Pith Number

pith:ZYRPIWRL

pith:2026:ZYRPIWRLEX22JIJ4O2MPH4KE2Q

not attested not anchored not stored refs resolved

The modal theory of linear orders

Wojciech Aleksander Wo{\l}oszyn

Modal logic on linear orders allows elimination of modalities under embeddings and monotone maps, while condensations render scatteredness definable.

arxiv:2605.14182 v1 · 2026-05-13 · math.LO

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\pithnumber{ZYRPIWRLEX22JIJ4O2MPH4KE2Q}

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4 Citations 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

I prove modality elimination for embeddings and monotone maps, show that condensations make scatteredness modally definable, and compute exact propositional modal validities in the main cases.

C2weakest assumption

That standard Kripke semantics on linear orders, together with the listed map classes, suffice to capture the intended modal behavior without hidden assumptions about the underlying orders or the modal language.

C3one line summary

Proves modality elimination for embeddings and monotone maps on linear orders, establishes modal definability of scatteredness under condensations, and computes exact modal validities.

References

15 extracted · 15 resolved · 1 Pith anchors

[1] Patrick Blackburn and Maarten de Rijke and Yde Venema , title =

[2] Alexander Chagrov and Michael Zakharyaschev , title =

[3] R. A. Bull , title =. 1966 , pages = 1966

[4] 2016 , note = 2016

[5] Modal model theory , journaltitle = 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:11.236132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce22f45a2b25f5a4a13c7698f3f144d42eaea0857bf5cd3339f39f97d0c6586e

Aliases

arxiv: 2605.14182 · arxiv_version: 2605.14182v1 · doi: 10.48550/arxiv.2605.14182 · pith_short_12: ZYRPIWRLEX22 · pith_short_16: ZYRPIWRLEX22JIJ4 · pith_short_8: ZYRPIWRL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZYRPIWRLEX22JIJ4O2MPH4KE2Q \
  | 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: ce22f45a2b25f5a4a13c7698f3f144d42eaea0857bf5cd3339f39f97d0c6586e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b6c509d50529e545f4686db9d0001dc3d899346d2fcc3a77a7531722ba8c579",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-05-13T23:04:51Z",
    "title_canon_sha256": "0603c9e93e9865e5655c3e985823194cabd70d8500c8b96f5a77ed0c39bc69e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14182",
    "kind": "arxiv",
    "version": 1
  }
}