{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IXKOKHMPPVHTJAH6XDIZ4OJVLR","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":"5cd2e4be14a7164026a596f92d284805962e68349754e15e01e2ae6012b9ee99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-10T11:40:58Z","title_canon_sha256":"895994562d7a6408c0b16229a6c8732fb781f9e47155c0bfc8da09c1530f92ae"},"schema_version":"1.0","source":{"id":"1101.1776","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1776","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1776v1","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1776","created_at":"2026-05-18T02:22:59Z"},{"alias_kind":"pith_short_12","alias_value":"IXKOKHMPPVHT","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"IXKOKHMPPVHTJAH6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"IXKOKHMP","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:61db2498183dd30a8cc2cb878d54d9abb53751e2c56022636bea7ede5ad5d05c","target":"graph","created_at":"2026-05-18T02:22:59Z","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":"Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing optimal approximating spline for each function proved to be very hard. In fact, no polynomial time algorithm of adaptive spline approximation can be designed and no exact formula for the optimal error of approximation can be given. Therefore, the next natural question would be to study the asymptotic behavior of the error and construct asymptotically optimal","authors_text":"Jean-Marie Mirebeau, Tatyana Leskevich, Yuliya Babenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-10T11:40:58Z","title":"Sharp asymptotics of the Lp approximation error for interpolation on block partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1776","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":"sha256:747f61c602847e7d99d59d3c4e7ffc71b34a4f00e0dc21a7ec39da30484f7755","target":"record","created_at":"2026-05-18T02:22:59Z","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":"5cd2e4be14a7164026a596f92d284805962e68349754e15e01e2ae6012b9ee99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-01-10T11:40:58Z","title_canon_sha256":"895994562d7a6408c0b16229a6c8732fb781f9e47155c0bfc8da09c1530f92ae"},"schema_version":"1.0","source":{"id":"1101.1776","kind":"arxiv","version":1}},"canonical_sha256":"45d4e51d8f7d4f3480feb8d19e39355c667509138b954a08f1ce4a210cd790c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45d4e51d8f7d4f3480feb8d19e39355c667509138b954a08f1ce4a210cd790c4","first_computed_at":"2026-05-18T02:22:59.453434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:59.453434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5oKti8+dX1p1ls6u8oxuyimFRMcctMma1RpUMVo08ITYNhGLoxB5TN9dYb0+Y3dCkuWpq7w5hzLxhVzTRmStAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:59.454162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1776","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:747f61c602847e7d99d59d3c4e7ffc71b34a4f00e0dc21a7ec39da30484f7755","sha256:61db2498183dd30a8cc2cb878d54d9abb53751e2c56022636bea7ede5ad5d05c"],"state_sha256":"8b7736cfbaec6adc0cbabf7e24f6404b9d142f90dded533b7d960444e879a7f4"}