Pith Number

pith:PAVRJDMV

pith:2026:PAVRJDMVK474PNPP5EWTSLQCPI

not attested not anchored not stored refs pending

Set-like operations on propositional logic programs

Christian Anti\'c

Every minimalist Horn logic program decomposes into Krom programs so its least model can be recovered exactly from the least models of those components.

arxiv:2605.03613 v2 · 2026-05-05 · cs.LO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PAVRJDMVK474PNPP5EWTSLQCPI}

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.

Claims

C1strongest claim

every minimalist program can be decomposed into Krom programs -- consisting only of rules with at most one body atom -- such that its least model can be computed from the least models of its components

C2weakest assumption

The definitions of 'minimalist program' and 'Krom program' together with the set-like operations allow exact reconstruction of least-model semantics for the minimalist case; this assumption is stated as the main technical result but its precise scope and any hidden restrictions on rule forms are not detailed in the abstract.

C3one line summary

Propositional Horn logic programs can be decomposed into Krom programs such that least models of the original programs can be reconstructed or approximated from the least models of the components.

Receipt and verification

First computed	2026-06-03T01:05:14.453022Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

782b148d95573fc7b5efe92d392e027a3ae7cf616aaea87cd2dae057c57e3764

Aliases

arxiv: 2605.03613 · arxiv_version: 2605.03613v2 · doi: 10.48550/arxiv.2605.03613 · pith_short_12: PAVRJDMVK474 · pith_short_16: PAVRJDMVK474PNPP · pith_short_8: PAVRJDMV

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/PAVRJDMVK474PNPP5EWTSLQCPI \
  | 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: 782b148d95573fc7b5efe92d392e027a3ae7cf616aaea87cd2dae057c57e3764

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc7da99be9dad2c440c420b6ba588a350ffe77aae615b7c7a4ba1ec78db52ea0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-05T10:39:59Z",
    "title_canon_sha256": "26f5958f1fb541f11081aeb66e8f3a660af494b43a268128eca072645d1220bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.03613",
    "kind": "arxiv",
    "version": 2
  }
}