{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:POMRSSIZXGRK5IRXMGWGSL3RZ4","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":"3f8a01088e5891ea0f54bdb070850a7b0fa50b20c2c6411b4cf38fd2a88b192b","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-12-26T12:23:01Z","title_canon_sha256":"87f9698a5ae706c2b28f07a35b7ff83d4dd13814c65c94de812905f3db87fac9"},"schema_version":"1.0","source":{"id":"1012.5512","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5512","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5512v1","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5512","created_at":"2026-05-18T02:43:01Z"},{"alias_kind":"pith_short_12","alias_value":"POMRSSIZXGRK","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"POMRSSIZXGRK5IRX","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"POMRSSIZ","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:78bf1d768e60d2318a217890fd00fc0ac3db44313c3b6be2d1b0fc5cb5c16068","target":"graph","created_at":"2026-05-18T02:43:01Z","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 prove that a continuous image of a Radon-Nikod\\'ym compact space of weight less than b is Radon-Nikod\\'ym compact. As a Banach space counterpart, subspaces of Asplund generated Banach spaces of density character less than b are Asplund generated. In this case, in addition, there exists a subspace of an Asplund generated space which is not Asplund generated which has density character exactly b.","authors_text":"Antonio Avil\\'es","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-12-26T12:23:01Z","title":"Radon-Nikod\\'ym compact spaces of low weight and Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5512","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:a78e44fec58a17d335b049bae582e4feb4df77017c966cba6dfa0a6396283a14","target":"record","created_at":"2026-05-18T02:43:01Z","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":"3f8a01088e5891ea0f54bdb070850a7b0fa50b20c2c6411b4cf38fd2a88b192b","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-12-26T12:23:01Z","title_canon_sha256":"87f9698a5ae706c2b28f07a35b7ff83d4dd13814c65c94de812905f3db87fac9"},"schema_version":"1.0","source":{"id":"1012.5512","kind":"arxiv","version":1}},"canonical_sha256":"7b99194919b9a2aea23761ac692f71cf228ba483cf628a7da3e1ed9571330b54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b99194919b9a2aea23761ac692f71cf228ba483cf628a7da3e1ed9571330b54","first_computed_at":"2026-05-18T02:43:01.010270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:01.010270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SddrUGbAzAD2gg8Exw8aDNWpgcs6l9GR3j9jX0WDscmZs2CSPT+n8hiVzVhR2oHRnlzGReYid0LxVoRMyX8SBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:01.010907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5512","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a78e44fec58a17d335b049bae582e4feb4df77017c966cba6dfa0a6396283a14","sha256:78bf1d768e60d2318a217890fd00fc0ac3db44313c3b6be2d1b0fc5cb5c16068"],"state_sha256":"643fa6026379a6c1a6e1800a105092d28a6eacc2f06445d9134b4c8364cd108c"}