Pith Number

pith:GZKC3YTN

pith:2009:GZKC3YTNXN3LL2ERNDII6GOK4U

not attested not anchored not stored refs pending

Log-concavity, ultra-log-concavity, and a maximum entropy property of discrete compound Poisson measures

Ioannis Kontoyiannis, Mokshay Madiman, Oliver Johnson

arxiv:0912.0581 v2 · 2009-12-03 · math.CO · cs.IT · math.IT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GZKC3YTNXN3LL2ERNDII6GOK4U}

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	2026-05-18T03:30:28.430251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36542de26dbb76b5e89168d08f19cae531a68f7b162a6f383edf49d6121561c5

Aliases

arxiv: 0912.0581 · arxiv_version: 0912.0581v2 · doi: 10.48550/arxiv.0912.0581 · pith_short_12: GZKC3YTNXN3L · pith_short_16: GZKC3YTNXN3LL2ER · pith_short_8: GZKC3YTN

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/GZKC3YTNXN3LL2ERNDII6GOK4U \
  | 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: 36542de26dbb76b5e89168d08f19cae531a68f7b162a6f383edf49d6121561c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e72a31599028121b1d9dbf273f541f4438ab6b59e1921b17fc75ea6dbbc91e15",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-12-03T05:41:46Z",
    "title_canon_sha256": "5f9bb3ded3304bba15be58390bcd96237965ddd273a13c719d64600faa64d4b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0581",
    "kind": "arxiv",
    "version": 2
  }
}