Pith Number

pith:5L2U3DOQ

pith:2010:5L2U3DOQMRN245KN4M7ZKXKYNN

not attested not anchored not stored refs pending

The arity gap of order-preserving functions and extensions of pseudo-Boolean functions

Erkko Lehtonen, Miguel Couceiro, Tam\'as Waldhauser

arxiv:1003.2192 v3 · 2010-03-10 · 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{5L2U3DOQMRN245KN4M7ZKXKYNN}

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	2026-05-18T00:57:38.736530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eaf54d8dd0645bae754de33f955d586b7249db39b250b7f0fce0fca2e6dedafb

Aliases

arxiv: 1003.2192 · arxiv_version: 1003.2192v3 · doi: 10.48550/arxiv.1003.2192 · pith_short_12: 5L2U3DOQMRN2 · pith_short_16: 5L2U3DOQMRN245KN · pith_short_8: 5L2U3DOQ

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/5L2U3DOQMRN245KN4M7ZKXKYNN \
  | 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: eaf54d8dd0645bae754de33f955d586b7249db39b250b7f0fce0fca2e6dedafb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9e140533d0ac87ea4ba6691c864bf03a7dbe47fbfc403d11fc4549348ee957a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-03-10T20:31:42Z",
    "title_canon_sha256": "6b5b40a804bf85dfaadd56fbd1798fbadc8a2bdbb3e487b1ac99642112d6a972"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2192",
    "kind": "arxiv",
    "version": 3
  }
}