Pith Number

pith:KUU2EMJN

pith:2026:KUU2EMJNDZCMDMIV5ZAAII3ECX

not attested not anchored not stored refs pending

The endomorphism tower of a finite symmetric group

Ambroise Grau, Jamie Smith, Marianne Johnson, Victoria Gould

arxiv:2606.24274 v1 · 2026-06-23 · math.GR · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KUU2EMJNDZCMDMIV5ZAAII3ECX}

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	2026-06-24T01:14:48.715133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5529a2312d1e44c1b115ee4004236415c5a680a97258a734b177bd0f35f02e5f

Aliases

arxiv: 2606.24274 · arxiv_version: 2606.24274v1 · doi: 10.48550/arxiv.2606.24274 · pith_short_12: KUU2EMJNDZCM · pith_short_16: KUU2EMJNDZCMDMIV · pith_short_8: KUU2EMJN

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/KUU2EMJNDZCMDMIV5ZAAII3ECX \
  | 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: 5529a2312d1e44c1b115ee4004236415c5a680a97258a734b177bd0f35f02e5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07af2f1028c575226616702fcb79ead31424b87eb6037ca33fc28ed49009aa88",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-06-23T07:58:12Z",
    "title_canon_sha256": "b761f2bc60559523ab3b62854fbe67d221c44ea343df7ef41cf618a459b21f91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.24274",
    "kind": "arxiv",
    "version": 1
  }
}