Pith Number

pith:PO4I7T2C

pith:2026:PO4I7T2CIXBSLMJLBUVUNK2H2V

not attested not anchored not stored refs pending

Log-convexity and log-concavity of noncentral gamma sums and differences

Fr\'ed\'eric Ouimet, Robert E. Gaunt

arxiv:2607.09499 v1 · 2026-07-10 · math.PR · math.CA · math.ST · 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{PO4I7T2CIXBSLMJLBUVUNK2H2V}

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	2026-07-13T01:20:14.173112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bb88fcf4245c325b12b0d2b46ab47d578471b34a65ad0cccfe21b2f1d0bc78c

Aliases

arxiv: 2607.09499 · arxiv_version: 2607.09499v1 · doi: 10.48550/arxiv.2607.09499 · pith_short_12: PO4I7T2CIXBS · pith_short_16: PO4I7T2CIXBSLMJL · pith_short_8: PO4I7T2C

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/PO4I7T2CIXBSLMJLBUVUNK2H2V \
  | 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: 7bb88fcf4245c325b12b0d2b46ab47d578471b34a65ad0cccfe21b2f1d0bc78c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "08322277b857d5b2f79afa63e7cbe493dc86640363e8d27a00015a1f130825f5",
    "cross_cats_sorted": [
      "math.CA",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-10T15:15:36Z",
    "title_canon_sha256": "757f5d96c84fa06b8fd7a77432d7a806460b111e4a4359c33144d2fde7cb69d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.09499",
    "kind": "arxiv",
    "version": 1
  }
}