{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NO2JA2EM5DNSFH7OYON7HIFJHX","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":"3ffa9fed10c241e9c38e605fb53bc7acfaa004a25d6b9d1ef87dbce64b814464","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-23T06:17:32Z","title_canon_sha256":"8eb24cbaebf51b1277e5f403acfac25b249ef3c10f6969d8a38b7db18c253182"},"schema_version":"1.0","source":{"id":"1308.5055","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5055","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5055v3","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5055","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"pith_short_12","alias_value":"NO2JA2EM5DNS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NO2JA2EM5DNSFH7O","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NO2JA2EM","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:4a3cc73443da24eead7586868ef7e71ee4314178cfb85fc19f9c938ab31b5cf4","target":"graph","created_at":"2026-05-18T02:25:49Z","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":"Given any natural number $k$ and any dense point sequence $(t_n)$, we prove that the corresponding orthonormal spline system of order $k$ is an unconditional basis in reflexive $L^p$.","authors_text":"Markus Passenbrunner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-23T06:17:32Z","title":"Unconditionality of orthogonal spline systems in $L^p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5055","kind":"arxiv","version":3},"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":"sha256:16a3e01d7e483dd3b167c78efdd404e5e254d4947baf720b676fcd381077a9bf","target":"record","created_at":"2026-05-18T02:25:49Z","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":"3ffa9fed10c241e9c38e605fb53bc7acfaa004a25d6b9d1ef87dbce64b814464","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-23T06:17:32Z","title_canon_sha256":"8eb24cbaebf51b1277e5f403acfac25b249ef3c10f6969d8a38b7db18c253182"},"schema_version":"1.0","source":{"id":"1308.5055","kind":"arxiv","version":3}},"canonical_sha256":"6bb490688ce8db229feec39bf3a0a93dc83c32c1ea529d76c14499653de0c98f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bb490688ce8db229feec39bf3a0a93dc83c32c1ea529d76c14499653de0c98f","first_computed_at":"2026-05-18T02:25:49.310691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:49.310691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2C9iEs4bD+/dUtx8Ovu7N//6cVKOJtXPUaxdfd6LUeWYJTG4d0PVb1cQVUusBuszuXsny71hvXqhKdgR+X6WBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:49.311144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5055","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16a3e01d7e483dd3b167c78efdd404e5e254d4947baf720b676fcd381077a9bf","sha256:4a3cc73443da24eead7586868ef7e71ee4314178cfb85fc19f9c938ab31b5cf4"],"state_sha256":"fc5febb9804585fda19e58bc43d6d53563d78d7334a077a7c535c71951a6d49f"}