Pith Number

pith:K4KYNZJE

pith:2009:K4KYNZJE74DL3C34N7TNM75PIH

not attested not anchored not stored refs pending

Bertrand's postulate and subgroup growth

D. B. McReynolds, K. Bou-Rabee

arxiv:0909.1343 v1 · 2009-09-07 · math.GR · 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{K4KYNZJE74DL3C34N7TNM75PIH}

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	2026-05-18T03:40:25.989945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

571586e524ff06bd8b7c6fe6d67faf41f12378601bb4eb609595dea167e83e51

Aliases

arxiv: 0909.1343 · arxiv_version: 0909.1343v1 · doi: 10.48550/arxiv.0909.1343 · pith_short_12: K4KYNZJE74DL · pith_short_16: K4KYNZJE74DL3C34 · pith_short_8: K4KYNZJE

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/K4KYNZJE74DL3C34N7TNM75PIH \
  | 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: 571586e524ff06bd8b7c6fe6d67faf41f12378601bb4eb609595dea167e83e51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a3f59e8d71c86bafe753a9ac76ce4a1f97f60b79236f261decf67ef607b4ac4",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-09-07T21:08:23Z",
    "title_canon_sha256": "2b5383dde272b9a6619bf85a403661882749d1f4baa776359109fe2daae949e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1343",
    "kind": "arxiv",
    "version": 1
  }
}