{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:SMQD2BWR5M66JLN4V7H46UILE3","short_pith_number":"pith:SMQD2BWR","schema_version":"1.0","canonical_sha256":"93203d06d1eb3de4adbcafcfcf510b26d7a2c28f0fb2a915ab9c8b5020d1f424","source":{"kind":"arxiv","id":"1008.2519","version":2},"attestation_state":"computed","paper":{"title":"Approximation properties of the $q$-sine bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.SP","authors_text":"Gabriel Lord, Lyonell Boulton","submitted_at":"2010-08-15T13:37:00Z","abstract_excerpt":"For $q>12/11$ the eigenfunctions of the non-linear eigenvalue problem associated to the one-dimensional $q$-Laplacian are known to form a Riesz basis of $L^2(0,1)$. We examine in this paper the approximation properties of this family of functions and its dual, in order to establish non-orthogonal spectral methods for the $p$-Poisson boundary value problem and its corresponding parabolic time evolution initial value problem. The principal objective of our analysis is the determination of optimal values of $q$ for which the best approximation is achieved for a given $p$ problem."},"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":"1008.2519","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-08-15T13:37:00Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"3a3b18c6892be665c185fde0dfd9b9424dbf9ea6c843733ac8d75b10e7811d5d","abstract_canon_sha256":"b0d1abb979a6d6e995baf5b02b52fb4f2f9bb40d799c9cdb5b34d4c94ab01631"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:05:48.215234Z","signature_b64":"vINLffdXIPmbG3dJ0CeShASgnOhtGMCJT86m40y7BRsp/Kb9yB0f0wYBVp1EbjUSHBNnn1ndp6BHne45WfbRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93203d06d1eb3de4adbcafcfcf510b26d7a2c28f0fb2a915ab9c8b5020d1f424","last_reissued_at":"2026-05-18T02:05:48.214546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:05:48.214546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation properties of the $q$-sine bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.SP","authors_text":"Gabriel Lord, Lyonell Boulton","submitted_at":"2010-08-15T13:37:00Z","abstract_excerpt":"For $q>12/11$ the eigenfunctions of the non-linear eigenvalue problem associated to the one-dimensional $q$-Laplacian are known to form a Riesz basis of $L^2(0,1)$. We examine in this paper the approximation properties of this family of functions and its dual, in order to establish non-orthogonal spectral methods for the $p$-Poisson boundary value problem and its corresponding parabolic time evolution initial value problem. The principal objective of our analysis is the determination of optimal values of $q$ for which the best approximation is achieved for a given $p$ problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2519","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":""},"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":"1008.2519","created_at":"2026-05-18T02:05:48.214656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.2519v2","created_at":"2026-05-18T02:05:48.214656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2519","created_at":"2026-05-18T02:05:48.214656+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMQD2BWR5M66","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMQD2BWR5M66JLN4","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMQD2BWR","created_at":"2026-05-18T12:26:13.927090+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/SMQD2BWR5M66JLN4V7H46UILE3","json":"https://pith.science/pith/SMQD2BWR5M66JLN4V7H46UILE3.json","graph_json":"https://pith.science/api/pith-number/SMQD2BWR5M66JLN4V7H46UILE3/graph.json","events_json":"https://pith.science/api/pith-number/SMQD2BWR5M66JLN4V7H46UILE3/events.json","paper":"https://pith.science/paper/SMQD2BWR"},"agent_actions":{"view_html":"https://pith.science/pith/SMQD2BWR5M66JLN4V7H46UILE3","download_json":"https://pith.science/pith/SMQD2BWR5M66JLN4V7H46UILE3.json","view_paper":"https://pith.science/paper/SMQD2BWR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.2519&json=true","fetch_graph":"https://pith.science/api/pith-number/SMQD2BWR5M66JLN4V7H46UILE3/graph.json","fetch_events":"https://pith.science/api/pith-number/SMQD2BWR5M66JLN4V7H46UILE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMQD2BWR5M66JLN4V7H46UILE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMQD2BWR5M66JLN4V7H46UILE3/action/storage_attestation","attest_author":"https://pith.science/pith/SMQD2BWR5M66JLN4V7H46UILE3/action/author_attestation","sign_citation":"https://pith.science/pith/SMQD2BWR5M66JLN4V7H46UILE3/action/citation_signature","submit_replication":"https://pith.science/pith/SMQD2BWR5M66JLN4V7H46UILE3/action/replication_record"}},"created_at":"2026-05-18T02:05:48.214656+00:00","updated_at":"2026-05-18T02:05:48.214656+00:00"}