{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BHXW2VCLBL75EC54DXSD2QZGFZ","short_pith_number":"pith:BHXW2VCL","canonical_record":{"source":{"id":"1302.5609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-22T14:38:08Z","cross_cats_sorted":[],"title_canon_sha256":"e6dd27d49e86db20288d92619dc42e966a280b8dc9df90c3dd61f10df491531e","abstract_canon_sha256":"4b5d00abc1a67117dce910c5070ebe2c2ac034f6cda30394ff2dc2274a08bea5"},"schema_version":"1.0"},"canonical_sha256":"09ef6d544b0affd20bbc1de43d43262e5b1bc3be0d13387cffc0fe4200792edd","source":{"kind":"arxiv","id":"1302.5609","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5609","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5609v1","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5609","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"BHXW2VCLBL75","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BHXW2VCLBL75EC54","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BHXW2VCL","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BHXW2VCLBL75EC54DXSD2QZGFZ","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-22T14:38:08Z","cross_cats_sorted":[],"title_canon_sha256":"e6dd27d49e86db20288d92619dc42e966a280b8dc9df90c3dd61f10df491531e","abstract_canon_sha256":"4b5d00abc1a67117dce910c5070ebe2c2ac034f6cda30394ff2dc2274a08bea5"},"schema_version":"1.0"},"canonical_sha256":"09ef6d544b0affd20bbc1de43d43262e5b1bc3be0d13387cffc0fe4200792edd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:46.253749Z","signature_b64":"84TzOs3KPvpB0z6NByyooTayoKazrkDQ+YMX4bpEZawtFp3VZqLGJFPSuNl4QIcF48tiiRapWSVPPxGtwOYKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09ef6d544b0affd20bbc1de43d43262e5b1bc3be0d13387cffc0fe4200792edd","last_reissued_at":"2026-05-18T03:32:46.253137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:46.253137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5609","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":"2026-05-18T03:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8hPBpmZbRDD9nTpFuh8Jo0fITR41UhhYn5GRiaKa54O+GBiRKPw+KtxyTyYsUVmEV5/DHOEK7BPGhzsSF7S3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T18:42:37.734971Z"},"content_sha256":"843add1ed2d3e66db5a6202385e1fc39e51e6b15de1e5aecbc36053d3e4bb297","schema_version":"1.0","event_id":"sha256:843add1ed2d3e66db5a6202385e1fc39e51e6b15de1e5aecbc36053d3e4bb297"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BHXW2VCLBL75EC54DXSD2QZGFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dualities in modal logic from the point of view of triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dirk Hofmann, Pedro Nora","submitted_at":"2013-02-22T14:38:08Z","abstract_excerpt":"In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on the other. Furthermore, we investigate the monoidal structure induced by Cartesian product on the relational side and show that in some cases the corresponding operation on the algebraic side represents bimorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5609","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":""},"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":"2026-05-18T03:32:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSSdoj7fLSUYC7mIR6vxP+XB2drZ+GExntB5LwFgThvLLYBqaS/gmTmhZLy2glEotr7VILVSmc23qDYInDaWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T18:42:37.735360Z"},"content_sha256":"852dd1582f034b791b6027fef892bf40b6acb2a0665bf79d27e073ff2f4b6bda","schema_version":"1.0","event_id":"sha256:852dd1582f034b791b6027fef892bf40b6acb2a0665bf79d27e073ff2f4b6bda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BHXW2VCLBL75EC54DXSD2QZGFZ/bundle.json","state_url":"https://pith.science/pith/BHXW2VCLBL75EC54DXSD2QZGFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BHXW2VCLBL75EC54DXSD2QZGFZ/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":"2026-05-19T18:42:37Z","links":{"resolver":"https://pith.science/pith/BHXW2VCLBL75EC54DXSD2QZGFZ","bundle":"https://pith.science/pith/BHXW2VCLBL75EC54DXSD2QZGFZ/bundle.json","state":"https://pith.science/pith/BHXW2VCLBL75EC54DXSD2QZGFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BHXW2VCLBL75EC54DXSD2QZGFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BHXW2VCLBL75EC54DXSD2QZGFZ","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":"4b5d00abc1a67117dce910c5070ebe2c2ac034f6cda30394ff2dc2274a08bea5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-22T14:38:08Z","title_canon_sha256":"e6dd27d49e86db20288d92619dc42e966a280b8dc9df90c3dd61f10df491531e"},"schema_version":"1.0","source":{"id":"1302.5609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5609","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5609v1","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5609","created_at":"2026-05-18T03:32:46Z"},{"alias_kind":"pith_short_12","alias_value":"BHXW2VCLBL75","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BHXW2VCLBL75EC54","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BHXW2VCL","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:852dd1582f034b791b6027fef892bf40b6acb2a0665bf79d27e073ff2f4b6bda","target":"graph","created_at":"2026-05-18T03:32:46Z","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":"In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on the other. Furthermore, we investigate the monoidal structure induced by Cartesian product on the relational side and show that in some cases the corresponding operation on the algebraic side represents bimorphisms.","authors_text":"Dirk Hofmann, Pedro Nora","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-22T14:38:08Z","title":"Dualities in modal logic from the point of view of triples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5609","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":"sha256:843add1ed2d3e66db5a6202385e1fc39e51e6b15de1e5aecbc36053d3e4bb297","target":"record","created_at":"2026-05-18T03:32:46Z","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":"4b5d00abc1a67117dce910c5070ebe2c2ac034f6cda30394ff2dc2274a08bea5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-22T14:38:08Z","title_canon_sha256":"e6dd27d49e86db20288d92619dc42e966a280b8dc9df90c3dd61f10df491531e"},"schema_version":"1.0","source":{"id":"1302.5609","kind":"arxiv","version":1}},"canonical_sha256":"09ef6d544b0affd20bbc1de43d43262e5b1bc3be0d13387cffc0fe4200792edd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09ef6d544b0affd20bbc1de43d43262e5b1bc3be0d13387cffc0fe4200792edd","first_computed_at":"2026-05-18T03:32:46.253137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:46.253137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"84TzOs3KPvpB0z6NByyooTayoKazrkDQ+YMX4bpEZawtFp3VZqLGJFPSuNl4QIcF48tiiRapWSVPPxGtwOYKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:46.253749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:843add1ed2d3e66db5a6202385e1fc39e51e6b15de1e5aecbc36053d3e4bb297","sha256:852dd1582f034b791b6027fef892bf40b6acb2a0665bf79d27e073ff2f4b6bda"],"state_sha256":"a4c981a2bfb82b16d63163a7475b3e562ae8c3460aa1a30e93aaf4c34f84aea7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6ATR1acy07zpEL46RGoInm/fPJAX6QBFhKNPHRrONcQJKsF/3rTz6JphiDvhl8O6Y3d94H0ezKvuMH5SRX3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T18:42:37.737950Z","bundle_sha256":"1699fe6e4f4b1f2e27223c1cc7d87a4d8ce0f1ae1ad2fb141949f600dbda9b91"}}