{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MEKBQ3H73UYXQKJWO7TFBZPRXQ","short_pith_number":"pith:MEKBQ3H7","schema_version":"1.0","canonical_sha256":"6114186cffdd3178293677e650e5f1bc3a6d7708b8e79015121377b4c9090c99","source":{"kind":"arxiv","id":"1503.02587","version":1},"attestation_state":"computed","paper":{"title":"Strongly Hit and Far Miss Hypertopology and Hit and Strongly Far Miss Hypertopology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"C. Guadagni, J.F. Peters","submitted_at":"2015-03-09T17:56:13Z","abstract_excerpt":"This article introduces the {\\it strongly hit and far-miss as well as hit and strongly far miss hypertopologies on $\\textrm{CL}(X)$ associated with} ${\\mathscr{B}}$, a nonempty family of subsets on the topological space $X$. They result from the strong farness and strong nearness proximities. The main results in this paper stem from the Hausdorffness of $(\\textrm{CL}(X), \\tau_{\\doublevee, \\mathscr{B}})$ and $(\\textrm{RCL}(X), \\tau^\\doublewedge_\\mathscr{B} ) $, where $\\textrm{RCL}(X)$ is the space of regular closed subsets of $X$. To obtain the results, special local families are introduced."},"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":"1503.02587","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-03-09T17:56:13Z","cross_cats_sorted":[],"title_canon_sha256":"11c80bf2da2856caf9d822ffdffa0edbd23e5f8096b320f07cedff23a1c2525a","abstract_canon_sha256":"0f8b9805ea23ea1563df74fbc1cfca134617cc590d964ae043e122f4e4824f66"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.352179Z","signature_b64":"/Da41czf6iheyqI0cWHmCJTGJG0NLWur3VfW+DOeCYxzWLGxNhyxaOLmztWoowEoZ/3ulTRL+T6KUGnXa8tpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6114186cffdd3178293677e650e5f1bc3a6d7708b8e79015121377b4c9090c99","last_reissued_at":"2026-05-18T02:25:19.351844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.351844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strongly Hit and Far Miss Hypertopology and Hit and Strongly Far Miss Hypertopology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"C. Guadagni, J.F. Peters","submitted_at":"2015-03-09T17:56:13Z","abstract_excerpt":"This article introduces the {\\it strongly hit and far-miss as well as hit and strongly far miss hypertopologies on $\\textrm{CL}(X)$ associated with} ${\\mathscr{B}}$, a nonempty family of subsets on the topological space $X$. They result from the strong farness and strong nearness proximities. The main results in this paper stem from the Hausdorffness of $(\\textrm{CL}(X), \\tau_{\\doublevee, \\mathscr{B}})$ and $(\\textrm{RCL}(X), \\tau^\\doublewedge_\\mathscr{B} ) $, where $\\textrm{RCL}(X)$ is the space of regular closed subsets of $X$. To obtain the results, special local families are introduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02587","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":"1503.02587","created_at":"2026-05-18T02:25:19.351898+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02587v1","created_at":"2026-05-18T02:25:19.351898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02587","created_at":"2026-05-18T02:25:19.351898+00:00"},{"alias_kind":"pith_short_12","alias_value":"MEKBQ3H73UYX","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MEKBQ3H73UYXQKJW","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MEKBQ3H7","created_at":"2026-05-18T12:29:32.376354+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/MEKBQ3H73UYXQKJWO7TFBZPRXQ","json":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ.json","graph_json":"https://pith.science/api/pith-number/MEKBQ3H73UYXQKJWO7TFBZPRXQ/graph.json","events_json":"https://pith.science/api/pith-number/MEKBQ3H73UYXQKJWO7TFBZPRXQ/events.json","paper":"https://pith.science/paper/MEKBQ3H7"},"agent_actions":{"view_html":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ","download_json":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ.json","view_paper":"https://pith.science/paper/MEKBQ3H7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02587&json=true","fetch_graph":"https://pith.science/api/pith-number/MEKBQ3H73UYXQKJWO7TFBZPRXQ/graph.json","fetch_events":"https://pith.science/api/pith-number/MEKBQ3H73UYXQKJWO7TFBZPRXQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/action/storage_attestation","attest_author":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/action/author_attestation","sign_citation":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/action/citation_signature","submit_replication":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/action/replication_record"}},"created_at":"2026-05-18T02:25:19.351898+00:00","updated_at":"2026-05-18T02:25:19.351898+00:00"}