Pith Number

pith:XRFRKMO6

pith:2009:XRFRKMO6CGALULYGMTAX22SS7C

not attested not anchored not stored refs pending

Galois connection for sets of operations closed under permutation, cylindrification and composition

Erkko Lehtonen, Miguel Couceiro

arxiv:0910.5409 v3 · 2009-10-28 · 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{XRFRKMO6CGALULYGMTAX22SS7C}

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	2026-05-18T00:57:38.772925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc4b1531de1180ba2f0664c17d6a52f89ab561710b30756a258e90c55d92b639

Aliases

arxiv: 0910.5409 · arxiv_version: 0910.5409v3 · doi: 10.48550/arxiv.0910.5409 · pith_short_12: XRFRKMO6CGAL · pith_short_16: XRFRKMO6CGALULYG · pith_short_8: XRFRKMO6

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/XRFRKMO6CGALULYGMTAX22SS7C \
  | 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: bc4b1531de1180ba2f0664c17d6a52f89ab561710b30756a258e90c55d92b639

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f3ffed251afec4d0f9b7eda7f624b2b9568fec884599594c5c652e414f1761b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2009-10-28T16:00:17Z",
    "title_canon_sha256": "915a677f6e1a79196584ecfcac40fede0adcef6f3dba4bfc476b73c1fcde4008"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.5409",
    "kind": "arxiv",
    "version": 3
  }
}