Pith Number

pith:VXMDCA66

pith:2025:VXMDCA66ARDN5ZHC5AXBXPWTAF

not attested not anchored not stored refs pending

Rook sums in the symmetric group algebra

Darij Grinberg

arxiv:2507.22386 v1 · 2025-07-30 · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VXMDCA66ARDN5ZHC5AXBXPWTAF}

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	2026-07-05T11:45:41.046679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

add83103de0446dee4e2e82e1bbed30148ff54fb320fe31821d0a0a2a81dae69

Aliases

arxiv: 2507.22386 · arxiv_version: 2507.22386v1 · doi: 10.48550/arxiv.2507.22386 · pith_short_12: VXMDCA66ARDN · pith_short_16: VXMDCA66ARDN5ZHC · pith_short_8: VXMDCA66

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/VXMDCA66ARDN5ZHC5AXBXPWTAF \
  | 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: add83103de0446dee4e2e82e1bbed30148ff54fb320fe31821d0a0a2a81dae69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "542e63a8c81de6a83b2c6a94a12e282354a5887e649e0bc03b94828377417e06",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-30T05:16:39Z",
    "title_canon_sha256": "71f2cb88d1a2f2a6f1ef833399749f1bb6dbb91b0bf33f5888417d81ec3ef441"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.22386",
    "kind": "arxiv",
    "version": 1
  }
}