{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5DSGH55SNLDWJ2RMKV3WBEJVID","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":"42aec9639840e5f4cdc566d3d5f0ec1ed18dc8e4ec116ad6507480a824cfc280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-03-12T03:51:39Z","title_canon_sha256":"151e71f45f306c69f38542045a272c7323478775bf39de594d4706a11ff11fa9"},"schema_version":"1.0","source":{"id":"2103.07071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.07071","created_at":"2026-07-05T02:22:28Z"},{"alias_kind":"arxiv_version","alias_value":"2103.07071v1","created_at":"2026-07-05T02:22:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.07071","created_at":"2026-07-05T02:22:28Z"},{"alias_kind":"pith_short_12","alias_value":"5DSGH55SNLDW","created_at":"2026-07-05T02:22:28Z"},{"alias_kind":"pith_short_16","alias_value":"5DSGH55SNLDWJ2RM","created_at":"2026-07-05T02:22:28Z"},{"alias_kind":"pith_short_8","alias_value":"5DSGH55S","created_at":"2026-07-05T02:22:28Z"}],"graph_snapshots":[{"event_id":"sha256:abb6c0cdbef3ec80c01c335c72f39b2a861c163a84597810b525def9de4d8290","target":"graph","created_at":"2026-07-05T02:22:28Z","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/2103.07071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this paper is devoted to studying representation of measures of non generalized compactness, in particular, measures of noncompactness, of non-weak compactness, and of non-super weak compactness, etc, defined on Banach spaces and its applications. With the aid of a three-time order preserving embedding theorem, we show that for every Banach space $X$, there exist a Banach function space $C(K)$ for some compact Hausdorff space $K$, and an order-preserving affine mapping $\\mathbb T$ from the super space $\\mathscr B$ of all nonempty bounded subsets of $X$ endowed with the Hausdorff","authors_text":"Lixin Cheng, Xiaoling Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-03-12T03:51:39Z","title":"Representation of measures of noncompactness and its applications related to an initial-value problem in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.07071","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:ad2ffa2088ad7ac788c5aaf6b4d08dc664734b299cf19d9e1dd9d2b30eb0b87d","target":"record","created_at":"2026-07-05T02:22:28Z","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":"42aec9639840e5f4cdc566d3d5f0ec1ed18dc8e4ec116ad6507480a824cfc280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-03-12T03:51:39Z","title_canon_sha256":"151e71f45f306c69f38542045a272c7323478775bf39de594d4706a11ff11fa9"},"schema_version":"1.0","source":{"id":"2103.07071","kind":"arxiv","version":1}},"canonical_sha256":"e8e463f7b26ac764ea2c557760913540e8476c119f103141ccd64f0f3edd2b84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8e463f7b26ac764ea2c557760913540e8476c119f103141ccd64f0f3edd2b84","first_computed_at":"2026-07-05T02:22:28.357199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:22:28.357199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s6k65LxmcRrzt95bX9BRwpTtN4r+M1IaJtJpW4p66rwt0YxzQcZYUf5tr9+lDyiMaBPBxtdDkfgH+ZVx8CAxDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:22:28.357596Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.07071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad2ffa2088ad7ac788c5aaf6b4d08dc664734b299cf19d9e1dd9d2b30eb0b87d","sha256:abb6c0cdbef3ec80c01c335c72f39b2a861c163a84597810b525def9de4d8290"],"state_sha256":"c4f6997518e9107d4ade1765a4445033e499ab8892cbb0e6e6bb270a26ee05b3"}