Pith Number

pith:3XUTOKFD

pith:2015:3XUTOKFD7PH4WNYAUU6YH7NBCE

not attested not anchored not stored refs pending

The Smith and Critical Groups of the Square Rook's Graph and its Complement

Jonathan Gerhard, Joshua E. Ducey, Noah Watson

arxiv:1507.06583 v1 · 2015-07-23 · 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{3XUTOKFD7PH4WNYAUU6YH7NBCE}

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	2026-05-18T01:36:24.568889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dde93728a3fbcfcb3700a53d83fda1112e55eef9fbaf5327493c22b1629b99d5

Aliases

arxiv: 1507.06583 · arxiv_version: 1507.06583v1 · doi: 10.48550/arxiv.1507.06583 · pith_short_12: 3XUTOKFD7PH4 · pith_short_16: 3XUTOKFD7PH4WNYA · pith_short_8: 3XUTOKFD

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/3XUTOKFD7PH4WNYAUU6YH7NBCE \
  | 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: dde93728a3fbcfcb3700a53d83fda1112e55eef9fbaf5327493c22b1629b99d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "543d75a681f773349f29c135db1959eb4a8d331d310d633786b831d2d640818c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-23T17:39:30Z",
    "title_canon_sha256": "dc2e404f8e9c69373b915a95c2f713ef96c3fa60dd59296d79bfb3fdf44f9428"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.06583",
    "kind": "arxiv",
    "version": 1
  }
}