{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5DQLQPC7BLQSKJIOU2JWRDTHKZ","short_pith_number":"pith:5DQLQPC7","canonical_record":{"source":{"id":"1306.1097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-05T13:25:19Z","cross_cats_sorted":["cs.IT","math.CA","math.IT"],"title_canon_sha256":"5a2dd7c9915b84658d52fc13e08df549f15e4bbf1f7d1cf957480d3574d439f3","abstract_canon_sha256":"5300ee3bf4c71c93981d6b51dbb751d8c4e371816000b1011c5d97679efb13f2"},"schema_version":"1.0"},"canonical_sha256":"e8e0b83c5f0ae125250ea693688e675661c851c72c4ebdab808a7a2d8ce6a1d4","source":{"kind":"arxiv","id":"1306.1097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1097","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1097v1","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1097","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"5DQLQPC7BLQS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5DQLQPC7BLQSKJIO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5DQLQPC7","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5DQLQPC7BLQSKJIOU2JWRDTHKZ","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-05T13:25:19Z","cross_cats_sorted":["cs.IT","math.CA","math.IT"],"title_canon_sha256":"5a2dd7c9915b84658d52fc13e08df549f15e4bbf1f7d1cf957480d3574d439f3","abstract_canon_sha256":"5300ee3bf4c71c93981d6b51dbb751d8c4e371816000b1011c5d97679efb13f2"},"schema_version":"1.0"},"canonical_sha256":"e8e0b83c5f0ae125250ea693688e675661c851c72c4ebdab808a7a2d8ce6a1d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:44.349921Z","signature_b64":"r44rxoiPReHQI4d8kT/um25aBqDAYuQEsWm2D8e5aEQqGvkHQb0S9zLJ6X/75RoIbS9Nm47qybcUfJ08/W/cCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8e0b83c5f0ae125250ea693688e675661c851c72c4ebdab808a7a2d8ce6a1d4","last_reissued_at":"2026-05-18T03:21:44.349270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:44.349270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1097","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MV/fLtBnaiwMxmCqX4ygQLOx1Z6JWcjoOU4F7bsWg+IlKoVsURpRP9G6KLQmFsbRPJU9Iqc4nUB3nEBs0KrrCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:37:45.185646Z"},"content_sha256":"401d7b424eb3ca5ed14ae7d765e0c965df6afa2eca40148a332b657ec105feaf","schema_version":"1.0","event_id":"sha256:401d7b424eb3ca5ed14ae7d765e0c965df6afa2eca40148a332b657ec105feaf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5DQLQPC7BLQSKJIOU2JWRDTHKZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic signal sampling, Gibbs phenomenon and Prony-type systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CA","math.IT"],"primary_cat":"math.NA","authors_text":"Dmitry Batenkov, Yosef Yomdin","submitted_at":"2013-06-05T13:25:19Z","abstract_excerpt":"Systems of Prony type appear in various signal reconstruction problems such as finite rate of innovation, superresolution and Fourier inversion of piecewise smooth functions. We propose a novel approach for solving Prony-type systems, which requires sampling the signal at arithmetic progressions. By keeping the number of equations small and fixed, we demonstrate that such \"decimation\" can lead to practical improvements in the reconstruction accuracy. As an application, we provide a solution to the so-called Eckhoff's conjecture, which asked for reconstructing jump positions and magnitudes of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1097","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vu9tjk8KHQpVy0++4+5Cg9kqGDrxvBGdsqF75GcWDISy330rPYJu5PwBcOcnZnWOoqCCH6DyVvHOycwTYTZLAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:37:45.186296Z"},"content_sha256":"a4b6315df94eefc0bf426c16ef4a2676224995b3ed5c94a0dff48cbb63b85725","schema_version":"1.0","event_id":"sha256:a4b6315df94eefc0bf426c16ef4a2676224995b3ed5c94a0dff48cbb63b85725"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DQLQPC7BLQSKJIOU2JWRDTHKZ/bundle.json","state_url":"https://pith.science/pith/5DQLQPC7BLQSKJIOU2JWRDTHKZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DQLQPC7BLQSKJIOU2JWRDTHKZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T14:37:45Z","links":{"resolver":"https://pith.science/pith/5DQLQPC7BLQSKJIOU2JWRDTHKZ","bundle":"https://pith.science/pith/5DQLQPC7BLQSKJIOU2JWRDTHKZ/bundle.json","state":"https://pith.science/pith/5DQLQPC7BLQSKJIOU2JWRDTHKZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DQLQPC7BLQSKJIOU2JWRDTHKZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5DQLQPC7BLQSKJIOU2JWRDTHKZ","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":"5300ee3bf4c71c93981d6b51dbb751d8c4e371816000b1011c5d97679efb13f2","cross_cats_sorted":["cs.IT","math.CA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-05T13:25:19Z","title_canon_sha256":"5a2dd7c9915b84658d52fc13e08df549f15e4bbf1f7d1cf957480d3574d439f3"},"schema_version":"1.0","source":{"id":"1306.1097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1097","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1097v1","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1097","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"5DQLQPC7BLQS","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5DQLQPC7BLQSKJIO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5DQLQPC7","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:a4b6315df94eefc0bf426c16ef4a2676224995b3ed5c94a0dff48cbb63b85725","target":"graph","created_at":"2026-05-18T03:21:44Z","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":"Systems of Prony type appear in various signal reconstruction problems such as finite rate of innovation, superresolution and Fourier inversion of piecewise smooth functions. We propose a novel approach for solving Prony-type systems, which requires sampling the signal at arithmetic progressions. By keeping the number of equations small and fixed, we demonstrate that such \"decimation\" can lead to practical improvements in the reconstruction accuracy. As an application, we provide a solution to the so-called Eckhoff's conjecture, which asked for reconstructing jump positions and magnitudes of a","authors_text":"Dmitry Batenkov, Yosef Yomdin","cross_cats":["cs.IT","math.CA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-05T13:25:19Z","title":"Algebraic signal sampling, Gibbs phenomenon and Prony-type systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1097","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":"sha256:401d7b424eb3ca5ed14ae7d765e0c965df6afa2eca40148a332b657ec105feaf","target":"record","created_at":"2026-05-18T03:21:44Z","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":"5300ee3bf4c71c93981d6b51dbb751d8c4e371816000b1011c5d97679efb13f2","cross_cats_sorted":["cs.IT","math.CA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-06-05T13:25:19Z","title_canon_sha256":"5a2dd7c9915b84658d52fc13e08df549f15e4bbf1f7d1cf957480d3574d439f3"},"schema_version":"1.0","source":{"id":"1306.1097","kind":"arxiv","version":1}},"canonical_sha256":"e8e0b83c5f0ae125250ea693688e675661c851c72c4ebdab808a7a2d8ce6a1d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8e0b83c5f0ae125250ea693688e675661c851c72c4ebdab808a7a2d8ce6a1d4","first_computed_at":"2026-05-18T03:21:44.349270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:44.349270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r44rxoiPReHQI4d8kT/um25aBqDAYuQEsWm2D8e5aEQqGvkHQb0S9zLJ6X/75RoIbS9Nm47qybcUfJ08/W/cCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:44.349921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:401d7b424eb3ca5ed14ae7d765e0c965df6afa2eca40148a332b657ec105feaf","sha256:a4b6315df94eefc0bf426c16ef4a2676224995b3ed5c94a0dff48cbb63b85725"],"state_sha256":"295d2ce77d15cfb3819bd0ba85bf321249703406811ad846eb284f1be5f565e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jwV00+u7n0Hu4AOVFKZkkHprPA/5HrNRjILKp5hGcxaar5QGI1l8i1R2U3gISf0oIcaNwbrQzFqQ+7y2jI/wDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:37:45.189967Z","bundle_sha256":"3222d3159028c6740f7c3cee8f81692fc4b576b3cd9514ea4a2e5f8e1aa16803"}}