Pith Number

pith:5ZFEN3ZD

pith:2009:5ZFEN3ZDGPGECF7MZCLBXB4VUC

not attested not anchored not stored refs pending

Logarithmic convexity of Gini means

Bai-Ni Guo, Feng Qi

arxiv:0903.1208 v1 · 2009-03-06 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ZFEN3ZDGPGECF7MZCLBXB4VUC}

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	2026-05-18T03:46:32.199847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee4a46ef2333cc4117ecc8961b8795a0955924f373df41a0d47a31b4ba5abf69

Aliases

arxiv: 0903.1208 · arxiv_version: 0903.1208v1 · doi: 10.48550/arxiv.0903.1208 · pith_short_12: 5ZFEN3ZDGPGE · pith_short_16: 5ZFEN3ZDGPGECF7M · pith_short_8: 5ZFEN3ZD

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/5ZFEN3ZDGPGECF7MZCLBXB4VUC \
  | 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: ee4a46ef2333cc4117ecc8961b8795a0955924f373df41a0d47a31b4ba5abf69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b2de1af07a71b7baa9aed706dad8d683788b04d4f668685a643140c1d021663",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2009-03-06T13:54:20Z",
    "title_canon_sha256": "e7dfb80b8a0970dae4267d4514fc6541cfd8301756188b03459a19baf96b3541"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.1208",
    "kind": "arxiv",
    "version": 1
  }
}