Pith Number

pith:CTOB5HQ7

pith:2013:CTOB5HQ7ALXIUFVVUGWG3Q5MET

not attested not anchored not stored refs pending

Varieties with too many rational points

D. Loughran, T.D. Browning

arxiv:1311.5755 v3 · 2013-11-22 · 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{CTOB5HQ7ALXIUFVVUGWG3Q5MET}

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	2026-05-18T00:48:10.232231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14dc1e9e1f02ee8a16b5a1ac6dc3ac24f210388b526247a0ed638e113bc9fd88

Aliases

arxiv: 1311.5755 · arxiv_version: 1311.5755v3 · doi: 10.48550/arxiv.1311.5755 · pith_short_12: CTOB5HQ7ALXI · pith_short_16: CTOB5HQ7ALXIUFVV · pith_short_8: CTOB5HQ7

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/CTOB5HQ7ALXIUFVVUGWG3Q5MET \
  | 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: 14dc1e9e1f02ee8a16b5a1ac6dc3ac24f210388b526247a0ed638e113bc9fd88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "913cf94da15c012716696e2a8c105a4993d55d4d0c989527bbbde8eaa6f47c24",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-22T14:04:16Z",
    "title_canon_sha256": "93d4c029a45e7509b8f01f4f7c381792629bf1e3775d8c1b951a8dc0ec3a4056"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5755",
    "kind": "arxiv",
    "version": 3
  }
}