Pith Number

pith:TYIPYWNN

pith:2011:TYIPYWNNLZODECCJSOWBI4ISGR

not attested not anchored not stored refs pending

Bernoulli inequality and hypergeometric functions

Matti Vuorinen, Riku Kl\'en, Slavko Simi\'c, Vesna Manojlovi\'c

arxiv:1106.1768 v2 · 2011-06-09 · math.CA · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TYIPYWNNLZODECCJSOWBI4ISGR}

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	2026-05-18T01:13:31.425713Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e10fc59ad5e5c32084993ac1471123459847802ef2cf189b6af91328d0db4b3

Aliases

arxiv: 1106.1768 · arxiv_version: 1106.1768v2 · doi: 10.48550/arxiv.1106.1768 · pith_short_12: TYIPYWNNLZOD · pith_short_16: TYIPYWNNLZODECCJ · pith_short_8: TYIPYWNN

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/TYIPYWNNLZODECCJSOWBI4ISGR \
  | 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: 9e10fc59ad5e5c32084993ac1471123459847802ef2cf189b6af91328d0db4b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b90a6a4f6bdff56a008188b4ea410d742e788cb9f1e37f894f4e419d002ad5b",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-06-09T10:27:17Z",
    "title_canon_sha256": "132e4eedc09b51076b357cb0b3330efc249d950450fe432085b2dfb2ff25f931"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.1768",
    "kind": "arxiv",
    "version": 2
  }
}