{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YF3V5NZMCWQGA3Y3DI7V4DZAV2","short_pith_number":"pith:YF3V5NZM","schema_version":"1.0","canonical_sha256":"c1775eb72c15a0606f1b1a3f5e0f20aeaeb2f188cf3f351ad073fa023b43c50a","source":{"kind":"arxiv","id":"2607.12804","version":1},"attestation_state":"computed","paper":{"title":"L^{p}-Approximation and Shape-preserving Properties of the Max-product Generalized Sampling Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gianluca Vinti, Lorenzo Boccali","submitted_at":"2026-07-14T14:19:30Z","abstract_excerpt":"In this paper, we investigate the convergence in the $L^{p}$-norm and certain shape-preserving properties of the max-product generalized sampling operators. More precisely, we establish quantitative estimates for the approximation error in the $L^{p}$-norm, for $ 1 \\le p < +\\infty$, in the case of non-negative and bounded functions defined on $[-1,1]$. These estimates are derived by means of the so-called $\\tau$-modulus, an averaged modulus of smoothness introduced by Sendov and Popov. As a direct consequence, we prove that the max-product generalized sampling operators $L^{p}$-converge to non"},"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":"2607.12804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-07-14T14:19:30Z","cross_cats_sorted":[],"title_canon_sha256":"015514e1ab37dd6057c30d6135e39fbba760b82e1c90a04262f33610edb28293","abstract_canon_sha256":"0d0a24f24b26ba41cd44e4b161d491d622f018f5b6551cfca45fc8a9ec72d267"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:22:18.693349Z","signature_b64":"13MNjzDf5/4jpHCZt5GsM7XKSSamLY2kGNvtga9ltOWXYaVaxMflhOhQJ4ZsPkUSP6Iy4Y9WwRprK/PlTHj7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1775eb72c15a0606f1b1a3f5e0f20aeaeb2f188cf3f351ad073fa023b43c50a","last_reissued_at":"2026-07-15T01:22:18.692534Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:22:18.692534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L^{p}-Approximation and Shape-preserving Properties of the Max-product Generalized Sampling Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gianluca Vinti, Lorenzo Boccali","submitted_at":"2026-07-14T14:19:30Z","abstract_excerpt":"In this paper, we investigate the convergence in the $L^{p}$-norm and certain shape-preserving properties of the max-product generalized sampling operators. More precisely, we establish quantitative estimates for the approximation error in the $L^{p}$-norm, for $ 1 \\le p < +\\infty$, in the case of non-negative and bounded functions defined on $[-1,1]$. These estimates are derived by means of the so-called $\\tau$-modulus, an averaged modulus of smoothness introduced by Sendov and Popov. As a direct consequence, we prove that the max-product generalized sampling operators $L^{p}$-converge to non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12804","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12804/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":"2607.12804","created_at":"2026-07-15T01:22:18.692946+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.12804v1","created_at":"2026-07-15T01:22:18.692946+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12804","created_at":"2026-07-15T01:22:18.692946+00:00"},{"alias_kind":"pith_short_12","alias_value":"YF3V5NZMCWQG","created_at":"2026-07-15T01:22:18.692946+00:00"},{"alias_kind":"pith_short_16","alias_value":"YF3V5NZMCWQGA3Y3","created_at":"2026-07-15T01:22:18.692946+00:00"},{"alias_kind":"pith_short_8","alias_value":"YF3V5NZM","created_at":"2026-07-15T01:22:18.692946+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/YF3V5NZMCWQGA3Y3DI7V4DZAV2","json":"https://pith.science/pith/YF3V5NZMCWQGA3Y3DI7V4DZAV2.json","graph_json":"https://pith.science/api/pith-number/YF3V5NZMCWQGA3Y3DI7V4DZAV2/graph.json","events_json":"https://pith.science/api/pith-number/YF3V5NZMCWQGA3Y3DI7V4DZAV2/events.json","paper":"https://pith.science/paper/YF3V5NZM"},"agent_actions":{"view_html":"https://pith.science/pith/YF3V5NZMCWQGA3Y3DI7V4DZAV2","download_json":"https://pith.science/pith/YF3V5NZMCWQGA3Y3DI7V4DZAV2.json","view_paper":"https://pith.science/paper/YF3V5NZM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.12804&json=true","fetch_graph":"https://pith.science/api/pith-number/YF3V5NZMCWQGA3Y3DI7V4DZAV2/graph.json","fetch_events":"https://pith.science/api/pith-number/YF3V5NZMCWQGA3Y3DI7V4DZAV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YF3V5NZMCWQGA3Y3DI7V4DZAV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YF3V5NZMCWQGA3Y3DI7V4DZAV2/action/storage_attestation","attest_author":"https://pith.science/pith/YF3V5NZMCWQGA3Y3DI7V4DZAV2/action/author_attestation","sign_citation":"https://pith.science/pith/YF3V5NZMCWQGA3Y3DI7V4DZAV2/action/citation_signature","submit_replication":"https://pith.science/pith/YF3V5NZMCWQGA3Y3DI7V4DZAV2/action/replication_record"}},"created_at":"2026-07-15T01:22:18.692946+00:00","updated_at":"2026-07-15T01:22:18.692946+00:00"}