{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UDVTKAPDFNSDNR3WAYJ7SMWE5D","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":"c2020f26bb041664584b5160be6433bffac9d3478020fb7795d8b0e03057ee48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-14T17:53:48Z","title_canon_sha256":"5726a5faf936d9066a19ae831ef653f2b9db6255c0bbc34f6a85f54a219b3281"},"schema_version":"1.0","source":{"id":"1611.04498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.04498","created_at":"2026-05-18T00:27:48Z"},{"alias_kind":"arxiv_version","alias_value":"1611.04498v2","created_at":"2026-05-18T00:27:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04498","created_at":"2026-05-18T00:27:48Z"},{"alias_kind":"pith_short_12","alias_value":"UDVTKAPDFNSD","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UDVTKAPDFNSDNR3W","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UDVTKAPD","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:ce12d6d7baaa2d4a43d51dd103ea1bc3dd89e252299cbf1e668d84de43430361","target":"graph","created_at":"2026-05-18T00:27:48Z","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"},"paper":{"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.","authors_text":"Carlos Pastor, Fernando Chamizo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-14T17:53:48Z","title":"Lattice points in elliptic paraboloids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04498","kind":"arxiv","version":2},"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":"sha256:12cd7c35ac88e4c4bd67f89311ea8a8e92bcf5689839193fb51065ea5861ef4e","target":"record","created_at":"2026-05-18T00:27:48Z","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":"c2020f26bb041664584b5160be6433bffac9d3478020fb7795d8b0e03057ee48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-11-14T17:53:48Z","title_canon_sha256":"5726a5faf936d9066a19ae831ef653f2b9db6255c0bbc34f6a85f54a219b3281"},"schema_version":"1.0","source":{"id":"1611.04498","kind":"arxiv","version":2}},"canonical_sha256":"a0eb3501e32b6436c7760613f932c4e8f5fda5c02629c499bf24b20446583257","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0eb3501e32b6436c7760613f932c4e8f5fda5c02629c499bf24b20446583257","first_computed_at":"2026-05-18T00:27:48.438988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:48.438988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZoZWNEPObHF6ziiq2S+klqQCjsO6elv+Oj1wMYxpD+zQm2s5bu4HRddwmKPOrWUMGYerVw6TI/GX6tF2gMMABA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:48.439629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.04498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12cd7c35ac88e4c4bd67f89311ea8a8e92bcf5689839193fb51065ea5861ef4e","sha256:ce12d6d7baaa2d4a43d51dd103ea1bc3dd89e252299cbf1e668d84de43430361"],"state_sha256":"80075df65b57f56e38254103971511550a59a8dd89ae422dd37f891103e7ca61"}