{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WZ3EFI2TPZN7Y7MCSD5CLACAZS","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":"f17edf835ecfd017dafe15dee13d2665844f8ce923658792be53adc33fe0c17b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-15T10:57:59Z","title_canon_sha256":"9f2c53bb60e7079d01c9b564a059419546318c36e2b3d3f247699da2b95aaa99"},"schema_version":"1.0","source":{"id":"1611.04787","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04787","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04787v2","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04787","created_at":"2026-05-18T00:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"WZ3EFI2TPZN7","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WZ3EFI2TPZN7Y7MC","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WZ3EFI2T","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:46003172293759ec36155a63c60fb215bebdbc84db1df4efd2705cf68780b5a2","target":"graph","created_at":"2026-05-18T00:16:09Z","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 provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our more general results suggest an intermediate notion of subtransversality, what we call weak intrinsic subtransversality, which lies between intrinsic transversality and subtransversality in Asplund spaces.","authors_text":"Alexander Y. Kruger, D. Russell Luke, Nguyen H. Thao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-15T10:57:59Z","title":"About subtransversality of collections of sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04787","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":"sha256:85ec3898fac43af9f18cc6c397bc5f93ee25effa170d09fb3325c00f771b39e8","target":"record","created_at":"2026-05-18T00:16:09Z","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":"f17edf835ecfd017dafe15dee13d2665844f8ce923658792be53adc33fe0c17b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-11-15T10:57:59Z","title_canon_sha256":"9f2c53bb60e7079d01c9b564a059419546318c36e2b3d3f247699da2b95aaa99"},"schema_version":"1.0","source":{"id":"1611.04787","kind":"arxiv","version":2}},"canonical_sha256":"b67642a3537e5bfc7d8290fa258040cc840bf742f57f9bee4f9a0d3f9600ca2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b67642a3537e5bfc7d8290fa258040cc840bf742f57f9bee4f9a0d3f9600ca2e","first_computed_at":"2026-05-18T00:16:09.494226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:09.494226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P0pLD0pgOCjtnybUf86a2No//Xq0lKOk2+gN5NCUwwRobjt1QDsanELsOCVwhvB4TkgjlGD2BhSEKXj2vkhkCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:09.494861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04787","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85ec3898fac43af9f18cc6c397bc5f93ee25effa170d09fb3325c00f771b39e8","sha256:46003172293759ec36155a63c60fb215bebdbc84db1df4efd2705cf68780b5a2"],"state_sha256":"065e7c82ef24829cb239611e97a7ea92d9cea7baf9673d2f5f06be20ceacc03c"}