Pith Number

pith:W5DOV5NC

pith:2012:W5DOV5NCFPEOQLHBOVL2XFBTF3

not attested not anchored not stored refs pending

Algebraic Semigroups are Strongly {\pi}-regular

Lex E. Renner, Michel Brion

arxiv:1209.2042 v2 · 2012-09-10 · math.AG · 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{W5DOV5NCFPEOQLHBOVL2XFBTF3}

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	2026-05-18T03:18:08.261567Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b746eaf5a22bc8e82ce17557ab94332ec7dc12d94253972b889701bbe03266f1

Aliases

arxiv: 1209.2042 · arxiv_version: 1209.2042v2 · doi: 10.48550/arxiv.1209.2042 · pith_short_12: W5DOV5NCFPEO · pith_short_16: W5DOV5NCFPEOQLHB · pith_short_8: W5DOV5NC

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/W5DOV5NCFPEOQLHBOVL2XFBTF3 \
  | 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: b746eaf5a22bc8e82ce17557ab94332ec7dc12d94253972b889701bbe03266f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd6aa7d687842d51b471b23193c503a903357f170ce80f85b59a5eeb88a1953b",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-09-10T15:43:06Z",
    "title_canon_sha256": "db68cdfc4dd0f8d14055d026f6f3399ee42b9c6ef6e7a41f30947942e136c11b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2042",
    "kind": "arxiv",
    "version": 2
  }
}