{"paper":{"title":"Coalgebraic Non-Wellfounded Proofs: Recursiveness and GTC","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Non-wellfounded proofs satisfy the global trace condition exactly when a related coalgebra is recursive, which ensures soundness through a unique semantic morphism.","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Mayuko Kori","submitted_at":"2026-05-15T06:38:43Z","abstract_excerpt":"Non-wellfounded proof systems impose a global condition called the global trace condition (GTC) on a derivation tree to ensure soundness. Providing a categorical characterisation of the GTC that guarantees soundness remains challenging due to the global, non-compositional nature of these conditions and the infinitary structure of non-wellfounded proofs. We develop a coalgebraic framework for non-wellfounded proof systems where derivation trees are modelled as coalgebras of generalised polynomial functors on presheaves. Since the GTC is a constraint on infinite paths in derivation graphs, we em"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Non-wellfounded proofs satisfy the global trace condition exactly when a related coalgebra is recursive, which ensures soundness through a unique semantic morphism.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"740f1dd0f2c32a9cda143ab4e336117d2f81aef52d77340800ae750c520693e0"},"source":{"id":"2605.15664","kind":"arxiv","version":1},"verdict":{"id":"3708fd6b-4756-4c28-93fd-3acdf521dd24","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:33:32.130039Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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).","pith_extraction_headline":"Non-wellfounded proofs satisfy the global trace condition exactly when a related coalgebra is recursive, which ensures soundness through a unique semantic morphism."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15664/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.245559Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:41:03.326421Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:35.307236Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:56.071008Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fed011e264beaa182296917c1693b4639d80d0fe4ed68fc7cde3396233cd1327"},"references":{"count":38,"sample":[{"doi":"","year":1974,"title":"Free algebras and automata realizations in the language of categories","work_id":"fd3ffabd-e095-4268-bf23-1ec2942845b0","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"Bahareh Afshari and Graham E. 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