Pith Number

pith:YRCWEOP5

pith:2003:YRCWEOP5JTOQMLYUWVBHK5JDAO

not attested not anchored not stored refs pending

The combinatorics of a three-line circulant determinant

Gregory S. Warrington, Herbert S. Wilf, Nicholas A. Loehr

arxiv:math/0312350 v1 · 2003-12-18 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YRCWEOP5JTOQMLYUWVBHK5JDAO}

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	2026-07-04T14:38:06.279332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4456239fd4cdd062f14b54275752303837bb8d1c178576388fcee812e157380

Aliases

arxiv: math/0312350 · arxiv_version: math/0312350v1 · doi: 10.48550/arxiv.math/0312350 · pith_short_12: YRCWEOP5JTOQ · pith_short_16: YRCWEOP5JTOQMLYU · pith_short_8: YRCWEOP5

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/YRCWEOP5JTOQMLYUWVBHK5JDAO \
  | 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: c4456239fd4cdd062f14b54275752303837bb8d1c178576388fcee812e157380

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "989888824dca84c9cd639fb1852486aca7c0e7cf82c03d42d30d1f0eca8b61b1",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2003-12-18T19:07:20Z",
    "title_canon_sha256": "58e3f0a08ddd2ab3db82ef1872678d0e1efc08e82285792113a284d0bb8cadd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312350",
    "kind": "arxiv",
    "version": 1
  }
}