{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:HDN3GEXD63ZUISLGMFE2J2PEGN","short_pith_number":"pith:HDN3GEXD","canonical_record":{"source":{"id":"2208.07430","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-08-15T20:40:12Z","cross_cats_sorted":[],"title_canon_sha256":"6d759abd1a3919b398a6ea2b9a98ae15c6c3f1e57472d6c1493dc8299d1e4702","abstract_canon_sha256":"0f90fd8dc9d8fd1e74ebcec3fbf1a575876968de2971b07724d4e9cf08c26773"},"schema_version":"1.0"},"canonical_sha256":"38dbb312e3f6f34449666149a4e9e4334b2e18d7f893a69dbc4c0ddf65a3b99b","source":{"kind":"arxiv","id":"2208.07430","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.07430","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"2208.07430v2","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.07430","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"HDN3GEXD63ZU","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"pith_short_16","alias_value":"HDN3GEXD63ZUISLG","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"pith_short_8","alias_value":"HDN3GEXD","created_at":"2026-07-05T06:03:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:HDN3GEXD63ZUISLGMFE2J2PEGN","target":"record","payload":{"canonical_record":{"source":{"id":"2208.07430","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-08-15T20:40:12Z","cross_cats_sorted":[],"title_canon_sha256":"6d759abd1a3919b398a6ea2b9a98ae15c6c3f1e57472d6c1493dc8299d1e4702","abstract_canon_sha256":"0f90fd8dc9d8fd1e74ebcec3fbf1a575876968de2971b07724d4e9cf08c26773"},"schema_version":"1.0"},"canonical_sha256":"38dbb312e3f6f34449666149a4e9e4334b2e18d7f893a69dbc4c0ddf65a3b99b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:03:56.629878Z","signature_b64":"7Wn+77b/0t6EQAMgjn76qQ4p8mApawYAL6yUpnmpb277SYp6XLj1T5yX4zy8ebB/xmokxujV/Zml/cdD5ScQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38dbb312e3f6f34449666149a4e9e4334b2e18d7f893a69dbc4c0ddf65a3b99b","last_reissued_at":"2026-07-05T06:03:56.629362Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:03:56.629362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.07430","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gAVfVaa9Ijur2+KeUio5bCOwj6LDT3OoaF5lWFXceWf+oUeT0pDAHUX7XR+h9qFUlQZCFWLgBu/ReEwcfporBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T02:38:44.371013Z"},"content_sha256":"5d43394cb1b8bfe64fa90edba24842266a34d943a0263ead9364e1878559f452","schema_version":"1.0","event_id":"sha256:5d43394cb1b8bfe64fa90edba24842266a34d943a0263ead9364e1878559f452"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:HDN3GEXD63ZUISLGMFE2J2PEGN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological duality for orthomodular lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Joseph McDonald, Katalin Bimb\\'o","submitted_at":"2022-08-15T20:40:12Z","abstract_excerpt":"A class of ordered relational topological spaces is described, which we call orthomodular spaces. Our construction of these spaces involves adding a topology to the class of orthomodular frames introduced by Hartonas, along the lines of Bimb\\'o's topologization of the class of orthoframes employed by Goldblatt in his representation of ortholattices. We then prove that the category of orthomodular lattices and homomorphisms is dually equivalent to the category of orthomodular spaces and certain continuous frame morphisms, which we call continuous weak p-morphisms. It is well-known that orthomod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07430","kind":"arxiv","version":2},"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/2208.07430/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":"2026-07-05T06:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szCGGX8iNnQi/kvtSPAV27+cnr59VxO6DG1PthncYm9T3WkChd8Oh/t+z6mQylVl0ZlYGGlCcAUEkx/EFmlBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T02:38:44.371706Z"},"content_sha256":"297627c263b66331b46e1e82592f70bbbbf8361945260bb780adfcffe02796e7","schema_version":"1.0","event_id":"sha256:297627c263b66331b46e1e82592f70bbbbf8361945260bb780adfcffe02796e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HDN3GEXD63ZUISLGMFE2J2PEGN/bundle.json","state_url":"https://pith.science/pith/HDN3GEXD63ZUISLGMFE2J2PEGN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HDN3GEXD63ZUISLGMFE2J2PEGN/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":"2026-07-07T02:38:44Z","links":{"resolver":"https://pith.science/pith/HDN3GEXD63ZUISLGMFE2J2PEGN","bundle":"https://pith.science/pith/HDN3GEXD63ZUISLGMFE2J2PEGN/bundle.json","state":"https://pith.science/pith/HDN3GEXD63ZUISLGMFE2J2PEGN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HDN3GEXD63ZUISLGMFE2J2PEGN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:HDN3GEXD63ZUISLGMFE2J2PEGN","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":"0f90fd8dc9d8fd1e74ebcec3fbf1a575876968de2971b07724d4e9cf08c26773","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-08-15T20:40:12Z","title_canon_sha256":"6d759abd1a3919b398a6ea2b9a98ae15c6c3f1e57472d6c1493dc8299d1e4702"},"schema_version":"1.0","source":{"id":"2208.07430","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.07430","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"2208.07430v2","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.07430","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"HDN3GEXD63ZU","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"pith_short_16","alias_value":"HDN3GEXD63ZUISLG","created_at":"2026-07-05T06:03:56Z"},{"alias_kind":"pith_short_8","alias_value":"HDN3GEXD","created_at":"2026-07-05T06:03:56Z"}],"graph_snapshots":[{"event_id":"sha256:297627c263b66331b46e1e82592f70bbbbf8361945260bb780adfcffe02796e7","target":"graph","created_at":"2026-07-05T06:03:56Z","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/2208.07430/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A class of ordered relational topological spaces is described, which we call orthomodular spaces. Our construction of these spaces involves adding a topology to the class of orthomodular frames introduced by Hartonas, along the lines of Bimb\\'o's topologization of the class of orthoframes employed by Goldblatt in his representation of ortholattices. We then prove that the category of orthomodular lattices and homomorphisms is dually equivalent to the category of orthomodular spaces and certain continuous frame morphisms, which we call continuous weak p-morphisms. It is well-known that orthomod","authors_text":"Joseph McDonald, Katalin Bimb\\'o","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-08-15T20:40:12Z","title":"Topological duality for orthomodular lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.07430","kind":"arxiv","version":2},"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":"sha256:5d43394cb1b8bfe64fa90edba24842266a34d943a0263ead9364e1878559f452","target":"record","created_at":"2026-07-05T06:03:56Z","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":"0f90fd8dc9d8fd1e74ebcec3fbf1a575876968de2971b07724d4e9cf08c26773","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2022-08-15T20:40:12Z","title_canon_sha256":"6d759abd1a3919b398a6ea2b9a98ae15c6c3f1e57472d6c1493dc8299d1e4702"},"schema_version":"1.0","source":{"id":"2208.07430","kind":"arxiv","version":2}},"canonical_sha256":"38dbb312e3f6f34449666149a4e9e4334b2e18d7f893a69dbc4c0ddf65a3b99b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38dbb312e3f6f34449666149a4e9e4334b2e18d7f893a69dbc4c0ddf65a3b99b","first_computed_at":"2026-07-05T06:03:56.629362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:03:56.629362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Wn+77b/0t6EQAMgjn76qQ4p8mApawYAL6yUpnmpb277SYp6XLj1T5yX4zy8ebB/xmokxujV/Zml/cdD5ScQAg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:03:56.629878Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.07430","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d43394cb1b8bfe64fa90edba24842266a34d943a0263ead9364e1878559f452","sha256:297627c263b66331b46e1e82592f70bbbbf8361945260bb780adfcffe02796e7"],"state_sha256":"4e9f474f2ef0dd3d66393b5fb36f38d9c952c0351e75da59b7218a329ce3e5f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VRECw1J2UWv8FROEvFim9UaFRPYfsx+NeaZhmB7vxiiEEInfFxHKKZ+CWH4rczJoHJRTGtq3KvkepB8Bxo0DAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T02:38:44.375212Z","bundle_sha256":"c2f6e4e55d8dadca723d2dc3535508fe8ad92fe845acf45564d0baab359d76b8"}}