Pith Number

pith:2YL3MHWL

pith:2012:2YL3MHWLAHNX36JJQL55GCDFFD

not attested not anchored not stored refs pending

Density of Ch\^atelet surfaces failing the Hasse principle

R. de la Bret\`eche, T. D. Browning

arxiv:1210.4010 v2 · 2012-10-15 · 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{2YL3MHWLAHNX36JJQL55GCDFFD}

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	2026-05-18T00:15:59.793617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d617b61ecb01db7df92982fbd3086528f4fc84705439410510a1db7a3244b6d7

Aliases

arxiv: 1210.4010 · arxiv_version: 1210.4010v2 · doi: 10.48550/arxiv.1210.4010 · pith_short_12: 2YL3MHWLAHNX · pith_short_16: 2YL3MHWLAHNX36JJ · pith_short_8: 2YL3MHWL

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/2YL3MHWLAHNX36JJQL55GCDFFD \
  | 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: d617b61ecb01db7df92982fbd3086528f4fc84705439410510a1db7a3244b6d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae074974d30d2a016312a4753b37004be5fdbd2f4adf04f0b0e8a883ecc3f590",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-10-15T12:49:36Z",
    "title_canon_sha256": "aee82bd6da4922ce999aec423770e214b0ee1af716d86695209066a6acdbb8e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4010",
    "kind": "arxiv",
    "version": 2
  }
}