Pith Number

pith:WX7CVCIP

pith:2013:WX7CVCIPK66U3YRXWIWSJ72MJU

not attested not anchored not stored refs pending

Ramanujan circulant graphs and the conjecture of Hardy-Littlewood and Bateman-Horn

Kohei Katata, Miki Hirano, Yoshinori Yamasaki

arxiv:1310.2130 v3 · 2013-10-08 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WX7CVCIPK66U3YRXWIWSJ72MJU}

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	2026-05-18T02:23:58.864343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5fe2a890f57bd4de237b22d24ff4c4d03ab01a98c60b4331c0b7c86f5202f40

Aliases

arxiv: 1310.2130 · arxiv_version: 1310.2130v3 · doi: 10.48550/arxiv.1310.2130 · pith_short_12: WX7CVCIPK66U · pith_short_16: WX7CVCIPK66U3YRX · pith_short_8: WX7CVCIP

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/WX7CVCIPK66U3YRXWIWSJ72MJU \
  | 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: b5fe2a890f57bd4de237b22d24ff4c4d03ab01a98c60b4331c0b7c86f5202f40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15d004ae93ccb4f1f0ba06ce198ad02125a9e47b2f873b37722895aa5c916a91",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-10-08T13:30:43Z",
    "title_canon_sha256": "b600ca328d61fe59109942d2a0a82dcb3cbdab8ff915c1d1948b1becaa363068"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.2130",
    "kind": "arxiv",
    "version": 3
  }
}