Pith Number

pith:4CVTRSZ5

pith:2012:4CVTRSZ5IOK4RKECR2V4EJHE6Y

not attested not anchored not stored refs pending

Bounds on the diameter of Cayley graphs of the symmetric group

\'Akos Seress, Harald Helfgott, John Bamberg, Nick Gill, Pablo Spiga, Thomas Hayes

arxiv:1205.1596 v1 · 2012-05-08 · math.GR · 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{4CVTRSZ5IOK4RKECR2V4EJHE6Y}

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	2026-05-18T03:56:09.855487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0ab38cb3d4395c8a8828eabc224e4f635d29bc2f4a3235d9339cc8be8863c2f

Aliases

arxiv: 1205.1596 · arxiv_version: 1205.1596v1 · doi: 10.48550/arxiv.1205.1596 · pith_short_12: 4CVTRSZ5IOK4 · pith_short_16: 4CVTRSZ5IOK4RKEC · pith_short_8: 4CVTRSZ5

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/4CVTRSZ5IOK4RKECR2V4EJHE6Y \
  | 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: e0ab38cb3d4395c8a8828eabc224e4f635d29bc2f4a3235d9339cc8be8863c2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "509041eabef81899d7b29489dd9c3f9402602f8fa9a974ea7423ab2388892da0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-05-08T06:11:11Z",
    "title_canon_sha256": "11369e95abc2b922e9e5606ea2287bab5debe95420e41e54fab636e67774e9a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1596",
    "kind": "arxiv",
    "version": 1
  }
}