Pith Number

pith:QYFIF5VU

pith:2026:QYFIF5VUQ2Z6JDXNTBMZONPG5A

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Coalgebraic Non-Wellfounded Proofs: Recursiveness and GTC

Mayuko Kori

Non-wellfounded proofs satisfy the global trace condition exactly when a related coalgebra is recursive, which ensures soundness through a unique semantic morphism.

arxiv:2605.15664 v1 · 2026-05-15 · cs.LO

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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Claims

C1strongest claim

A coalgebra satisfies the GTC if and only if its image under a suitable adjoint is recursive; under an appropriate assumption on the given semantic algebra this yields soundness, that is, every proof admits a unique coalgebra-to-algebra morphism.

C2weakest assumption

The paper relies on an appropriate assumption on the given semantic algebra that guarantees the existence of the unique coalgebra-to-algebra morphism once recursiveness is established (stated in the paragraph following the main theorem on recursive coalgebras).

C3one line summary

The paper shows that a derivation graph satisfies the global trace condition if and only if its image under a suitable adjoint is a recursive coalgebra, yielding soundness under an assumption on the semantic algebra.

References

38 extracted · 38 resolved · 0 Pith anchors

[1] Free algebras and automata realizations in the language of categories 1974

[2] Bahareh Afshari and Graham E. Leigh. Cut-free completeness for modal mu-calculus. In LICS , pages 1--12. IEEE Computer Society, 2017 2017

[3] Recursive coalgebras of finitary functors 2007

[4] Jir \' Ad \' a mek, Stefan Milius, and Lawrence S. Moss. Fixed points of functors. J. Log. Algebraic Methods Program. , 95:41--81, 2018 2018

[5] Jir \' Ad \' a mek, Stefan Milius, and Lawrence S. Moss. On well-founded and recursive coalgebras. In Jean Goubault - Larrecq and Barbara K \" o nig, editors, Foundations of Software Science and Compu 2020

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:11.064670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

860a82f6b486b3e48eed98599735e6e80f2f06bef13e5551b210a430c6437f28

Aliases

arxiv: 2605.15664 · arxiv_version: 2605.15664v1 · doi: 10.48550/arxiv.2605.15664 · pith_short_12: QYFIF5VUQ2Z6 · pith_short_16: QYFIF5VUQ2Z6JDXN · pith_short_8: QYFIF5VU

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/QYFIF5VUQ2Z6JDXNTBMZONPG5A \
  | 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: 860a82f6b486b3e48eed98599735e6e80f2f06bef13e5551b210a430c6437f28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fb1d475a8792b7d910c495d7a6c9728350ab302fb5e67e811e7e6fdded57b3f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-05-15T06:38:43Z",
    "title_canon_sha256": "a39d5c07f055380908aa3ae0f884aa3cbb9d4b912d58011a286ac22eb74c139a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15664",
    "kind": "arxiv",
    "version": 1
  }
}