Pith Number

pith:GMKFKYRJ

pith:2026:GMKFKYRJ7Z325INOFSCKLSALEO

not attested not anchored not stored refs pending

Implementing Grassroots Logic Programs with Multiagent Transition Systems and AI (Full Version)

Ehud Shapiro

Grassroots logic programs can be implemented correctly via deterministic multiagent transition systems using local links for shared variables.

arxiv:2602.06934 v4 · 2026-02-06 · cs.PL · cs.AI · cs.DC · cs.LO · cs.MA

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\pithnumber{GMKFKYRJ7Z325INOFSCKLSALEO}

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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

✓ 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

We prove that both madGLP and maGLP are grassroots. dGLP and madGLP are proved correct with respect to their abstract counterparts GLP and maGLP.

C2weakest assumption

The single-occurrence invariant of GLP programs, which is invoked to establish disjoint substitution commutativity and thereby the correctness of the shared-variable implementation via local links.

C3one line summary

Derives correct deterministic semantics for multiagent logic programs from abstract ones and uses them as specs for AI-generated Dart implementations.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-09T02:07:19.822111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3314556229fe77aea1ae2c84a5c80b23986c0b12bbb5b727161cd02144f2bfd2

Aliases

arxiv: 2602.06934 · arxiv_version: 2602.06934v4 · doi: 10.48550/arxiv.2602.06934 · pith_short_12: GMKFKYRJ7Z32 · pith_short_16: GMKFKYRJ7Z325INO · pith_short_8: GMKFKYRJ

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/GMKFKYRJ7Z325INOFSCKLSALEO \
  | 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: 3314556229fe77aea1ae2c84a5c80b23986c0b12bbb5b727161cd02144f2bfd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b847c081fbec5501a7129a9a1c7d005dada562b88b75ad27f7413e201ce9cb34",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.DC",
      "cs.LO",
      "cs.MA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.PL",
    "submitted_at": "2026-02-06T18:30:11Z",
    "title_canon_sha256": "10d5b857383eb7976c8d88e238589d30d3869ddf083a5689c208b4db031a3572"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.06934",
    "kind": "arxiv",
    "version": 4
  }
}