Pith Number

pith:IW7USZGN

pith:2023:IW7USZGNDUFIYRUG2SQZQID7CY

not attested not anchored not stored refs pending

Log-concavity with respect to the number of orbits for infinite tuples of commuting permutations

Abdelmalek Abdesselam

arxiv:2309.07358 v2 · 2023-09-14 · math.CO · math.NT · 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{IW7USZGNDUFIYRUG2SQZQID7CY}

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	2026-07-05T07:32:23.342528Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45bf4964cd1d0a8c4686d4a198207f162e63b1ec26baac4ee5cd29142093da6a

Aliases

arxiv: 2309.07358 · arxiv_version: 2309.07358v2 · doi: 10.48550/arxiv.2309.07358 · pith_short_12: IW7USZGNDUFI · pith_short_16: IW7USZGNDUFIYRUG · pith_short_8: IW7USZGN

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/IW7USZGNDUFIYRUG2SQZQID7CY \
  | 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: 45bf4964cd1d0a8c4686d4a198207f162e63b1ec26baac4ee5cd29142093da6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0bdb8a8b6c3758a2f5df0c31fda5908822b99b3b292deb174bf4f8792674a2ba",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-09-14T00:14:19Z",
    "title_canon_sha256": "6320ecb393bb8ce1b296463c693d77ba593b1b7aa7f06ee81c97522a7d6cc22b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2309.07358",
    "kind": "arxiv",
    "version": 2
  }
}