{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UDVTKAPDFNSDNR3WAYJ7SMWE5D","short_pith_number":"pith:UDVTKAPD","schema_version":"1.0","canonical_sha256":"a0eb3501e32b6436c7760613f932c4e8f5fda5c02629c499bf24b20446583257","source":{"kind":"arxiv","id":"1611.04498","version":2},"attestation_state":"computed","paper":{"title":"Lattice points in elliptic paraboloids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carlos Pastor, Fernando Chamizo","submitted_at":"2016-11-14T17:53:48Z","abstract_excerpt":"We consider the lattice point problem corresponding to a family of elliptic paraboloids in $\\mathbb{R}^d$ with $d\\ge3$ and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for $d=3$ because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case $d=2$, getting for a simple parabolic region an $\\Omega$-result that is unknown for the classical circle and divisor problems."},"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":"1611.04498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-14T17:53:48Z","cross_cats_sorted":[],"title_canon_sha256":"5726a5faf936d9066a19ae831ef653f2b9db6255c0bbc34f6a85f54a219b3281","abstract_canon_sha256":"c2020f26bb041664584b5160be6433bffac9d3478020fb7795d8b0e03057ee48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:48.439629Z","signature_b64":"ZoZWNEPObHF6ziiq2S+klqQCjsO6elv+Oj1wMYxpD+zQm2s5bu4HRddwmKPOrWUMGYerVw6TI/GX6tF2gMMABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0eb3501e32b6436c7760613f932c4e8f5fda5c02629c499bf24b20446583257","last_reissued_at":"2026-05-18T00:27:48.438988Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:48.438988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattice points in elliptic paraboloids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carlos Pastor, Fernando Chamizo","submitted_at":"2016-11-14T17:53:48Z","abstract_excerpt":"We consider the lattice point problem corresponding to a family of elliptic paraboloids in $\\mathbb{R}^d$ with $d\\ge3$ and we prove the expected to be optimal exponent, improving previous results. This is especially noticeable for $d=3$ because the optimal exponent is conjectural even for the sphere. We also treat some aspects of the case $d=2$, getting for a simple parabolic region an $\\Omega$-result that is unknown for the classical circle and divisor problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04498","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":"1611.04498","created_at":"2026-05-18T00:27:48.439089+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.04498v2","created_at":"2026-05-18T00:27:48.439089+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04498","created_at":"2026-05-18T00:27:48.439089+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDVTKAPDFNSD","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDVTKAPDFNSDNR3W","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDVTKAPD","created_at":"2026-05-18T12:30:46.583412+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/UDVTKAPDFNSDNR3WAYJ7SMWE5D","json":"https://pith.science/pith/UDVTKAPDFNSDNR3WAYJ7SMWE5D.json","graph_json":"https://pith.science/api/pith-number/UDVTKAPDFNSDNR3WAYJ7SMWE5D/graph.json","events_json":"https://pith.science/api/pith-number/UDVTKAPDFNSDNR3WAYJ7SMWE5D/events.json","paper":"https://pith.science/paper/UDVTKAPD"},"agent_actions":{"view_html":"https://pith.science/pith/UDVTKAPDFNSDNR3WAYJ7SMWE5D","download_json":"https://pith.science/pith/UDVTKAPDFNSDNR3WAYJ7SMWE5D.json","view_paper":"https://pith.science/paper/UDVTKAPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.04498&json=true","fetch_graph":"https://pith.science/api/pith-number/UDVTKAPDFNSDNR3WAYJ7SMWE5D/graph.json","fetch_events":"https://pith.science/api/pith-number/UDVTKAPDFNSDNR3WAYJ7SMWE5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDVTKAPDFNSDNR3WAYJ7SMWE5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDVTKAPDFNSDNR3WAYJ7SMWE5D/action/storage_attestation","attest_author":"https://pith.science/pith/UDVTKAPDFNSDNR3WAYJ7SMWE5D/action/author_attestation","sign_citation":"https://pith.science/pith/UDVTKAPDFNSDNR3WAYJ7SMWE5D/action/citation_signature","submit_replication":"https://pith.science/pith/UDVTKAPDFNSDNR3WAYJ7SMWE5D/action/replication_record"}},"created_at":"2026-05-18T00:27:48.439089+00:00","updated_at":"2026-05-18T00:27:48.439089+00:00"}