{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TJZZ2NO4XPQELOQLJ4GC3N2L2R","short_pith_number":"pith:TJZZ2NO4","schema_version":"1.0","canonical_sha256":"9a739d35dcbbe045ba0b4f0c2db74bd4633c7cc8795e260424ac37dd8de30f7d","source":{"kind":"arxiv","id":"1606.07591","version":1},"attestation_state":"computed","paper":{"title":"Piecewise Extended Chebyshev Spaces: a numerical test for design","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carolina Vittoria Beccari, Giulio Casciola, Marie-Laurence Mazure","submitted_at":"2016-06-24T07:57:56Z","abstract_excerpt":"Given a number of Extended Chebyshev (EC) spaces on adjacent intervals, all of the same dimension, we join them via convenient connection matrices without increasing the dimension. The global space is called a Piecewise Extended Chebyshev (PEC) Space. In such a space one can count the total number of zeroes of any non-zero element, exactly as in each EC-section-space. When this number is bounded above in the global space the same way as in its section-spaces, we say that it is an Extended Chebyshev Piecewise (ECP) space. A thorough study of ECP-spaces has been developed in the last two decades"},"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":"1606.07591","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-24T07:57:56Z","cross_cats_sorted":[],"title_canon_sha256":"c7b84ad73fd7fa3a92a75bfe843136022aa19dbe3b8136f351607f76602855be","abstract_canon_sha256":"2fb85f155c5d7d63e246a075fc587a9d0e5e068a1766b56e690cb093eefe54e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:57.191400Z","signature_b64":"B5t61bleR70pspyYI7jLnH0pgii/W3VZYOIBM6Gte7r7QUNketr+gqCXaQnjIFj6RLTeV9wHogF2mhMMPTulCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a739d35dcbbe045ba0b4f0c2db74bd4633c7cc8795e260424ac37dd8de30f7d","last_reissued_at":"2026-05-18T01:11:57.190935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:57.190935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Piecewise Extended Chebyshev Spaces: a numerical test for design","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carolina Vittoria Beccari, Giulio Casciola, Marie-Laurence Mazure","submitted_at":"2016-06-24T07:57:56Z","abstract_excerpt":"Given a number of Extended Chebyshev (EC) spaces on adjacent intervals, all of the same dimension, we join them via convenient connection matrices without increasing the dimension. The global space is called a Piecewise Extended Chebyshev (PEC) Space. In such a space one can count the total number of zeroes of any non-zero element, exactly as in each EC-section-space. When this number is bounded above in the global space the same way as in its section-spaces, we say that it is an Extended Chebyshev Piecewise (ECP) space. A thorough study of ECP-spaces has been developed in the last two decades"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07591","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.07591","created_at":"2026-05-18T01:11:57.191006+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.07591v1","created_at":"2026-05-18T01:11:57.191006+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07591","created_at":"2026-05-18T01:11:57.191006+00:00"},{"alias_kind":"pith_short_12","alias_value":"TJZZ2NO4XPQE","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"TJZZ2NO4XPQELOQL","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"TJZZ2NO4","created_at":"2026-05-18T12:30:44.179134+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/TJZZ2NO4XPQELOQLJ4GC3N2L2R","json":"https://pith.science/pith/TJZZ2NO4XPQELOQLJ4GC3N2L2R.json","graph_json":"https://pith.science/api/pith-number/TJZZ2NO4XPQELOQLJ4GC3N2L2R/graph.json","events_json":"https://pith.science/api/pith-number/TJZZ2NO4XPQELOQLJ4GC3N2L2R/events.json","paper":"https://pith.science/paper/TJZZ2NO4"},"agent_actions":{"view_html":"https://pith.science/pith/TJZZ2NO4XPQELOQLJ4GC3N2L2R","download_json":"https://pith.science/pith/TJZZ2NO4XPQELOQLJ4GC3N2L2R.json","view_paper":"https://pith.science/paper/TJZZ2NO4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.07591&json=true","fetch_graph":"https://pith.science/api/pith-number/TJZZ2NO4XPQELOQLJ4GC3N2L2R/graph.json","fetch_events":"https://pith.science/api/pith-number/TJZZ2NO4XPQELOQLJ4GC3N2L2R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TJZZ2NO4XPQELOQLJ4GC3N2L2R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TJZZ2NO4XPQELOQLJ4GC3N2L2R/action/storage_attestation","attest_author":"https://pith.science/pith/TJZZ2NO4XPQELOQLJ4GC3N2L2R/action/author_attestation","sign_citation":"https://pith.science/pith/TJZZ2NO4XPQELOQLJ4GC3N2L2R/action/citation_signature","submit_replication":"https://pith.science/pith/TJZZ2NO4XPQELOQLJ4GC3N2L2R/action/replication_record"}},"created_at":"2026-05-18T01:11:57.191006+00:00","updated_at":"2026-05-18T01:11:57.191006+00:00"}