Pith Number

pith:GR56LI6P

pith:2013:GR56LI6P25PNLY4J727QUBBCRA

not attested not anchored not stored refs pending

The geometric mean is a Bernstein function

Feng Qi, Wen-Hui Li, Xiao-Jing Zhang

arxiv:1301.6848 v1 · 2013-01-29 · 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{GR56LI6P25PNLY4J727QUBBCRA}

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	2026-05-18T02:57:00.043135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

347be5a3cfd75ed5e389febf0a042288041ee37a8b7fbb1c7aea8e4922bf0f13

Aliases

arxiv: 1301.6848 · arxiv_version: 1301.6848v1 · doi: 10.48550/arxiv.1301.6848 · pith_short_12: GR56LI6P25PN · pith_short_16: GR56LI6P25PNLY4J · pith_short_8: GR56LI6P

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/GR56LI6P25PNLY4J727QUBBCRA \
  | 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: 347be5a3cfd75ed5e389febf0a042288041ee37a8b7fbb1c7aea8e4922bf0f13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2283de3d68fa6de1d8f2dd1f5c4a29f946e9b79756cbd7ee7d7f31828a7483d",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-01-29T07:23:30Z",
    "title_canon_sha256": "63e557fdf58a3572368beedcb7a494e110a27c40e638a6f7b5e8e341a430ab2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.6848",
    "kind": "arxiv",
    "version": 1
  }
}