{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2H6I6GI7HZFNKX7KX5MXGYOZBO","short_pith_number":"pith:2H6I6GI7","canonical_record":{"source":{"id":"2401.08445","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-01-16T15:45:49Z","cross_cats_sorted":[],"title_canon_sha256":"a6f6eb6df8f9179e355c234f5e8a484f64ce3c0e846a571021862d5b2f0163e4","abstract_canon_sha256":"ab7b2d991f34680fac2d9ce4b5531e14a313f41e467e6873af5de60ba9736520"},"schema_version":"1.0"},"canonical_sha256":"d1fc8f191f3e4ad55feabf597361d90b8d59382d7511104533c1d216351726d6","source":{"kind":"arxiv","id":"2401.08445","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.08445","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"2401.08445v5","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.08445","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"2H6I6GI7HZFN","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"pith_short_16","alias_value":"2H6I6GI7HZFNKX7K","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"pith_short_8","alias_value":"2H6I6GI7","created_at":"2026-07-05T09:50:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2H6I6GI7HZFNKX7KX5MXGYOZBO","target":"record","payload":{"canonical_record":{"source":{"id":"2401.08445","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-01-16T15:45:49Z","cross_cats_sorted":[],"title_canon_sha256":"a6f6eb6df8f9179e355c234f5e8a484f64ce3c0e846a571021862d5b2f0163e4","abstract_canon_sha256":"ab7b2d991f34680fac2d9ce4b5531e14a313f41e467e6873af5de60ba9736520"},"schema_version":"1.0"},"canonical_sha256":"d1fc8f191f3e4ad55feabf597361d90b8d59382d7511104533c1d216351726d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:50:29.921260Z","signature_b64":"1fKKoc8MBOve7LljX+/GKRzaH9+TWene6YCnHevr29mV9nVbbml4wXKzdxvDXcJTiXvlxb6VO5NWjNrqIenaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1fc8f191f3e4ad55feabf597361d90b8d59382d7511104533c1d216351726d6","last_reissued_at":"2026-07-05T09:50:29.920771Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:50:29.920771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.08445","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:50:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VVxNClGQ0cb/9znPfSOVXKyaX0m/+kYDw9rQJgAtT9il8dQHdp2NpqDs1SPakJPql/NnmRjyMXwt3mATYyNFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:31:49.428773Z"},"content_sha256":"e1000456a4d5e941ed90bf2d727b2f6fa231b1e20598460fed3d9dc6c45be2aa","schema_version":"1.0","event_id":"sha256:e1000456a4d5e941ed90bf2d727b2f6fa231b1e20598460fed3d9dc6c45be2aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2H6I6GI7HZFNKX7KX5MXGYOZBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Reasoning over Relational Structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Henning Urbat, Jan Jurka, Stefan Milius","submitted_at":"2024-01-16T15:45:49Z","abstract_excerpt":"Many important computational structures involve an intricate interplay between algebraic features (given by operations on the underlying set) and relational features (taking account of notions such as order or distance). This paper investigates algebras over relational structures axiomatized by an infinitary Horn theory, which subsume, for example, partial algebras, various incarnations of ordered algebras, quantitative algebras introduced by Mardare, Panangaden, and Plotkin, and their recent extension to generalized metric spaces and lifted algebraic signatures by Mio, Sarkis, and Vignudelli."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08445","kind":"arxiv","version":5},"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/2401.08445/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":"2026-07-05T09:50:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nG9P2xhaHvIejXJWW9CNh3tBPcph3iceQKJI8UuiOf5HgnMmCXJJBDMK64E8HHHKatiPvW3E5EqBMksoPkxnBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T12:31:49.429277Z"},"content_sha256":"f51c4920101720345fb4171e3820ce4972d3a650378b8b9d900c29f2d6fa9058","schema_version":"1.0","event_id":"sha256:f51c4920101720345fb4171e3820ce4972d3a650378b8b9d900c29f2d6fa9058"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2H6I6GI7HZFNKX7KX5MXGYOZBO/bundle.json","state_url":"https://pith.science/pith/2H6I6GI7HZFNKX7KX5MXGYOZBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2H6I6GI7HZFNKX7KX5MXGYOZBO/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":"2026-08-10T12:31:49Z","links":{"resolver":"https://pith.science/pith/2H6I6GI7HZFNKX7KX5MXGYOZBO","bundle":"https://pith.science/pith/2H6I6GI7HZFNKX7KX5MXGYOZBO/bundle.json","state":"https://pith.science/pith/2H6I6GI7HZFNKX7KX5MXGYOZBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2H6I6GI7HZFNKX7KX5MXGYOZBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2H6I6GI7HZFNKX7KX5MXGYOZBO","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":"ab7b2d991f34680fac2d9ce4b5531e14a313f41e467e6873af5de60ba9736520","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-01-16T15:45:49Z","title_canon_sha256":"a6f6eb6df8f9179e355c234f5e8a484f64ce3c0e846a571021862d5b2f0163e4"},"schema_version":"1.0","source":{"id":"2401.08445","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.08445","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"2401.08445v5","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.08445","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"2H6I6GI7HZFN","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"pith_short_16","alias_value":"2H6I6GI7HZFNKX7K","created_at":"2026-07-05T09:50:29Z"},{"alias_kind":"pith_short_8","alias_value":"2H6I6GI7","created_at":"2026-07-05T09:50:29Z"}],"graph_snapshots":[{"event_id":"sha256:f51c4920101720345fb4171e3820ce4972d3a650378b8b9d900c29f2d6fa9058","target":"graph","created_at":"2026-07-05T09:50:29Z","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/2401.08445/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many important computational structures involve an intricate interplay between algebraic features (given by operations on the underlying set) and relational features (taking account of notions such as order or distance). This paper investigates algebras over relational structures axiomatized by an infinitary Horn theory, which subsume, for example, partial algebras, various incarnations of ordered algebras, quantitative algebras introduced by Mardare, Panangaden, and Plotkin, and their recent extension to generalized metric spaces and lifted algebraic signatures by Mio, Sarkis, and Vignudelli.","authors_text":"Henning Urbat, Jan Jurka, Stefan Milius","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-01-16T15:45:49Z","title":"Algebraic Reasoning over Relational Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08445","kind":"arxiv","version":5},"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:e1000456a4d5e941ed90bf2d727b2f6fa231b1e20598460fed3d9dc6c45be2aa","target":"record","created_at":"2026-07-05T09:50:29Z","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":"ab7b2d991f34680fac2d9ce4b5531e14a313f41e467e6873af5de60ba9736520","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2024-01-16T15:45:49Z","title_canon_sha256":"a6f6eb6df8f9179e355c234f5e8a484f64ce3c0e846a571021862d5b2f0163e4"},"schema_version":"1.0","source":{"id":"2401.08445","kind":"arxiv","version":5}},"canonical_sha256":"d1fc8f191f3e4ad55feabf597361d90b8d59382d7511104533c1d216351726d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1fc8f191f3e4ad55feabf597361d90b8d59382d7511104533c1d216351726d6","first_computed_at":"2026-07-05T09:50:29.920771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:50:29.920771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1fKKoc8MBOve7LljX+/GKRzaH9+TWene6YCnHevr29mV9nVbbml4wXKzdxvDXcJTiXvlxb6VO5NWjNrqIenaDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:50:29.921260Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.08445","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1000456a4d5e941ed90bf2d727b2f6fa231b1e20598460fed3d9dc6c45be2aa","sha256:f51c4920101720345fb4171e3820ce4972d3a650378b8b9d900c29f2d6fa9058"],"state_sha256":"8be2761255f1a7ea02f67b29289dd97925e07eb99ad196b11e54596fcfa36cac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZHrN5KVc5IJrzlArUOeCu0kkBeW1TSkKykqX1oG+7UNOadqEXqQcQ9qpJoYT2M8DL7vgA1k2OsgOsBJmTRIBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T12:31:49.433062Z","bundle_sha256":"a018f17b113c43a05a27241526afb57eb72cfacfb42d226ca37847c8852f59e0"}}