Pith Number

pith:IFNJL5GR

pith:2013:IFNJL5GRCZ2DHPBBZ72FQEZ7IG

not attested not anchored not stored refs pending

Perfect commuting graphs

John R. Britnell, Nick Gill

arxiv:1309.2237 v2 · 2013-09-09 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IFNJL5GRCZ2DHPBBZ72FQEZ7IG}

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	2026-05-18T01:29:29.871118Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

415a95f4d1167433bc21cff458133f41aebc35b2922cc4433cb2163aa7f3c554

Aliases

arxiv: 1309.2237 · arxiv_version: 1309.2237v2 · doi: 10.48550/arxiv.1309.2237 · pith_short_12: IFNJL5GRCZ2D · pith_short_16: IFNJL5GRCZ2DHPBB · pith_short_8: IFNJL5GR

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/IFNJL5GRCZ2DHPBBZ72FQEZ7IG \
  | 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: 415a95f4d1167433bc21cff458133f41aebc35b2922cc4433cb2163aa7f3c554

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af6f5869bdbf5a806112af0a641f8c6ec871a6acf0bfdce0ca7e975d89c86b3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-09T17:45:04Z",
    "title_canon_sha256": "513c109e0a7306955277c726f93e4deb1a37e9ed83fc8edbfdcd65e861fa5f63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.2237",
    "kind": "arxiv",
    "version": 2
  }
}