{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LJTQWTLXCPWC4KCS2VIW3ZGLFT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dc7d86bad7837de0b50b0efb6b19ed22f96af73009de7750aab52cbb5df39efc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-06-30T16:01:42Z","title_canon_sha256":"687c9852ef75a60b3139c21af599e2c997ddc1f635244a2cbd2de40a8907e282"},"schema_version":"1.0","source":{"id":"2606.31890","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31890","created_at":"2026-07-01T01:18:18Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31890v1","created_at":"2026-07-01T01:18:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31890","created_at":"2026-07-01T01:18:18Z"},{"alias_kind":"pith_short_12","alias_value":"LJTQWTLXCPWC","created_at":"2026-07-01T01:18:18Z"},{"alias_kind":"pith_short_16","alias_value":"LJTQWTLXCPWC4KCS","created_at":"2026-07-01T01:18:18Z"},{"alias_kind":"pith_short_8","alias_value":"LJTQWTLX","created_at":"2026-07-01T01:18:18Z"}],"graph_snapshots":[{"event_id":"sha256:046dbf0a26fa6db6472deaaa2603b4c304b23b3b20c822fa688b38aa3eb6933c","target":"graph","created_at":"2026-07-01T01:18:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.31890/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Non-wellfounded proof theory has been applied to establish uniform interpolation and Lyndon interpolation (separately) for multiple logics. However, it has not yet been used to prove uniform Lyndon interpolation. We close this gap by showing uniform Lyndon interpolation for the provability logic GLS. This logic was known to have uniform interpolation, but it was open whether it has uniform Lyndon interpolation (or at least non-uniform Lyndon interpolation). The methodology we provide is easy to adapt to other provability logics if a non-wellfounded sequent calculus is available for them. In ad","authors_text":"Borja Sierra Miranda (University of Bern), Thomas Studer (University of Bern)","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-06-30T16:01:42Z","title":"Uniform Lyndon Interpolation via Non-wellfounded Proofs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31890","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f0178af47f82c59858019f9a53e95a565d86bfdef6209e56aae8210f06abe5d8","target":"record","created_at":"2026-07-01T01:18:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dc7d86bad7837de0b50b0efb6b19ed22f96af73009de7750aab52cbb5df39efc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-06-30T16:01:42Z","title_canon_sha256":"687c9852ef75a60b3139c21af599e2c997ddc1f635244a2cbd2de40a8907e282"},"schema_version":"1.0","source":{"id":"2606.31890","kind":"arxiv","version":1}},"canonical_sha256":"5a670b4d7713ec2e2852d5516de4cb2cde84d2522b24a28472967eee2429375c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a670b4d7713ec2e2852d5516de4cb2cde84d2522b24a28472967eee2429375c","first_computed_at":"2026-07-01T01:18:18.547482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:18:18.547482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"94i0WQpE7gO3iZKIG1HXPts2ScT7ko7Dqvj691UkGvfgs7Cbve3mTl2Y/up7gWnAWM1PHh0IB+nLaIMrCUX+Cw==","signature_status":"signed_v1","signed_at":"2026-07-01T01:18:18.547966Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.31890","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0178af47f82c59858019f9a53e95a565d86bfdef6209e56aae8210f06abe5d8","sha256:046dbf0a26fa6db6472deaaa2603b4c304b23b3b20c822fa688b38aa3eb6933c"],"state_sha256":"d956679c4d44496fec98932129f59ec22a746cfcc0bdbd4d39927bc00c5cf2fa"}