Pith Number

pith:VEU4UCZP

pith:2025:VEU4UCZP43BWYCDZVG3WMH5RIY

not attested not anchored not stored refs pending

An introduction to the symmetric group algebra

Darij Grinberg

arxiv:2507.20706 v1 · 2025-07-28 · math.CO · math.RA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VEU4UCZP43BWYCDZVG3WMH5RIY}

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	2026-07-05T11:44:24.485850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a929ca0b2fe6c36c0879a9b7661fb14613fd6cae65794724673c084f63db0c0c

Aliases

arxiv: 2507.20706 · arxiv_version: 2507.20706v1 · doi: 10.48550/arxiv.2507.20706 · pith_short_12: VEU4UCZP43BW · pith_short_16: VEU4UCZP43BWYCDZ · pith_short_8: VEU4UCZP

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/VEU4UCZP43BWYCDZVG3WMH5RIY \
  | 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: a929ca0b2fe6c36c0879a9b7661fb14613fd6cae65794724673c084f63db0c0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b68ed1358f543c2b7be01fc1e8457fbae5be3d52c95767955dec2a5081f83e0",
    "cross_cats_sorted": [
      "math.RA",
      "math.RT"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-28T11:00:27Z",
    "title_canon_sha256": "6afd15f1a7e1f1c86fda3a2578e6e0aa15d9480ddf6c10fd45f3bdcd13386b92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20706",
    "kind": "arxiv",
    "version": 1
  }
}