Pith Number

pith:LCFOYYYN

pith:2013:LCFOYYYNFEWTJUAMWFNVG7F3TM

not attested not anchored not stored refs pending

A complete classification of equational classes of threshold functions included in clones

Erkko Lehtonen, Karsten Sch\"olzel, Miguel Couceiro

arxiv:1310.7041 v1 · 2013-10-25 · math.RA · 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{LCFOYYYNFEWTJUAMWFNVG7F3TM}

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	2026-05-18T00:57:38.626091Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

588aec630d292d34d00cb15b537cbb9b13987dc1f6bedcf6e0ae98b8d70aab21

Aliases

arxiv: 1310.7041 · arxiv_version: 1310.7041v1 · doi: 10.48550/arxiv.1310.7041 · pith_short_12: LCFOYYYNFEWT · pith_short_16: LCFOYYYNFEWTJUAM · pith_short_8: LCFOYYYN

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/LCFOYYYNFEWTJUAMWFNVG7F3TM \
  | 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: 588aec630d292d34d00cb15b537cbb9b13987dc1f6bedcf6e0ae98b8d70aab21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "205a5d8dee7fb2be3de8253122433a30456cf9d1123eaae0c89ba57f329f7816",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-10-25T21:00:23Z",
    "title_canon_sha256": "c1a1c692f3781bbeffb39640a0ef03a63b3b82bff8f2d615677f53d93c3f11d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.7041",
    "kind": "arxiv",
    "version": 1
  }
}