{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:TTQRDZC4ZWKF4G3JGQ2TPYSRZO","short_pith_number":"pith:TTQRDZC4","schema_version":"1.0","canonical_sha256":"9ce111e45ccd945e1b69343537e251cbae25d5126bcf75812002c724725acb8d","source":{"kind":"arxiv","id":"2012.08954","version":2},"attestation_state":"computed","paper":{"title":"Shortest-support Multi-Spline Bases for Generalized Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alexis Goujon, Alireza Naderi, Michael Unser, Shayan Aziznejad","submitted_at":"2020-12-16T13:54:57Z","abstract_excerpt":"Generalized sampling consists in the recovery of a function $f$, from the samples of the responses of a collection of linear shift-invariant systems to the input $f$. The reconstructed function is typically a member of a finitely generated integer-shift-invariant space that can reproduce polynomials up to a given degree $M$. While this property allows for an approximation power of order $(M+1)$, it comes with a tradeoff on the length of the support of the basis functions. Specifically, we prove that the sum of the length of the support of the generators is at least $(M+1)$. Following this resu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2012.08954","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-12-16T13:54:57Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6679517a52e9180ef5063082ada6c7313501c641c3232ec6a84bbfa26e26ff0c","abstract_canon_sha256":"72edbbfd0dc2a4946bd71dc9ff36663ede1577cce8d04ff928470a6d360ebbf1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:50:08.336979Z","signature_b64":"ENQOY4Q7zuB5YCT6/cA7BqEme/vMARoyh+tZCZFBI3rFUFm6cG729tYAydPCdGa6heC0utnmxxi9fRz2tbWcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ce111e45ccd945e1b69343537e251cbae25d5126bcf75812002c724725acb8d","last_reissued_at":"2026-07-05T02:50:08.336487Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:50:08.336487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shortest-support Multi-Spline Bases for Generalized Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alexis Goujon, Alireza Naderi, Michael Unser, Shayan Aziznejad","submitted_at":"2020-12-16T13:54:57Z","abstract_excerpt":"Generalized sampling consists in the recovery of a function $f$, from the samples of the responses of a collection of linear shift-invariant systems to the input $f$. The reconstructed function is typically a member of a finitely generated integer-shift-invariant space that can reproduce polynomials up to a given degree $M$. While this property allows for an approximation power of order $(M+1)$, it comes with a tradeoff on the length of the support of the basis functions. Specifically, we prove that the sum of the length of the support of the generators is at least $(M+1)$. Following this resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.08954","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.08954/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2012.08954","created_at":"2026-07-05T02:50:08.336557+00:00"},{"alias_kind":"arxiv_version","alias_value":"2012.08954v2","created_at":"2026-07-05T02:50:08.336557+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.08954","created_at":"2026-07-05T02:50:08.336557+00:00"},{"alias_kind":"pith_short_12","alias_value":"TTQRDZC4ZWKF","created_at":"2026-07-05T02:50:08.336557+00:00"},{"alias_kind":"pith_short_16","alias_value":"TTQRDZC4ZWKF4G3J","created_at":"2026-07-05T02:50:08.336557+00:00"},{"alias_kind":"pith_short_8","alias_value":"TTQRDZC4","created_at":"2026-07-05T02:50:08.336557+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO","json":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO.json","graph_json":"https://pith.science/api/pith-number/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/graph.json","events_json":"https://pith.science/api/pith-number/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/events.json","paper":"https://pith.science/paper/TTQRDZC4"},"agent_actions":{"view_html":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO","download_json":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO.json","view_paper":"https://pith.science/paper/TTQRDZC4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2012.08954&json=true","fetch_graph":"https://pith.science/api/pith-number/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/graph.json","fetch_events":"https://pith.science/api/pith-number/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/action/storage_attestation","attest_author":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/action/author_attestation","sign_citation":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/action/citation_signature","submit_replication":"https://pith.science/pith/TTQRDZC4ZWKF4G3JGQ2TPYSRZO/action/replication_record"}},"created_at":"2026-07-05T02:50:08.336557+00:00","updated_at":"2026-07-05T02:50:08.336557+00:00"}