Pith Number

pith:WBK5PION

pith:2011:WBK5PIONQ2KLTYEPFU3SP4YZQW

not attested not anchored not stored refs pending

Generalized Ramanujan Primes

Jonathan Sondow, Nadine Amersi, Olivia Beckwith, Ryan Ronan, Steven J. Miller

arxiv:1108.0475 v4 · 2011-08-02 · 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{WBK5PIONQ2KLTYEPFU3SP4YZQW}

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	2026-05-18T02:31:27.748442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b055d7a1cd8694b9e08f2d3727f31985adf71489e6012f461eb7a86ea199e4e6

Aliases

arxiv: 1108.0475 · arxiv_version: 1108.0475v4 · doi: 10.48550/arxiv.1108.0475 · pith_short_12: WBK5PIONQ2KL · pith_short_16: WBK5PIONQ2KLTYEP · pith_short_8: WBK5PION

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/WBK5PIONQ2KLTYEPFU3SP4YZQW \
  | 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: b055d7a1cd8694b9e08f2d3727f31985adf71489e6012f461eb7a86ea199e4e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0bc502f8133eca7c208f1073c19ffd4bc0ec4d0481a66dd8fa7d103be3be16f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-02T02:55:50Z",
    "title_canon_sha256": "98972bfe22fe9d6687f28ab0ee0188eb3ceef383b116196479f657ee70745049"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0475",
    "kind": "arxiv",
    "version": 4
  }
}