Pith Number

pith:V4NYB4ZY

pith:2010:V4NYB4ZYSJJV7KOBIWIKYTLKH4

not attested not anchored not stored refs pending

Minimal paths in the commuting graphs of semigroups

Janusz Konieczny, Joao Araujo, Michael Kinyon

arxiv:1003.2809 v3 · 2010-03-14 · 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{V4NYB4ZYSJJV7KOBIWIKYTLKH4}

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	2026-05-18T04:15:17.041275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af1b80f33892535fa9c14590ac4d6a3f28523b8dd448047e7fccb7d36fb1afa6

Aliases

arxiv: 1003.2809 · arxiv_version: 1003.2809v3 · doi: 10.48550/arxiv.1003.2809 · pith_short_12: V4NYB4ZYSJJV · pith_short_16: V4NYB4ZYSJJV7KOB · pith_short_8: V4NYB4ZY

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/V4NYB4ZYSJJV7KOBIWIKYTLKH4 \
  | 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: af1b80f33892535fa9c14590ac4d6a3f28523b8dd448047e7fccb7d36fb1afa6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82e8dc9aa3df752188be3e5018b238a329d22391d8d4b48c171b9f963a7c5574",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-03-14T20:14:23Z",
    "title_canon_sha256": "0608a2ac5e97622ac8972795829d4ba65547c454d5031f5994f8b04f73ce9b66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2809",
    "kind": "arxiv",
    "version": 3
  }
}