{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:A4SWOZZXZVZUN7GFI3CZZJWTDS","short_pith_number":"pith:A4SWOZZX","canonical_record":{"source":{"id":"2605.29880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-28T13:05:21Z","cross_cats_sorted":[],"title_canon_sha256":"7ef5a092c0efee88eaf2d85ae8757c2ced673382db2c983a05e4fa1f81851c48","abstract_canon_sha256":"12ccb005744cccc70d80c009330ae80d85ce39aea30ea288904374c3460139ce"},"schema_version":"1.0"},"canonical_sha256":"0725676737cd7346fcc546c59ca6d31c8bef2efbbed81575dc834aca609236d0","source":{"kind":"arxiv","id":"2605.29880","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29880","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29880v1","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29880","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"A4SWOZZXZVZU","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"A4SWOZZXZVZUN7GF","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"A4SWOZZX","created_at":"2026-05-29T02:05:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:A4SWOZZXZVZUN7GFI3CZZJWTDS","target":"record","payload":{"canonical_record":{"source":{"id":"2605.29880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-28T13:05:21Z","cross_cats_sorted":[],"title_canon_sha256":"7ef5a092c0efee88eaf2d85ae8757c2ced673382db2c983a05e4fa1f81851c48","abstract_canon_sha256":"12ccb005744cccc70d80c009330ae80d85ce39aea30ea288904374c3460139ce"},"schema_version":"1.0"},"canonical_sha256":"0725676737cd7346fcc546c59ca6d31c8bef2efbbed81575dc834aca609236d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:57.462058Z","signature_b64":"JyLatBfJhS2WQ969EPuzxK1NV9scZn6tT9M/RFzVIPMik5Z9LPIFi7Vre+kuZB5lzKsgQK6aqTZ8seKT3sBHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0725676737cd7346fcc546c59ca6d31c8bef2efbbed81575dc834aca609236d0","last_reissued_at":"2026-05-29T02:05:57.461261Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:57.461261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.29880","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QT84O5sJJYmYx2Bm947975BylbSBuPKfSWtKWCAlq5+Q/ZcYAQXVpyzASJkhSDKDgFzcrIJYMw0yQdrwDnowDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T06:30:32.972284Z"},"content_sha256":"734b6b0f067d0a9d7f9efd7e315797e20ddd243e8cfadd78d00cdc8f4d76569f","schema_version":"1.0","event_id":"sha256:734b6b0f067d0a9d7f9efd7e315797e20ddd243e8cfadd78d00cdc8f4d76569f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:A4SWOZZXZVZUN7GFI3CZZJWTDS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Undecidability in Relevant Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"S{\\o}ren Brinck Knudstorp","submitted_at":"2026-05-28T13:05:21Z","abstract_excerpt":"We prove undecidability for every positive relevant logic extending the system axiomatized by hypothetical syllogism, prefixing, and suffixing and contained in the logic of the semilattice frame $(P_{\\mathrm{fin}}(\\mathbb{N}), \\cup, \\varnothing)$.\n  This settles the longstanding decision problem for the semilattice relevant logic S in the negative, contrary to prevailing expectations of decidability. It also provides a new proof of Urquhart's (1984) undecidability theorem for R, E, and T, now by reduction from the Wang tiling problem for arbitrarily large finite isosceles right triangular regi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29880","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29880/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8Eoe186OypepdSvGdGpISwolnZtm0S4SzjlnTa5U5O2AHv1dGgrunkIqGEb71xH1vgPs8pgtBa4y10jmVUEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T06:30:32.972678Z"},"content_sha256":"fbb03ce054720d5ec5ad778c6a9bb6e1a3ea701d1efcce21020d543c45628e76","schema_version":"1.0","event_id":"sha256:fbb03ce054720d5ec5ad778c6a9bb6e1a3ea701d1efcce21020d543c45628e76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4SWOZZXZVZUN7GFI3CZZJWTDS/bundle.json","state_url":"https://pith.science/pith/A4SWOZZXZVZUN7GFI3CZZJWTDS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4SWOZZXZVZUN7GFI3CZZJWTDS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-03T06:30:32Z","links":{"resolver":"https://pith.science/pith/A4SWOZZXZVZUN7GFI3CZZJWTDS","bundle":"https://pith.science/pith/A4SWOZZXZVZUN7GFI3CZZJWTDS/bundle.json","state":"https://pith.science/pith/A4SWOZZXZVZUN7GFI3CZZJWTDS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4SWOZZXZVZUN7GFI3CZZJWTDS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:A4SWOZZXZVZUN7GFI3CZZJWTDS","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":"12ccb005744cccc70d80c009330ae80d85ce39aea30ea288904374c3460139ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-28T13:05:21Z","title_canon_sha256":"7ef5a092c0efee88eaf2d85ae8757c2ced673382db2c983a05e4fa1f81851c48"},"schema_version":"1.0","source":{"id":"2605.29880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29880","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29880v1","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29880","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"A4SWOZZXZVZU","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"A4SWOZZXZVZUN7GF","created_at":"2026-05-29T02:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"A4SWOZZX","created_at":"2026-05-29T02:05:57Z"}],"graph_snapshots":[{"event_id":"sha256:fbb03ce054720d5ec5ad778c6a9bb6e1a3ea701d1efcce21020d543c45628e76","target":"graph","created_at":"2026-05-29T02:05:57Z","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/2605.29880/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove undecidability for every positive relevant logic extending the system axiomatized by hypothetical syllogism, prefixing, and suffixing and contained in the logic of the semilattice frame $(P_{\\mathrm{fin}}(\\mathbb{N}), \\cup, \\varnothing)$.\n  This settles the longstanding decision problem for the semilattice relevant logic S in the negative, contrary to prevailing expectations of decidability. It also provides a new proof of Urquhart's (1984) undecidability theorem for R, E, and T, now by reduction from the Wang tiling problem for arbitrarily large finite isosceles right triangular regi","authors_text":"S{\\o}ren Brinck Knudstorp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-28T13:05:21Z","title":"Undecidability in Relevant Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29880","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":"sha256:734b6b0f067d0a9d7f9efd7e315797e20ddd243e8cfadd78d00cdc8f4d76569f","target":"record","created_at":"2026-05-29T02:05:57Z","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":"12ccb005744cccc70d80c009330ae80d85ce39aea30ea288904374c3460139ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-28T13:05:21Z","title_canon_sha256":"7ef5a092c0efee88eaf2d85ae8757c2ced673382db2c983a05e4fa1f81851c48"},"schema_version":"1.0","source":{"id":"2605.29880","kind":"arxiv","version":1}},"canonical_sha256":"0725676737cd7346fcc546c59ca6d31c8bef2efbbed81575dc834aca609236d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0725676737cd7346fcc546c59ca6d31c8bef2efbbed81575dc834aca609236d0","first_computed_at":"2026-05-29T02:05:57.461261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:57.461261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JyLatBfJhS2WQ969EPuzxK1NV9scZn6tT9M/RFzVIPMik5Z9LPIFi7Vre+kuZB5lzKsgQK6aqTZ8seKT3sBHBw==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:57.462058Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:734b6b0f067d0a9d7f9efd7e315797e20ddd243e8cfadd78d00cdc8f4d76569f","sha256:fbb03ce054720d5ec5ad778c6a9bb6e1a3ea701d1efcce21020d543c45628e76"],"state_sha256":"1e8ccbcb683bc151fa249960e420a1c79a3788b47d235b2706a0e2ce2e6d1a63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0/a2L1sW4CdY82J9blyjJbzUtU7eYITlM9TCgSwFWXdEf5tz6WmJkXqi7odbT+fJvd+GkPE+pbOPqARjcyjICQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T06:30:32.974756Z","bundle_sha256":"1ddbe2bd0f8d7a872f522d928485423efb4c768720f27294406c6aadc34aa1f8"}}