Pith Number

pith:IIKPJ46W

pith:2013:IIKPJ46WF5WLYI2V34HWEM7536

not attested not anchored not stored refs pending

The straight line complexity of small factorials and primorials

Klas Markstr\"om

arxiv:1306.3091 v4 · 2013-06-13 · cs.CC · cs.DM · 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{IIKPJ46WF5WLYI2V34HWEM7536}

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	2026-05-18T02:31:27.550133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4214f4f3d62f6cbc2355df0f6233fddf910f93b0172aefaf0d9733a4f84c1256

Aliases

arxiv: 1306.3091 · arxiv_version: 1306.3091v4 · doi: 10.48550/arxiv.1306.3091 · pith_short_12: IIKPJ46WF5WL · pith_short_16: IIKPJ46WF5WLYI2V · pith_short_8: IIKPJ46W

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/IIKPJ46WF5WLYI2V34HWEM7536 \
  | 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: 4214f4f3d62f6cbc2355df0f6233fddf910f93b0172aefaf0d9733a4f84c1256

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59d320d19d02a1c2b881d9774cbeecbfe3a29682ee263eff554ceeda7a083e74",
    "cross_cats_sorted": [
      "cs.DM",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2013-06-13T12:08:12Z",
    "title_canon_sha256": "64882d1554a26e908d10a26b59f0d38dac55e009a6a1732f3d4ec31ca49e76d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.3091",
    "kind": "arxiv",
    "version": 4
  }
}