{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:FLYMHPYFBE2P3TABX4B3YJWV2F","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":"b46178ce473f8bcd82c0563cc0c6b950a146d64baff5836a6babd08944b8f737","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1996-04-05T00:00:00Z","title_canon_sha256":"b9d2aa45505c0635da56d18766094e4c1e167121410922ca8660e3721f3fad48"},"schema_version":"1.0","source":{"id":"math/9604212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9604212","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/9604212v1","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9604212","created_at":"2026-05-18T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"FLYMHPYFBE2P","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"FLYMHPYFBE2P3TAB","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"FLYMHPYF","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:b15e718fb6e6641005ba44dc7a2ea62c0612560f30bf08762ea4f0465f6523d3","target":"graph","created_at":"2026-05-18T01:05:47Z","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":"A sequence $\\{f_n\\}$ of strongly-measurable functions taking values in a Banach space $\\X$ is scalarly null a\\.e\\. (resp. scalarly null in measure) if $x^*f_n \\rightarrow0$ a\\.e\\. (resp. $x^*f_n \\rightarrow 0$ in measure) for every $x^*\\in \\X^*$. Let $1\\le p\\le \\infty$. The main questions addressed in this paper are whether an $L_p(\\X)$-bounded sequence that is scalarly null a\\.e\\. will converge weakly a\\.e\\. (or have a subsequence which converges weakly a\\.e\\.), and whether an $L_p(\\X)$-bounded sequence that is scalarly null in measure will have a subsequence that is scalarly null a\\.e. The a","authors_text":"Maria Girardi, Stephen J. Dilworth","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1996-04-05T00:00:00Z","title":"On Various Modes of Scalar Convergence in L_0(X)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9604212","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":"sha256:554b36d098e346b5371495134c6db2a8d28b2d076a7513ddd7b2cbb48bc3e071","target":"record","created_at":"2026-05-18T01:05:47Z","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":"b46178ce473f8bcd82c0563cc0c6b950a146d64baff5836a6babd08944b8f737","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1996-04-05T00:00:00Z","title_canon_sha256":"b9d2aa45505c0635da56d18766094e4c1e167121410922ca8660e3721f3fad48"},"schema_version":"1.0","source":{"id":"math/9604212","kind":"arxiv","version":1}},"canonical_sha256":"2af0c3bf050934fdcc01bf03bc26d5d14ab1e1e7ff3c5b2c2ddd70da6972668b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2af0c3bf050934fdcc01bf03bc26d5d14ab1e1e7ff3c5b2c2ddd70da6972668b","first_computed_at":"2026-05-18T01:05:47.658662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:47.658662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Okf8TvzrE2k7QH9+L0bSqIoNFqZufou7lnv59xZoJt7G9TfypaCuu/RQIl+uOud5JIn0MaO4tTC688HdpqxTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:47.659146Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9604212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:554b36d098e346b5371495134c6db2a8d28b2d076a7513ddd7b2cbb48bc3e071","sha256:b15e718fb6e6641005ba44dc7a2ea62c0612560f30bf08762ea4f0465f6523d3"],"state_sha256":"4ba17ab404c3ecfb2897a3e27a3ed8608b5ac164d8ff8e90b71fa656d8c001d9"}