Pith Number

pith:OUW4T7EU

pith:2014:OUW4T7EUVC4RGX5WQEOJBPT3HY

not attested not anchored not stored refs pending

Automorphism group of the modified bubble-sort graph

Ashwin Ganesan

arxiv:1409.5959 v3 · 2014-09-21 · math.CO · cs.DM · 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{OUW4T7EUVC4RGX5WQEOJBPT3HY}

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	2026-05-18T02:16:20.885999Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

752dc9fc94a8b9135fb6811c90be7b3e3784f0cbb0bb65171b83ff8f67556c0e

Aliases

arxiv: 1409.5959 · arxiv_version: 1409.5959v3 · doi: 10.48550/arxiv.1409.5959 · pith_short_12: OUW4T7EUVC4R · pith_short_16: OUW4T7EUVC4RGX5W · pith_short_8: OUW4T7EU

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/OUW4T7EUVC4RGX5WQEOJBPT3HY \
  | 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: 752dc9fc94a8b9135fb6811c90be7b3e3784f0cbb0bb65171b83ff8f67556c0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6548b1814ac222725dca2ed91589477093c02cce78e3f1f763b19087ee9b539f",
    "cross_cats_sorted": [
      "cs.DM",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-21T09:57:37Z",
    "title_canon_sha256": "ff10185799d5dc72d22f78fdd72cc4ab8521534cd37a562a2ccd0384f60b0272"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.5959",
    "kind": "arxiv",
    "version": 3
  }
}