Pith Number

pith:2GBUM4NE

pith:2013:2GBUM4NEBXYRTSNCXPC3Y4PG2G

not attested not anchored not stored refs pending

Growth rates of permutation grid classes, tours on graphs, and the spectral radius

David Bevan

arxiv:1302.2037 v4 · 2013-02-08 · 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{2GBUM4NEBXYRTSNCXPC3Y4PG2G}

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	2026-05-18T01:33:58.870067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1834671a40df119c9a2bbc5bc71e6d1a53c714a32dee5f69e49157531ad29be

Aliases

arxiv: 1302.2037 · arxiv_version: 1302.2037v4 · doi: 10.48550/arxiv.1302.2037 · pith_short_12: 2GBUM4NEBXYR · pith_short_16: 2GBUM4NEBXYRTSNC · pith_short_8: 2GBUM4NE

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/2GBUM4NEBXYRTSNCXPC3Y4PG2G \
  | 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: d1834671a40df119c9a2bbc5bc71e6d1a53c714a32dee5f69e49157531ad29be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c184ff7e01dbf030a513b00b164025031a2ecd22f83d7559404b54254cb96b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-08T14:11:02Z",
    "title_canon_sha256": "d09c80eb78442e06faaee658d6b2ec09f4a1a484c03a0c6be6a547a93346eebf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.2037",
    "kind": "arxiv",
    "version": 4
  }
}