{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:D6OQ7HFTQJBUUK6PSW45FDHYTZ","short_pith_number":"pith:D6OQ7HFT","canonical_record":{"source":{"id":"1710.00220","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.LO","submitted_at":"2017-09-30T16:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"4dbcf0c45a020f34f819a4e04d3f2d1a2457077c5edf98ffd59cca0bf8b87511","abstract_canon_sha256":"a58073bc1cab7fddf0eb940108a1e25dfe94a3bfad1fbf8ebd8b0912c1512744"},"schema_version":"1.0"},"canonical_sha256":"1f9d0f9cb382434a2bcf95b9d28cf89e7010a9133f7ffc453dec0a7f28ce4415","source":{"kind":"arxiv","id":"1710.00220","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00220","created_at":"2026-05-17T23:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00220v3","created_at":"2026-05-17T23:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00220","created_at":"2026-05-17T23:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"D6OQ7HFTQJBU","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D6OQ7HFTQJBUUK6P","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D6OQ7HFT","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:D6OQ7HFTQJBUUK6PSW45FDHYTZ","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00220","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.LO","submitted_at":"2017-09-30T16:23:02Z","cross_cats_sorted":[],"title_canon_sha256":"4dbcf0c45a020f34f819a4e04d3f2d1a2457077c5edf98ffd59cca0bf8b87511","abstract_canon_sha256":"a58073bc1cab7fddf0eb940108a1e25dfe94a3bfad1fbf8ebd8b0912c1512744"},"schema_version":"1.0"},"canonical_sha256":"1f9d0f9cb382434a2bcf95b9d28cf89e7010a9133f7ffc453dec0a7f28ce4415","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:23.977720Z","signature_b64":"AAIv09wu8LvaNhvOGl8336YSCxasGKnHGigLxMD5Sv7kGCbbFEWmQainZZTGiHyrxNF5VmZBYhnzq4NtaENtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f9d0f9cb382434a2bcf95b9d28cf89e7010a9133f7ffc453dec0a7f28ce4415","last_reissued_at":"2026-05-17T23:48:23.977106Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:23.977106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00220","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"250DpexPe4owLMy/zmeL+TNYeRJME6tfrQuD0g0Ye6gULbVnJq49+zE+EFUE8WkPGejj96LPAUzKTePtJQXHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:38:00.476948Z"},"content_sha256":"e14637a8008521435c6e77908b07efc776b639ca4737cd0ae28bd5f97892eeb9","schema_version":"1.0","event_id":"sha256:e14637a8008521435c6e77908b07efc776b639ca4737cd0ae28bd5f97892eeb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:D6OQ7HFTQJBUUK6PSW45FDHYTZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Abstract Approach to Consequence Relations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Francesco Paoli, Jos\\'e Gil F\\'erez, Petr Cintula, Tommaso Moraschini","submitted_at":"2017-09-30T16:23:02Z","abstract_excerpt":"We generalise the Blok-J\\'onsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and J\\'onsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariably aggregated via set-theoretical union. Our approach is more general in that non-idempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. In their abstract "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00220","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zwbopzt/0thBYq4HrAxmz2fyT7l87i5llyjr3tkuMGceTz0pxs03hsZsU+XhbbK/j+0RWYkLUMbtcp5BrjuwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:38:00.477657Z"},"content_sha256":"f094c095aac864fa83fc8d6fb12cef1e79ef42ac2fd65a7f3dc31b5dc90816a0","schema_version":"1.0","event_id":"sha256:f094c095aac864fa83fc8d6fb12cef1e79ef42ac2fd65a7f3dc31b5dc90816a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6OQ7HFTQJBUUK6PSW45FDHYTZ/bundle.json","state_url":"https://pith.science/pith/D6OQ7HFTQJBUUK6PSW45FDHYTZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6OQ7HFTQJBUUK6PSW45FDHYTZ/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":"2026-06-06T15:38:00Z","links":{"resolver":"https://pith.science/pith/D6OQ7HFTQJBUUK6PSW45FDHYTZ","bundle":"https://pith.science/pith/D6OQ7HFTQJBUUK6PSW45FDHYTZ/bundle.json","state":"https://pith.science/pith/D6OQ7HFTQJBUUK6PSW45FDHYTZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6OQ7HFTQJBUUK6PSW45FDHYTZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D6OQ7HFTQJBUUK6PSW45FDHYTZ","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":"a58073bc1cab7fddf0eb940108a1e25dfe94a3bfad1fbf8ebd8b0912c1512744","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.LO","submitted_at":"2017-09-30T16:23:02Z","title_canon_sha256":"4dbcf0c45a020f34f819a4e04d3f2d1a2457077c5edf98ffd59cca0bf8b87511"},"schema_version":"1.0","source":{"id":"1710.00220","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00220","created_at":"2026-05-17T23:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00220v3","created_at":"2026-05-17T23:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00220","created_at":"2026-05-17T23:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"D6OQ7HFTQJBU","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D6OQ7HFTQJBUUK6P","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D6OQ7HFT","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:f094c095aac864fa83fc8d6fb12cef1e79ef42ac2fd65a7f3dc31b5dc90816a0","target":"graph","created_at":"2026-05-17T23:48:23Z","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"},"paper":{"abstract_excerpt":"We generalise the Blok-J\\'onsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and J\\'onsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariably aggregated via set-theoretical union. Our approach is more general in that non-idempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. In their abstract ","authors_text":"Francesco Paoli, Jos\\'e Gil F\\'erez, Petr Cintula, Tommaso Moraschini","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.LO","submitted_at":"2017-09-30T16:23:02Z","title":"An Abstract Approach to Consequence Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00220","kind":"arxiv","version":3},"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:e14637a8008521435c6e77908b07efc776b639ca4737cd0ae28bd5f97892eeb9","target":"record","created_at":"2026-05-17T23:48:23Z","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":"a58073bc1cab7fddf0eb940108a1e25dfe94a3bfad1fbf8ebd8b0912c1512744","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.LO","submitted_at":"2017-09-30T16:23:02Z","title_canon_sha256":"4dbcf0c45a020f34f819a4e04d3f2d1a2457077c5edf98ffd59cca0bf8b87511"},"schema_version":"1.0","source":{"id":"1710.00220","kind":"arxiv","version":3}},"canonical_sha256":"1f9d0f9cb382434a2bcf95b9d28cf89e7010a9133f7ffc453dec0a7f28ce4415","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f9d0f9cb382434a2bcf95b9d28cf89e7010a9133f7ffc453dec0a7f28ce4415","first_computed_at":"2026-05-17T23:48:23.977106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:23.977106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AAIv09wu8LvaNhvOGl8336YSCxasGKnHGigLxMD5Sv7kGCbbFEWmQainZZTGiHyrxNF5VmZBYhnzq4NtaENtAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:23.977720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00220","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e14637a8008521435c6e77908b07efc776b639ca4737cd0ae28bd5f97892eeb9","sha256:f094c095aac864fa83fc8d6fb12cef1e79ef42ac2fd65a7f3dc31b5dc90816a0"],"state_sha256":"258db9086ba1ddb05969b6d343d1ca8260f7f471f424bc9e5b4cb205b070daca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FLaDF8JT1OydtkPoI7sCzqDbwD76oOUgNVOaDzFwu29tSWP+AA4Vzj/xq6vo7OF4u9/z7+QrLe+mmAeQDohHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:38:00.481265Z","bundle_sha256":"ed9dedede3baa7aa47438b3520778af61aa8e25e47408db1257f41a5cb522349"}}