{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:Q3WLR7RMMEI5F463JM6GLF4LN7","short_pith_number":"pith:Q3WLR7RM","schema_version":"1.0","canonical_sha256":"86ecb8fe2c6111d2f3db4b3c65978b6fc376f12301da475ebcfbd9e897a0de81","source":{"kind":"arxiv","id":"1301.5658","version":1},"attestation_state":"computed","paper":{"title":"A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Aleksandar Pavlovi\\'c, Milo\\v{s} S. Kurili\\'c","submitted_at":"2013-01-23T22:03:54Z","abstract_excerpt":"We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\\lambda_s$ (the algebraic convergence) and $\\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $\\lambda_{ls}$ is a topological convergence iff forcing by B does not produce new reals and that $\\lambda_{ls}$ is weakly topological if B satisfies condition $(\\hbar)$ (implied by the ${\\mathfrak t}$-cc). On the other hand, if $\\lambda_{ls}$ is a weakly topological convergence, then B is a $2^{\\mathfrak h}$-cc alge"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1301.5658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-01-23T22:03:54Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"3f4d9c5e3976de137d04b8034d4a3e00d98f55debada0f60e95e4c93f0c7e698","abstract_canon_sha256":"340c31342beff4fb9f28aeaaa848bea4dcfcc57729537f97ad14cb3a3264d8b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:47.848913Z","signature_b64":"OpYjKYyiW7ObC44m7kjXyn57z3oqD7q7h6MRuPbP+hKhVB7r1ukdJZcdCW3T8+cQop0j1iw9vlSse1NytQG8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86ecb8fe2c6111d2f3db4b3c65978b6fc376f12301da475ebcfbd9e897a0de81","last_reissued_at":"2026-05-18T00:04:47.848170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:47.848170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GN","authors_text":"Aleksandar Pavlovi\\'c, Milo\\v{s} S. Kurili\\'c","submitted_at":"2013-01-23T22:03:54Z","abstract_excerpt":"We compare the forcing related properties of a complete Boolean algebra B with the properties of the convergences $\\lambda_s$ (the algebraic convergence) and $\\lambda_{ls}$ on B generalizing the convergence on the Cantor and Aleksandrov cube respectively. In particular we show that $\\lambda_{ls}$ is a topological convergence iff forcing by B does not produce new reals and that $\\lambda_{ls}$ is weakly topological if B satisfies condition $(\\hbar)$ (implied by the ${\\mathfrak t}$-cc). On the other hand, if $\\lambda_{ls}$ is a weakly topological convergence, then B is a $2^{\\mathfrak h}$-cc alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5658","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1301.5658","created_at":"2026-05-18T00:04:47.848288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.5658v1","created_at":"2026-05-18T00:04:47.848288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5658","created_at":"2026-05-18T00:04:47.848288+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q3WLR7RMMEI5","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q3WLR7RMMEI5F463","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q3WLR7RM","created_at":"2026-05-18T12:27:57.521954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7","json":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7.json","graph_json":"https://pith.science/api/pith-number/Q3WLR7RMMEI5F463JM6GLF4LN7/graph.json","events_json":"https://pith.science/api/pith-number/Q3WLR7RMMEI5F463JM6GLF4LN7/events.json","paper":"https://pith.science/paper/Q3WLR7RM"},"agent_actions":{"view_html":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7","download_json":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7.json","view_paper":"https://pith.science/paper/Q3WLR7RM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.5658&json=true","fetch_graph":"https://pith.science/api/pith-number/Q3WLR7RMMEI5F463JM6GLF4LN7/graph.json","fetch_events":"https://pith.science/api/pith-number/Q3WLR7RMMEI5F463JM6GLF4LN7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7/action/storage_attestation","attest_author":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7/action/author_attestation","sign_citation":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7/action/citation_signature","submit_replication":"https://pith.science/pith/Q3WLR7RMMEI5F463JM6GLF4LN7/action/replication_record"}},"created_at":"2026-05-18T00:04:47.848288+00:00","updated_at":"2026-05-18T00:04:47.848288+00:00"}