Pith Number

pith:3JM27XA2

pith:2026:3JM27XA2JW6SDRJBPMQUHBVQ4G

not attested not anchored not stored refs resolved

Modal group theory

Wojciech Aleksander Wo{\l}oszyn

Embeddability among groups validates precisely the modal logic S4.2.

arxiv:2605.14197 v1 · 2026-05-13 · math.LO · math.GR

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\pithnumber{3JM27XA2JW6SDRJBPMQUHBVQ4G}

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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

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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

the formulaic propositional modal validities of groups under embeddings are precisely S4.2

C2weakest assumption

That embeddability in the category of groups provides a suitable accessibility relation for modal possibility, allowing HNN extensions and Britton's lemma to establish the claimed expressiveness and arithmetic interpretation.

C3one line summary

Modal group theory interprets true arithmetic and establishes that the propositional modal validities of groups under embeddings are exactly S4.2.

References

14 extracted · 14 resolved · 1 Pith anchors

[1] The modal logic of abelian groups , journal = 2023

[2] Chang, C. C. and Keisler, H. J. , title =

[3] Higman, Graham and Neumann, B. H. and Neumann, Hanna , title =. Journal of the London Mathematical Society , volume =. 1949 , pages = 1949

[4] Models and Sets , series = 1984

[5] Modal model theory , journal = 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:11.081449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da59afdc1a4dbd21c5217b214386b0e1be807efbe22435e298e81ab71d07e82f

Aliases

arxiv: 2605.14197 · arxiv_version: 2605.14197v1 · doi: 10.48550/arxiv.2605.14197 · pith_short_12: 3JM27XA2JW6S · pith_short_16: 3JM27XA2JW6SDRJB · pith_short_8: 3JM27XA2

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3JM27XA2JW6SDRJBPMQUHBVQ4G \
  | 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: da59afdc1a4dbd21c5217b214386b0e1be807efbe22435e298e81ab71d07e82f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82663357be72228535aa965d468189807b36c71767eb3b796f1d261e7bcea3e8",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-13T23:28:19Z",
    "title_canon_sha256": "73c2afb90f06d22d267335dda64b582fb4e8b4a1831a5f74c1ab45a1212dc157"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14197",
    "kind": "arxiv",
    "version": 1
  }
}