Pith Number

pith:5VZY3O3K

pith:2014:5VZY3O3KICSJOOGZD4LBUF5W6Z

not attested not anchored not stored refs pending

The Sch\"utzenberger category of a semigroup

Alfredo Costa, Benjamin Steinberg

arxiv:1408.1615 v1 · 2014-08-07 · math.GR · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5VZY3O3KICSJOOGZD4LBUF5W6Z}

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	2026-05-18T02:45:40.070487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed738dbb6a40a49738d91f161a17b6f66fe1d357185b55301c3375ae7dc2bab7

Aliases

arxiv: 1408.1615 · arxiv_version: 1408.1615v1 · doi: 10.48550/arxiv.1408.1615 · pith_short_12: 5VZY3O3KICSJ · pith_short_16: 5VZY3O3KICSJOOGZ · pith_short_8: 5VZY3O3K

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/5VZY3O3KICSJOOGZD4LBUF5W6Z \
  | 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: ed738dbb6a40a49738d91f161a17b6f66fe1d357185b55301c3375ae7dc2bab7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a520817de89c8a5ae63050c530210311fd53c4b431111d852ae81723070fc16",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-08-07T15:04:20Z",
    "title_canon_sha256": "0df8ce39b77daec1b146b7591ace074ddd4a51f49a6a5a3f5531a31f58f32ceb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.1615",
    "kind": "arxiv",
    "version": 1
  }
}