{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:UTK4WKI3G6H47MNWT5NPRHWM3H","short_pith_number":"pith:UTK4WKI3","canonical_record":{"source":{"id":"2309.03408","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-09-07T00:05:07Z","cross_cats_sorted":[],"title_canon_sha256":"4a5f902c5f289a4afd3c80c865255b1d8fcc99b686a374ccd3770f387378894e","abstract_canon_sha256":"d0f7f0a3ee4ebb36562ef2785b2c7adcce0e8c674a93814422a0c86c63c766c3"},"schema_version":"1.0"},"canonical_sha256":"a4d5cb291b378fcfb1b69f5af89eccd9fc7ab27783dacbda151ab75a36f3d196","source":{"kind":"arxiv","id":"2309.03408","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.03408","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"2309.03408v2","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.03408","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"UTK4WKI3G6H4","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_16","alias_value":"UTK4WKI3G6H47MNW","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_8","alias_value":"UTK4WKI3","created_at":"2026-07-05T09:11:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:UTK4WKI3G6H47MNWT5NPRHWM3H","target":"record","payload":{"canonical_record":{"source":{"id":"2309.03408","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-09-07T00:05:07Z","cross_cats_sorted":[],"title_canon_sha256":"4a5f902c5f289a4afd3c80c865255b1d8fcc99b686a374ccd3770f387378894e","abstract_canon_sha256":"d0f7f0a3ee4ebb36562ef2785b2c7adcce0e8c674a93814422a0c86c63c766c3"},"schema_version":"1.0"},"canonical_sha256":"a4d5cb291b378fcfb1b69f5af89eccd9fc7ab27783dacbda151ab75a36f3d196","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:11:45.554866Z","signature_b64":"b6eoTOEWUzbF84dKCaC7ad++9UBZBk6NAskzrV7qQqLx8X90F48G9Ug8ccw3ksS9eahlLylColuXF9H2VY4SCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4d5cb291b378fcfb1b69f5af89eccd9fc7ab27783dacbda151ab75a36f3d196","last_reissued_at":"2026-07-05T09:11:45.554324Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:11:45.554324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.03408","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QbExJdmZzRftgjSbVre1fBErEXrjYnZAXOcMTKfnXdSx3gFnwZgDYr6MohUhh2q0q+oIzhqA1x+n7k6HgZHpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:25:09.098124Z"},"content_sha256":"aeb5dbad7b0405564483696d897b63f6a54a9a8d3ef6b3dc92febca5e7fe3e3c","schema_version":"1.0","event_id":"sha256:aeb5dbad7b0405564483696d897b63f6a54a9a8d3ef6b3dc92febca5e7fe3e3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:UTK4WKI3G6H47MNWT5NPRHWM3H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subtransversality and Strong CHIP of Closed Sets in Asplund Spaces","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jen-Chih Yao, Michel Th\\'era, Zhou Wei","submitted_at":"2023-09-07T00:05:07Z","abstract_excerpt":"In this paper, we mainly study subtransversality and two types of strong CHIP (given via Fr\\'echet and limiting normal cones) for a collection of finitely many closed sets. We first prove characterizations of Asplund spaces in terms of subtransversality and intersection formulae of Fr\\'echet normal cones. Several necessary conditions for subtransversality of closed sets are obtained via Fr\\'echet/limiting normal cones in Asplund spaces. Then, we consider subtransversality for some special closed sets in convex-composite optimization. In this frame we prove an equivalence result on subtransvers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.03408","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.03408/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGg0L04/csE6W7v9I+pZejhjgly2NfuK2FypeD16EzItSDHRm1vi+CNKzMNysQ8HCK+DcjuwQzW6TkMNoXY2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:25:09.099089Z"},"content_sha256":"8b8ac285cb3d0a9a6bcc4011864716ca8f44408527f3cd8252c9e94a2d3ecd41","schema_version":"1.0","event_id":"sha256:8b8ac285cb3d0a9a6bcc4011864716ca8f44408527f3cd8252c9e94a2d3ecd41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTK4WKI3G6H47MNWT5NPRHWM3H/bundle.json","state_url":"https://pith.science/pith/UTK4WKI3G6H47MNWT5NPRHWM3H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTK4WKI3G6H47MNWT5NPRHWM3H/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":"2026-08-05T14:25:09Z","links":{"resolver":"https://pith.science/pith/UTK4WKI3G6H47MNWT5NPRHWM3H","bundle":"https://pith.science/pith/UTK4WKI3G6H47MNWT5NPRHWM3H/bundle.json","state":"https://pith.science/pith/UTK4WKI3G6H47MNWT5NPRHWM3H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTK4WKI3G6H47MNWT5NPRHWM3H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:UTK4WKI3G6H47MNWT5NPRHWM3H","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":"d0f7f0a3ee4ebb36562ef2785b2c7adcce0e8c674a93814422a0c86c63c766c3","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-09-07T00:05:07Z","title_canon_sha256":"4a5f902c5f289a4afd3c80c865255b1d8fcc99b686a374ccd3770f387378894e"},"schema_version":"1.0","source":{"id":"2309.03408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.03408","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"2309.03408v2","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.03408","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"UTK4WKI3G6H4","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_16","alias_value":"UTK4WKI3G6H47MNW","created_at":"2026-07-05T09:11:45Z"},{"alias_kind":"pith_short_8","alias_value":"UTK4WKI3","created_at":"2026-07-05T09:11:45Z"}],"graph_snapshots":[{"event_id":"sha256:8b8ac285cb3d0a9a6bcc4011864716ca8f44408527f3cd8252c9e94a2d3ecd41","target":"graph","created_at":"2026-07-05T09:11:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.03408/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we mainly study subtransversality and two types of strong CHIP (given via Fr\\'echet and limiting normal cones) for a collection of finitely many closed sets. We first prove characterizations of Asplund spaces in terms of subtransversality and intersection formulae of Fr\\'echet normal cones. Several necessary conditions for subtransversality of closed sets are obtained via Fr\\'echet/limiting normal cones in Asplund spaces. Then, we consider subtransversality for some special closed sets in convex-composite optimization. In this frame we prove an equivalence result on subtransvers","authors_text":"Jen-Chih Yao, Michel Th\\'era, Zhou Wei","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-09-07T00:05:07Z","title":"Subtransversality and Strong CHIP of Closed Sets in Asplund Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.03408","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:aeb5dbad7b0405564483696d897b63f6a54a9a8d3ef6b3dc92febca5e7fe3e3c","target":"record","created_at":"2026-07-05T09:11:45Z","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":"d0f7f0a3ee4ebb36562ef2785b2c7adcce0e8c674a93814422a0c86c63c766c3","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-09-07T00:05:07Z","title_canon_sha256":"4a5f902c5f289a4afd3c80c865255b1d8fcc99b686a374ccd3770f387378894e"},"schema_version":"1.0","source":{"id":"2309.03408","kind":"arxiv","version":2}},"canonical_sha256":"a4d5cb291b378fcfb1b69f5af89eccd9fc7ab27783dacbda151ab75a36f3d196","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4d5cb291b378fcfb1b69f5af89eccd9fc7ab27783dacbda151ab75a36f3d196","first_computed_at":"2026-07-05T09:11:45.554324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:11:45.554324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b6eoTOEWUzbF84dKCaC7ad++9UBZBk6NAskzrV7qQqLx8X90F48G9Ug8ccw3ksS9eahlLylColuXF9H2VY4SCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:11:45.554866Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.03408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeb5dbad7b0405564483696d897b63f6a54a9a8d3ef6b3dc92febca5e7fe3e3c","sha256:8b8ac285cb3d0a9a6bcc4011864716ca8f44408527f3cd8252c9e94a2d3ecd41"],"state_sha256":"5eea8cf92e8089a0d1557524b7ca27455c74dc47493098b76cfbdfff1737eac1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LePPtviNm8Wa+/lwkgPDFcrO2slZYj2GpItRKZw7Kixqqfq1Elj6xfp/jmCR3R9nH3+/9d0vtMuQKwRJVWJcCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T14:25:09.108795Z","bundle_sha256":"17e7483ef55d2788fab44a9d7376412746786dc1174763a10347c0a3cbda85e7"}}