818f

Aliases

arxiv: 1402.1131 · arxiv_version: 1402.1131v1 · doi: 10.48550/arxiv.1402.1131 · pith_short_12: 2K6F6AIXCWWO · pith_short_16: 2K6F6AIXCWWO77RD · pith_short_8: 2K6F6AIX

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/2K6F6AIXCWWO77RDE2WLGPDNM2 \
  | 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: d2bc5f011715aceffe2326acb33c6d66aaa60102b55a320d46f2d83c06e1818f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1d223d517c4df16298fdd7244259b33586dd8e50ffb2b265ccbb76d7298dc56",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-02-05T19:18:33Z",
    "title_canon_sha256": "38afdf48777446686c0b737e8f2c7e38fe06ef5a30078d4f3d2398e7f36cdfac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.1131",
    "kind": "arxiv",
    "version": 1
  }
}