{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YF3V5NZMCWQGA3Y3DI7V4DZAV2","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":"0d0a24f24b26ba41cd44e4b161d491d622f018f5b6551cfca45fc8a9ec72d267","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-07-14T14:19:30Z","title_canon_sha256":"015514e1ab37dd6057c30d6135e39fbba760b82e1c90a04262f33610edb28293"},"schema_version":"1.0","source":{"id":"2607.12804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.12804","created_at":"2026-07-15T01:22:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.12804v1","created_at":"2026-07-15T01:22:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12804","created_at":"2026-07-15T01:22:18Z"},{"alias_kind":"pith_short_12","alias_value":"YF3V5NZMCWQG","created_at":"2026-07-15T01:22:18Z"},{"alias_kind":"pith_short_16","alias_value":"YF3V5NZMCWQGA3Y3","created_at":"2026-07-15T01:22:18Z"},{"alias_kind":"pith_short_8","alias_value":"YF3V5NZM","created_at":"2026-07-15T01:22:18Z"}],"graph_snapshots":[{"event_id":"sha256:ea774081d373dec5c65cadf4d547186b99dc5e4cb6ed3ea3ed7b4faae0ffea22","target":"graph","created_at":"2026-07-15T01:22:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.12804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Gianluca Vinti, Lorenzo Boccali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-07-14T14:19:30Z","title":"L^{p}-Approximation and Shape-preserving Properties of the Max-product Generalized Sampling Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12804","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:b5543e7f465abac3288629a23a7d563d177cc5f86b4670d98a68a1f6adbbf3fd","target":"record","created_at":"2026-07-15T01:22:18Z","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":"0d0a24f24b26ba41cd44e4b161d491d622f018f5b6551cfca45fc8a9ec72d267","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-07-14T14:19:30Z","title_canon_sha256":"015514e1ab37dd6057c30d6135e39fbba760b82e1c90a04262f33610edb28293"},"schema_version":"1.0","source":{"id":"2607.12804","kind":"arxiv","version":1}},"canonical_sha256":"c1775eb72c15a0606f1b1a3f5e0f20aeaeb2f188cf3f351ad073fa023b43c50a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1775eb72c15a0606f1b1a3f5e0f20aeaeb2f188cf3f351ad073fa023b43c50a","first_computed_at":"2026-07-15T01:22:18.692534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-15T01:22:18.692534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"13MNjzDf5/4jpHCZt5GsM7XKSSamLY2kGNvtga9ltOWXYaVaxMflhOhQJ4ZsPkUSP6Iy4Y9WwRprK/PlTHj7CQ==","signature_status":"signed_v1","signed_at":"2026-07-15T01:22:18.693349Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.12804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5543e7f465abac3288629a23a7d563d177cc5f86b4670d98a68a1f6adbbf3fd","sha256:ea774081d373dec5c65cadf4d547186b99dc5e4cb6ed3ea3ed7b4faae0ffea22"],"state_sha256":"5028e4b30bee295c9c758cdfd02f81f0147eb1eba92a3dd77587113f16715d51"}