Pith Number

pith:KCK4TEA6

pith:2025:KCK4TEA62BIUI7RY7WL7RO54SI

not attested not anchored not stored refs pending

Proof of a conjecture by Starr and log-concavity for random commuting permutations

Abdelmalek Abdesselam

arxiv:2506.06894 v1 · 2025-06-07 · math.CO · hep-th · 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{KCK4TEA62BIUI7RY7WL7RO54SI}

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.

Cited by

1 paper in Pith

Dominant Zeros of Nekrasov--Okounkov Polynomials

Receipt and verification

First computed	2026-07-05T11:17:57.687530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5095c9901ed051447e38fd97f8bbbc921ba63867a817894259dbb33d7778c5f6

Aliases

arxiv: 2506.06894 · arxiv_version: 2506.06894v1 · doi: 10.48550/arxiv.2506.06894 · pith_short_12: KCK4TEA62BIU · pith_short_16: KCK4TEA62BIUI7RY · pith_short_8: KCK4TEA6

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/KCK4TEA62BIUI7RY7WL7RO54SI \
  | 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: 5095c9901ed051447e38fd97f8bbbc921ba63867a817894259dbb33d7778c5f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47df28eb64dd015ae5553bc8d9d0bf7536664760213ede8a60cba1759b54e834",
    "cross_cats_sorted": [
      "hep-th",
      "math.NT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-07T18:47:09Z",
    "title_canon_sha256": "277f78aff8f772424ccb886458e0094ba8230fbfba15ead25e0cb9f7e1bb5a07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.06894",
    "kind": "arxiv",
    "version": 1
  }
}