Pith Number

pith:2SXC5WKH

pith:2022:2SXC5WKH2FBYN6D27M4SN3P2KE

not attested not anchored not stored refs pending

First Order Logic on Pathwidth Revisited Again

Michael Lampis

All first-order expressible properties on bounded-pathwidth graphs can be decided with elementary dependence on the formula.

arxiv:2210.09899 v5 · 2022-10-18 · cs.DS · cs.CC · cs.LO

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\usepackage{pith}
\pithnumber{2SXC5WKH2FBYN6D27M4SN3P2KE}

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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.

Claims

C1strongest claim

all FO-expressible properties can be decided with an elementary dependence on the input formula, if the input graph has bounded pathwidth (rather than treewidth)

C2weakest assumption

The graphs under consideration have bounded pathwidth (as opposed to merely bounded treewidth), which is the structural restriction that permits the elementary dependence; this premise is invoked in the statement of the main meta-theorem.

C3one line summary

FO-expressible properties on bounded-pathwidth graphs admit elementary dependence on the formula, unlike the non-elementary case for treewidth.

Receipt and verification

First computed	2026-06-11T02:09:21.451622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4ae2ed947d14386f87afb3926edfa510615be06c7f91ae7f650a49c49483b2f

Aliases

arxiv: 2210.09899 · arxiv_version: 2210.09899v5 · doi: 10.48550/arxiv.2210.09899 · pith_short_12: 2SXC5WKH2FBY · pith_short_16: 2SXC5WKH2FBYN6D2 · pith_short_8: 2SXC5WKH

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/2SXC5WKH2FBYN6D27M4SN3P2KE \
  | 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: d4ae2ed947d14386f87afb3926edfa510615be06c7f91ae7f650a49c49483b2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad3439828114c032d8897fac9e94090fe43b5e3e8dfac9e7fea4eba8e21b59c3",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2022-10-18T14:41:26Z",
    "title_canon_sha256": "f43cdffacc151f6874e3414667376f52a452557dc31a31564b54d77b69e7476b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2210.09899",
    "kind": "arxiv",
    "version": 5
  }
}