{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7ACGCNIHJ5XSAZ74AT4QWG2Q6O","short_pith_number":"pith:7ACGCNIH","canonical_record":{"source":{"id":"1612.04652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-27T12:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"32b5c3cb4cb442e62e2b22d55f91ef7abfcb12194309c8096f77087c3a049a67","abstract_canon_sha256":"f39f7d282eda4083070a8f86896d0b1bb5ff4d1950185c0a5852edec46b8264f"},"schema_version":"1.0"},"canonical_sha256":"f8046135074f6f2067fc04f90b1b50f3865e00ba3e0494b58113c91790446ea9","source":{"kind":"arxiv","id":"1612.04652","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04652","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04652v1","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04652","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"7ACGCNIHJ5XS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7ACGCNIHJ5XSAZ74","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7ACGCNIH","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7ACGCNIHJ5XSAZ74AT4QWG2Q6O","target":"record","payload":{"canonical_record":{"source":{"id":"1612.04652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-27T12:32:40Z","cross_cats_sorted":[],"title_canon_sha256":"32b5c3cb4cb442e62e2b22d55f91ef7abfcb12194309c8096f77087c3a049a67","abstract_canon_sha256":"f39f7d282eda4083070a8f86896d0b1bb5ff4d1950185c0a5852edec46b8264f"},"schema_version":"1.0"},"canonical_sha256":"f8046135074f6f2067fc04f90b1b50f3865e00ba3e0494b58113c91790446ea9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:58.932168Z","signature_b64":"F132lOFVjNAnYe6U/6GetF0lANAsoiYiskV4e2BjBrIEd0BcxBrjXgTUh4Do8tUveZUqlimK0UUgL6j1EuaKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8046135074f6f2067fc04f90b1b50f3865e00ba3e0494b58113c91790446ea9","last_reissued_at":"2026-05-18T00:54:58.931549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:58.931549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.04652","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":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nmSHZ5EPemDOzU3JhlNvmUpZQfYU6+HosPEGW+xMIXRgrzSEYS6GDdWOEWYrDrjUnCshsbkqacgK6zWAFgQhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:51:15.128943Z"},"content_sha256":"42dc495559559c4312402ed7b39d950748429810a5a614ae209732f9e43147ca","schema_version":"1.0","event_id":"sha256:42dc495559559c4312402ed7b39d950748429810a5a614ae209732f9e43147ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7ACGCNIHJ5XSAZ74AT4QWG2Q6O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order and interval topologies on complete Boolean algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Dominic van der Zypen","submitted_at":"2016-10-27T12:32:40Z","abstract_excerpt":"We introduce and examine order convergence and the interval topology on partially ordered sets in general. Problem 76 of Birkhoff's \"Lattice Theory\" asks whether for complete Boolean algebras the order topology and the interval topology coincide. We answer this question in the negative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04652","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":"2026-05-18T00:54:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GJdYSjWExEx0YCL3Glc6MxJjv5LUfz+Pes9jyZUSQZb4GEO3u1w0x9YbD8CZiZaYpVd7ZRqweLKBzJlB44B2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:51:15.129571Z"},"content_sha256":"e4d129eccce73c4a7258436390e3a83f5e81595ff1b128d1a94879afcc36297d","schema_version":"1.0","event_id":"sha256:e4d129eccce73c4a7258436390e3a83f5e81595ff1b128d1a94879afcc36297d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ACGCNIHJ5XSAZ74AT4QWG2Q6O/bundle.json","state_url":"https://pith.science/pith/7ACGCNIHJ5XSAZ74AT4QWG2Q6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ACGCNIHJ5XSAZ74AT4QWG2Q6O/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":"2026-06-25T10:51:15Z","links":{"resolver":"https://pith.science/pith/7ACGCNIHJ5XSAZ74AT4QWG2Q6O","bundle":"https://pith.science/pith/7ACGCNIHJ5XSAZ74AT4QWG2Q6O/bundle.json","state":"https://pith.science/pith/7ACGCNIHJ5XSAZ74AT4QWG2Q6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ACGCNIHJ5XSAZ74AT4QWG2Q6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7ACGCNIHJ5XSAZ74AT4QWG2Q6O","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":"f39f7d282eda4083070a8f86896d0b1bb5ff4d1950185c0a5852edec46b8264f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-27T12:32:40Z","title_canon_sha256":"32b5c3cb4cb442e62e2b22d55f91ef7abfcb12194309c8096f77087c3a049a67"},"schema_version":"1.0","source":{"id":"1612.04652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04652","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04652v1","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04652","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"7ACGCNIHJ5XS","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7ACGCNIHJ5XSAZ74","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7ACGCNIH","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:e4d129eccce73c4a7258436390e3a83f5e81595ff1b128d1a94879afcc36297d","target":"graph","created_at":"2026-05-18T00:54:58Z","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 introduce and examine order convergence and the interval topology on partially ordered sets in general. Problem 76 of Birkhoff's \"Lattice Theory\" asks whether for complete Boolean algebras the order topology and the interval topology coincide. We answer this question in the negative.","authors_text":"Dominic van der Zypen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-27T12:32:40Z","title":"Order and interval topologies on complete Boolean algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04652","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":"sha256:42dc495559559c4312402ed7b39d950748429810a5a614ae209732f9e43147ca","target":"record","created_at":"2026-05-18T00:54:58Z","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":"f39f7d282eda4083070a8f86896d0b1bb5ff4d1950185c0a5852edec46b8264f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-27T12:32:40Z","title_canon_sha256":"32b5c3cb4cb442e62e2b22d55f91ef7abfcb12194309c8096f77087c3a049a67"},"schema_version":"1.0","source":{"id":"1612.04652","kind":"arxiv","version":1}},"canonical_sha256":"f8046135074f6f2067fc04f90b1b50f3865e00ba3e0494b58113c91790446ea9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8046135074f6f2067fc04f90b1b50f3865e00ba3e0494b58113c91790446ea9","first_computed_at":"2026-05-18T00:54:58.931549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:58.931549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F132lOFVjNAnYe6U/6GetF0lANAsoiYiskV4e2BjBrIEd0BcxBrjXgTUh4Do8tUveZUqlimK0UUgL6j1EuaKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:58.932168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42dc495559559c4312402ed7b39d950748429810a5a614ae209732f9e43147ca","sha256:e4d129eccce73c4a7258436390e3a83f5e81595ff1b128d1a94879afcc36297d"],"state_sha256":"7aab488ddef46b1c719a0a712a97a1b13f077137aa9f80ebfcb1fd0872d0ac2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eCAWrXMUn5r1+g7hORyBUvEBJDLg8RiFUkQ8974q2yP/ZqC27dPMngtFr3vGXLEs2lO3Qdr3HN9fbzVKQkrsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:51:15.131429Z","bundle_sha256":"a4f4aa636cc119b700f23f7bc805b5c9fc389bac93b2a89fe2b2caaafec5c903"}}