{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MEKBQ3H73UYXQKJWO7TFBZPRXQ","short_pith_number":"pith:MEKBQ3H7","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"},"canonical_sha256":"6114186cffdd3178293677e650e5f1bc3a6d7708b8e79015121377b4c9090c99","source":{"kind":"arxiv","id":"1503.02587","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02587","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02587v1","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02587","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"MEKBQ3H73UYX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEKBQ3H73UYXQKJW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEKBQ3H7","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MEKBQ3H73UYXQKJWO7TFBZPRXQ","target":"record","payload":{"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"},"canonical_sha256":"6114186cffdd3178293677e650e5f1bc3a6d7708b8e79015121377b4c9090c99","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"},"source_kind":"arxiv","source_id":"1503.02587","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":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m10Z4tSf6XFqU7nlLf4WqLpg65FgboFn4IkF4f3317I7D9MAFcTRJrvD9dF4YqwGEvwFCwIbtEbWBzReyNhvBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:11:45.292726Z"},"content_sha256":"32297b6f7c2891423283062300463cb53f272ef66bdea0a4b2b652ac2a58796c","schema_version":"1.0","event_id":"sha256:32297b6f7c2891423283062300463cb53f272ef66bdea0a4b2b652ac2a58796c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MEKBQ3H73UYXQKJWO7TFBZPRXQ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ns7NCa0QoF7do/RkSz5Fgwa1tLrVkgrY4JwnHyxqyUHTkV7VaKzOuiwFYb3qpJ682C3X3aNYZ+E1xObmdPY3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:11:45.293081Z"},"content_sha256":"d7b4963c54a403ff0ce84bd5b5bf59eff52791d05ad674d05b8325d9915b348c","schema_version":"1.0","event_id":"sha256:d7b4963c54a403ff0ce84bd5b5bf59eff52791d05ad674d05b8325d9915b348c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/bundle.json","state_url":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/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":"2026-06-03T13:11:45Z","links":{"resolver":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ","bundle":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/bundle.json","state":"https://pith.science/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEKBQ3H73UYXQKJWO7TFBZPRXQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MEKBQ3H73UYXQKJWO7TFBZPRXQ","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":"0f8b9805ea23ea1563df74fbc1cfca134617cc590d964ae043e122f4e4824f66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-03-09T17:56:13Z","title_canon_sha256":"11c80bf2da2856caf9d822ffdffa0edbd23e5f8096b320f07cedff23a1c2525a"},"schema_version":"1.0","source":{"id":"1503.02587","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02587","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02587v1","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02587","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"MEKBQ3H73UYX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MEKBQ3H73UYXQKJW","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MEKBQ3H7","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:d7b4963c54a403ff0ce84bd5b5bf59eff52791d05ad674d05b8325d9915b348c","target":"graph","created_at":"2026-05-18T02:25:19Z","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":"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.","authors_text":"C. Guadagni, J.F. Peters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-03-09T17:56:13Z","title":"Strongly Hit and Far Miss Hypertopology and Hit and Strongly Far Miss Hypertopology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02587","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":"sha256:32297b6f7c2891423283062300463cb53f272ef66bdea0a4b2b652ac2a58796c","target":"record","created_at":"2026-05-18T02:25:19Z","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":"0f8b9805ea23ea1563df74fbc1cfca134617cc590d964ae043e122f4e4824f66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-03-09T17:56:13Z","title_canon_sha256":"11c80bf2da2856caf9d822ffdffa0edbd23e5f8096b320f07cedff23a1c2525a"},"schema_version":"1.0","source":{"id":"1503.02587","kind":"arxiv","version":1}},"canonical_sha256":"6114186cffdd3178293677e650e5f1bc3a6d7708b8e79015121377b4c9090c99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6114186cffdd3178293677e650e5f1bc3a6d7708b8e79015121377b4c9090c99","first_computed_at":"2026-05-18T02:25:19.351844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:19.351844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Da41czf6iheyqI0cWHmCJTGJG0NLWur3VfW+DOeCYxzWLGxNhyxaOLmztWoowEoZ/3ulTRL+T6KUGnXa8tpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:19.352179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02587","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32297b6f7c2891423283062300463cb53f272ef66bdea0a4b2b652ac2a58796c","sha256:d7b4963c54a403ff0ce84bd5b5bf59eff52791d05ad674d05b8325d9915b348c"],"state_sha256":"66c5ca910a1a29d94729eca281066725f3c0857e29deb8a3dcdf68f3f311d25e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ObJsrFABJROzOTOFI4fpIcmG/sqdEX2A+5RUgI3O1Gduug9IEXmWo8wJzwq+bSm7Oo/86Mq1kBe+vSQ1/nlDAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:11:45.295055Z","bundle_sha256":"a349aef5d0fb03c3e80433eef614da7f9defbfaae925eae04229082161844a74"}}