Pith Number

pith:HKBC4VNA

pith:2011:HKBC4VNAUAAUWGZ2GP7DUVVGGF

not attested not anchored not stored refs pending

On Log-concavity of the Generalized Marcum Q Function

Yaming Yu

arxiv:1105.5762 v1 · 2011-05-29 · math.ST · cs.IT · math.CA · math.IT · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HKBC4VNAUAAUWGZ2GP7DUVVGGF}

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	2026-05-18T04:21:01.626647Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a822e55a0a0014b1b3a33fe3a56a6316381c599593c7ae01cdc387270fb38d4

Aliases

arxiv: 1105.5762 · arxiv_version: 1105.5762v1 · doi: 10.48550/arxiv.1105.5762 · pith_short_12: HKBC4VNAUAAU · pith_short_16: HKBC4VNAUAAUWGZ2 · pith_short_8: HKBC4VNA

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/HKBC4VNAUAAUWGZ2GP7DUVVGGF \
  | 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: 3a822e55a0a0014b1b3a33fe3a56a6316381c599593c7ae01cdc387270fb38d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83db4d17ba912a135ba2b4558ec91fee6c2ffdca86f5d225ab7c548d0fe8a73e",
    "cross_cats_sorted": [
      "cs.IT",
      "math.CA",
      "math.IT",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2011-05-29T06:49:13Z",
    "title_canon_sha256": "e8625ca5bd245f9aed6c7d3cd97cf2ad714f8abb88c3b1c09bc0176aa132a4c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5762",
    "kind": "arxiv",
    "version": 1
  }
}