Pith Number

pith:OWFHHD46

pith:2026:OWFHHD46TOFQTR3AE7BOLEXUCE

not attested not anchored not stored refs pending

Order-invariant cluster first-order logic on graph classes of bounded degree

Fatemeh Ghasemi, Julien Grange

Order-invariant cluster first-order logic has the same expressive power as plain first-order logic on bounded-degree graph classes.

arxiv:2604.27693 v2 · 2026-04-30 · cs.LO

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\pithnumber{OWFHHD46TOFQTR3AE7BOLEXUCE}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

We show that while order-invariant cluster first-order logic can define properties outside the scope of plain first-order logic in general, its expressive power is included in that of first-order logic when it comes to classes of bounded degree.

C2weakest assumption

That there exist linear orders on the universes of any two sufficiently similar bounded-degree structures such that the expanded structures remain similar (i.e., the local-to-global similarity-preserving construction succeeds).

C3one line summary

Order-invariant cluster first-order logic has the same expressive power as first-order logic on every class of graphs with bounded degree.

Receipt and verification

First computed	2026-06-26T01:15:52.860206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

758a738f9e9b8b09c76027c2e592f41123c67630c5e467d74ecdbd55478824a6

Aliases

arxiv: 2604.27693 · arxiv_version: 2604.27693v2 · doi: 10.48550/arxiv.2604.27693 · pith_short_12: OWFHHD46TOFQ · pith_short_16: OWFHHD46TOFQTR3A · pith_short_8: OWFHHD46

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/OWFHHD46TOFQTR3AE7BOLEXUCE \
  | 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: 758a738f9e9b8b09c76027c2e592f41123c67630c5e467d74ecdbd55478824a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85d34506d4bca81c4f2b1efdd1023bdcb74d137a05f50ef7e681c99a69109f1f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-04-30T10:34:30Z",
    "title_canon_sha256": "ed4f746fd3a7b37dd97e132c47741719070d68066771f6b4d5e1225471f72b7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.27693",
    "kind": "arxiv",
    "version": 2
  }
}