Pith Number

pith:EP4UJQ5C

pith:2025:EP4UJQ5C3U6N36VX6INFAFKVBC

not attested not anchored not stored refs resolved

Declarative distributed algorithms as axiomatic theories in three-valued modal logic over semitopologies

Murdoch J. Gabbay

Distributed algorithms admit declarative axiomatizations in three-valued modal logic over semitopologies.

arxiv:2512.21137 v3 · 2025-12-24 · cs.LO · cs.DC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EP4UJQ5C3U6N36VX6INFAFKVBC}

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

We illustrate how to formally specify distributed algorithms as declarative axiomatic theories in a modal logic... using as illustrative examples a simple voting protocol, a simple broadcast protocol (Bracha Broadcast), and a simple agreement protocol (Crusader Agreement). The proofs in this paper have been formalised in Lean 4.

C2weakest assumption

That three-valued modal logic over semitopologies can faithfully capture the essential correctness and resilience properties of the target distributed algorithms without omitting critical behavioral details that only appear in concrete executions.

C3one line summary

Distributed algorithms are expressed as axiomatic theories in three-valued modal logic over semitopologies, with examples including Bracha broadcast and Crusader agreement, and all proofs formalized in Lean 4.

References

36 extracted · 36 resolved · 0 Pith anchors

[1] Ofer Arieli, Arnon Avron, and Anna Zamansky, Ideal paraconsistent logics, Studia Logica 99 (2011), no. 1-3, 31--60 2011

[2] Ittai Abraham, Naama Ben-David, and Sravya Yandamuri, Efficient and adaptively secure asynchronous binary agreement via binding crusader agreement, Proceedings of the 2022 ACM Symposium on Principles 2022

[3] 184, Schloss Dagstuhl - Leibniz-Zentrum f \" u r Informatik, 2020, pp 2020

[4] 253, Schloss Dagstuhl - Leibniz-Zentrum f \" u r Informatik, 2022, pp 2022

[5] Orestis Alpos, Christian Cachin, Bj \" o rn Tackmann, and Luca Zanolini, Asymmetric distributed trust, Distributed Computing 37 (2024), no. 3, 247--277 2024

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:45:12.122431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23f944c3a2dd3cddfab7f21a501555089c13af592fd740488ff6575255fb9684

Aliases

arxiv: 2512.21137 · arxiv_version: 2512.21137v3 · doi: 10.48550/arxiv.2512.21137 · pith_short_12: EP4UJQ5C3U6N · pith_short_16: EP4UJQ5C3U6N36VX · pith_short_8: EP4UJQ5C

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/EP4UJQ5C3U6N36VX6INFAFKVBC \
  | 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: 23f944c3a2dd3cddfab7f21a501555089c13af592fd740488ff6575255fb9684

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a45073e022c0761b22f65f181b76b501e2f86c32f251fd251303b51e864dcfce",
    "cross_cats_sorted": [
      "cs.DC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2025-12-24T12:07:25Z",
    "title_canon_sha256": "db610e299948e8780635ef2b2da8ad23045e37747bb3d7d5cbed306f32505e37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.21137",
    "kind": "arxiv",
    "version": 3
  }
}