Pith Number

pith:AFCZHD2L

pith:2016:AFCZHD2LDHOK4BA6NMO6TMU4MD

not attested not anchored not stored refs pending

Permutations contained in transitive subgroups

Dimitris Koukoulopoulos, Kevin Ford, Sean Eberhard

arxiv:1605.01068 v3 · 2016-05-03 · 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{AFCZHD2LDHOK4BA6NMO6TMU4MD}

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	2026-05-18T00:42:44.431383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0145938f4b19dcae041e6b1de9b29c60ddc95d13fdbc05c2f71836921e299882

Aliases

arxiv: 1605.01068 · arxiv_version: 1605.01068v3 · doi: 10.48550/arxiv.1605.01068 · pith_short_12: AFCZHD2LDHOK · pith_short_16: AFCZHD2LDHOK4BA6 · pith_short_8: AFCZHD2L

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/AFCZHD2LDHOK4BA6NMO6TMU4MD \
  | 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: 0145938f4b19dcae041e6b1de9b29c60ddc95d13fdbc05c2f71836921e299882

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce1403b42577ec065fe6ca9b5772b89655dfc000633b93bb0808667924813e38",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-05-03T20:02:14Z",
    "title_canon_sha256": "5f89183ae1c52c872e6d8d776381b7910f357d4dbed4042ccf5e492c21241543"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.01068",
    "kind": "arxiv",
    "version": 3
  }
}