Pith Number

pith:LGIVT3I2

pith:2018:LGIVT3I2EDR4QLRESFX5LLQ3SP

not attested not anchored not stored refs pending

Stochastic orders for convolution of heterogeneous gamma and negative binomial random variables

Ying Zhang

arxiv:1811.11360 v1 · 2018-11-28 · 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{LGIVT3I2EDR4QLRESFX5LLQ3SP}

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	2026-05-17T23:59:44.113216Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

599159ed1a20e3c82e24916fd5ae1b93eb86b1318f8c0f428fcd99135bd68233

Aliases

arxiv: 1811.11360 · arxiv_version: 1811.11360v1 · doi: 10.48550/arxiv.1811.11360 · pith_short_12: LGIVT3I2EDR4 · pith_short_16: LGIVT3I2EDR4QLRE · pith_short_8: LGIVT3I2

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/LGIVT3I2EDR4QLRESFX5LLQ3SP \
  | 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: 599159ed1a20e3c82e24916fd5ae1b93eb86b1318f8c0f428fcd99135bd68233

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7251ec7cc27f37dc4524f2be93ac2098b017c6783ae8d2f6313fea7072455ddc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-11-28T02:38:53Z",
    "title_canon_sha256": "6479a18585e1a98ab47fd248acd1d575c93b200024cd67bd28a08fa5d6f90be1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.11360",
    "kind": "arxiv",
    "version": 1
  }
}