{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M55DFJR5M32Y3N37EZQVLLWTTE","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":"b60d827e822f5c2a244ce6b15a2234a0a0302c6b40b629124c5aa4b13835eea3","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-04T13:23:03Z","title_canon_sha256":"cb2dec7711347dd5be997b004dbf7253504e8f0de05b104e273c740335a52468"},"schema_version":"1.0","source":{"id":"1211.0680","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0680","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0680v2","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0680","created_at":"2026-05-18T02:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"M55DFJR5M32Y","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M55DFJR5M32Y3N37","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M55DFJR5","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:5c2e728719474647cafe62bcb5ac095fce122dfdd0928c6a979ca5c5a9dff780","target":"graph","created_at":"2026-05-18T02:56:12Z","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 this paper we provide a reconstruction algorithm for piecewise-smooth functions with a-priori known smoothness and number of discontinuities, from their Fourier coefficients, posessing the maximal possible asymptotic rate of convergence -- including the positions of the discontinuities and the pointwise values of the function. This algorithm is a modification of our earlier method, which is in turn based on the algebraic method of K.Eckhoff proposed in the 1990s. The key ingredient of the new algorithm is to use a different set of Eckhoff's equations for reconstructing the location of each ","authors_text":"Dmitry Batenkov","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-04T13:23:03Z","title":"Complete Algebraic Reconstruction of Piecewise-Smooth Functions from Fourier Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0680","kind":"arxiv","version":2},"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":"sha256:0932e24b38ecff8eef7a298a56e361a2096a31222499cdb6c813e6eddb49b3eb","target":"record","created_at":"2026-05-18T02:56:12Z","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":"b60d827e822f5c2a244ce6b15a2234a0a0302c6b40b629124c5aa4b13835eea3","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-11-04T13:23:03Z","title_canon_sha256":"cb2dec7711347dd5be997b004dbf7253504e8f0de05b104e273c740335a52468"},"schema_version":"1.0","source":{"id":"1211.0680","kind":"arxiv","version":2}},"canonical_sha256":"677a32a63d66f58db77f266155aed3992785818440c569d60838c764f631e542","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"677a32a63d66f58db77f266155aed3992785818440c569d60838c764f631e542","first_computed_at":"2026-05-18T02:56:12.805433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:12.805433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XKzeBL/puMTYHoe2VFKB030HwNTCwJ848AbvvQHNriZTF4jLdyWwZXWFjkplbj6XZILoTU9ZjmBpNhrAllhtCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:12.805871Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0680","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0932e24b38ecff8eef7a298a56e361a2096a31222499cdb6c813e6eddb49b3eb","sha256:5c2e728719474647cafe62bcb5ac095fce122dfdd0928c6a979ca5c5a9dff780"],"state_sha256":"c5991836771d4092e07b62963153776f8a474c1f1dbf7869b98cf501f0467a23"}