{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BDCX3BT5MVEGUPKHM5VEA4PJEN","short_pith_number":"pith:BDCX3BT5","canonical_record":{"source":{"id":"1710.10374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-10-28T02:28:19Z","cross_cats_sorted":[],"title_canon_sha256":"76655c3ea238ca459a8bd152138fefdd588a01bb5bb4633e36bbedf9a6f84487","abstract_canon_sha256":"582781d36fc103267f0af20401131ffd63f319c6d1908f1051204b224108cfa7"},"schema_version":"1.0"},"canonical_sha256":"08c57d867d65486a3d47676a4071e923427d7e908be8e04bdb9bc914e54c2521","source":{"kind":"arxiv","id":"1710.10374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10374","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10374v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10374","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"BDCX3BT5MVEG","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BDCX3BT5MVEGUPKH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BDCX3BT5","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BDCX3BT5MVEGUPKHM5VEA4PJEN","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-10-28T02:28:19Z","cross_cats_sorted":[],"title_canon_sha256":"76655c3ea238ca459a8bd152138fefdd588a01bb5bb4633e36bbedf9a6f84487","abstract_canon_sha256":"582781d36fc103267f0af20401131ffd63f319c6d1908f1051204b224108cfa7"},"schema_version":"1.0"},"canonical_sha256":"08c57d867d65486a3d47676a4071e923427d7e908be8e04bdb9bc914e54c2521","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:49.735729Z","signature_b64":"V4Bwa+5hKfAHtkyTBqamiWjP9nVf4adz5WiLcTk6fworX9W39Q+roZosIPKs7LfRVNqilfuPv5k2PiCM4NIKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08c57d867d65486a3d47676a4071e923427d7e908be8e04bdb9bc914e54c2521","last_reissued_at":"2026-05-18T00:31:49.735071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:49.735071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10374","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":"2026-05-18T00:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1UVou2C8ZGDOcrkeNoUyAVWXkxDDUUwFoLOm87I6+oPqXzYZyhyJzoRfkqJeeGWt9gB/s9miUVCPSJLQ/qtjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:39:59.763094Z"},"content_sha256":"77968a45cff106bd22d2bd38fd08ca6b754a574c6e1bff2d1df20a5adcebe037","schema_version":"1.0","event_id":"sha256:77968a45cff106bd22d2bd38fd08ca6b754a574c6e1bff2d1df20a5adcebe037"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BDCX3BT5MVEGUPKHM5VEA4PJEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotone Covering Properties defined by Closure-Preserving Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"John E. Porter, Strashimir G. Popvassilev","submitted_at":"2017-10-28T02:28:19Z","abstract_excerpt":"We continue Gartside, Moody, and Stares' study of versions of monotone paracompactness. We show that the class of spaces with a monotone closure-preserving open operator is strictly larger than those with a monotone open locally-finite operator. We prove that monotonically metacompact GO-spaces have a monotone open locally-finite operator, and so do GO-spaces with a monotone (open or not) closure-preserving operator, whose underlying LOTS has a $\\sigma$-closed-discrete dense subset. A GO-space with a $\\sigma$-closed-discrete dense subset and a monotone closure-preserving operator is metrizable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10374","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":"2026-05-18T00:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"siwWDymPAQtxTySIk1tZcIBMs1YzKm2SR5Vq2wuW1gZDZwvhGZuGn0e5iKHLRnO20XHvWsIUNb8RRPOhpAakAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:39:59.763465Z"},"content_sha256":"759df1f0982e83dcfaa424e18f268625ebf6e92c1ea5f2f236a57105d27f92ee","schema_version":"1.0","event_id":"sha256:759df1f0982e83dcfaa424e18f268625ebf6e92c1ea5f2f236a57105d27f92ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BDCX3BT5MVEGUPKHM5VEA4PJEN/bundle.json","state_url":"https://pith.science/pith/BDCX3BT5MVEGUPKHM5VEA4PJEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BDCX3BT5MVEGUPKHM5VEA4PJEN/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":"2026-05-28T04:39:59Z","links":{"resolver":"https://pith.science/pith/BDCX3BT5MVEGUPKHM5VEA4PJEN","bundle":"https://pith.science/pith/BDCX3BT5MVEGUPKHM5VEA4PJEN/bundle.json","state":"https://pith.science/pith/BDCX3BT5MVEGUPKHM5VEA4PJEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BDCX3BT5MVEGUPKHM5VEA4PJEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BDCX3BT5MVEGUPKHM5VEA4PJEN","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":"582781d36fc103267f0af20401131ffd63f319c6d1908f1051204b224108cfa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-10-28T02:28:19Z","title_canon_sha256":"76655c3ea238ca459a8bd152138fefdd588a01bb5bb4633e36bbedf9a6f84487"},"schema_version":"1.0","source":{"id":"1710.10374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10374","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10374v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10374","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"BDCX3BT5MVEG","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BDCX3BT5MVEGUPKH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BDCX3BT5","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:759df1f0982e83dcfaa424e18f268625ebf6e92c1ea5f2f236a57105d27f92ee","target":"graph","created_at":"2026-05-18T00:31:49Z","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 continue Gartside, Moody, and Stares' study of versions of monotone paracompactness. We show that the class of spaces with a monotone closure-preserving open operator is strictly larger than those with a monotone open locally-finite operator. We prove that monotonically metacompact GO-spaces have a monotone open locally-finite operator, and so do GO-spaces with a monotone (open or not) closure-preserving operator, whose underlying LOTS has a $\\sigma$-closed-discrete dense subset. A GO-space with a $\\sigma$-closed-discrete dense subset and a monotone closure-preserving operator is metrizable","authors_text":"John E. Porter, Strashimir G. Popvassilev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-10-28T02:28:19Z","title":"Monotone Covering Properties defined by Closure-Preserving Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10374","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":"sha256:77968a45cff106bd22d2bd38fd08ca6b754a574c6e1bff2d1df20a5adcebe037","target":"record","created_at":"2026-05-18T00:31:49Z","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":"582781d36fc103267f0af20401131ffd63f319c6d1908f1051204b224108cfa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-10-28T02:28:19Z","title_canon_sha256":"76655c3ea238ca459a8bd152138fefdd588a01bb5bb4633e36bbedf9a6f84487"},"schema_version":"1.0","source":{"id":"1710.10374","kind":"arxiv","version":1}},"canonical_sha256":"08c57d867d65486a3d47676a4071e923427d7e908be8e04bdb9bc914e54c2521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08c57d867d65486a3d47676a4071e923427d7e908be8e04bdb9bc914e54c2521","first_computed_at":"2026-05-18T00:31:49.735071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:49.735071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V4Bwa+5hKfAHtkyTBqamiWjP9nVf4adz5WiLcTk6fworX9W39Q+roZosIPKs7LfRVNqilfuPv5k2PiCM4NIKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:49.735729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77968a45cff106bd22d2bd38fd08ca6b754a574c6e1bff2d1df20a5adcebe037","sha256:759df1f0982e83dcfaa424e18f268625ebf6e92c1ea5f2f236a57105d27f92ee"],"state_sha256":"7bb2e5d3a0571c66b29ced1f5fcff08085da9fa74bbf3ddd5a1ee8530315e9da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+3WTYGLQTO3h9pnqUqLblNkyd7/JwGjfBDidv5Oe0pirj0QRYJ0ceZFQIjdY7VzE62WDitC1pqXnWywwSna3Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:39:59.765459Z","bundle_sha256":"cc3dc49b4716e00aab267a37131e4a35a49ca258dee8e71c4b3e8e06e1a3ac82"}}