{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PDZM4HAXRAFL6HZFHON7WEJIOS","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":"2f2773a9bc13184aed79f102094ca90e79262a4224cd4d198097522565f80e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-08-22T08:58:36Z","title_canon_sha256":"00a0a2f9e8c3777b32de798e7c196aa2395a161814676b42574d9a1096c7e1ef"},"schema_version":"1.0","source":{"id":"1808.07283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07283","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07283v1","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07283","created_at":"2026-05-18T00:07:29Z"},{"alias_kind":"pith_short_12","alias_value":"PDZM4HAXRAFL","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PDZM4HAXRAFL6HZF","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PDZM4HAX","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:4c89fffefde8bb9048cb30d6618e2e042fe0251dc4e0b4733a8fc4499a4061b9","target":"graph","created_at":"2026-05-18T00:07:29Z","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":"In the current paper, we study how the speed of convergence of a sequence of angles decreasing to zero influences the possibility of constructing a rare differentiation basis of rectangles in the plane, one side of which makes with the horizontal axis an angle belonging to the given sequence, that differentiates precisely a fixed Orlicz space.","authors_text":"Emma D 'Aniello, Joseph Rosenblatt, Laurent Moonens (LMO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-08-22T08:58:36Z","title":"Differentiating Orlicz spaces with rare bases of rectangles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07283","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":"sha256:3a085a187f0c558859a4ed7913492e98ef1f3dcd87064b1018267a19246b27d5","target":"record","created_at":"2026-05-18T00:07:29Z","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":"2f2773a9bc13184aed79f102094ca90e79262a4224cd4d198097522565f80e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-08-22T08:58:36Z","title_canon_sha256":"00a0a2f9e8c3777b32de798e7c196aa2395a161814676b42574d9a1096c7e1ef"},"schema_version":"1.0","source":{"id":"1808.07283","kind":"arxiv","version":1}},"canonical_sha256":"78f2ce1c17880abf1f253b9bfb112874895367362bec895d6c58a7168ede6cf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78f2ce1c17880abf1f253b9bfb112874895367362bec895d6c58a7168ede6cf9","first_computed_at":"2026-05-18T00:07:29.323171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:29.323171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q2kUfeJv4pIB2otcnMdtcAxLFcstyMBF7MClNxBA6DGOV8+MCLpvErK78Z1P9jeD5AU30qPmiBjO6aSA2mDyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:29.323886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a085a187f0c558859a4ed7913492e98ef1f3dcd87064b1018267a19246b27d5","sha256:4c89fffefde8bb9048cb30d6618e2e042fe0251dc4e0b4733a8fc4499a4061b9"],"state_sha256":"6b7a8d9972e5f199110f107d466d32e29855099ce3663459d4363fe759e9b422"}