{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GGRZXPC3R6YFBCVZDCOGLBJ7QW","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":"d9cdb025c69d1453a7ed6acb1cf301aa43fee8471f4290eee0f4421115c38c74","cross_cats_sorted":["math.NT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-09-05T23:26:59Z","title_canon_sha256":"6ebdd9a1efd1fa18f4410fcb92034b975492d4f6dae1b49d8607f9f936df0c6e"},"schema_version":"1.0","source":{"id":"1609.06172","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06172","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06172v2","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06172","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"GGRZXPC3R6YF","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GGRZXPC3R6YFBCVZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GGRZXPC3","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:aed0756adaa21dfdf3f3d619bde3baf6dd29fdf8950b973bf4689587d14c22ea","target":"graph","created_at":"2026-05-18T00:35:55Z","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 aim to maximize the number of first-quadrant lattice points in a convex domain with respect to reciprocal stretching in the coordinate directions. The optimal domain is shown to be asymptotically balanced, meaning that the stretch factor approaches 1 as the \"radius\" approaches infinity. In particular, the result implies that among all p-ellipses (or Lam\\'e curves), the p-circle encloses the most first-quadrant lattice points as the radius approaches infinity.\n  The case p=2 corresponds to minimization of high eigenvalues of the Dirichlet Laplacian on rectangles, and so our work generalizes ","authors_text":"Richard Laugesen, Shiya Liu","cross_cats":["math.NT","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-09-05T23:26:59Z","title":"Optimal stretching for lattice points and eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06172","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":"sha256:0d27946dc04f72d0c13796f26e97f8783bca255161ec35223d54058869d0d3b9","target":"record","created_at":"2026-05-18T00:35:55Z","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":"d9cdb025c69d1453a7ed6acb1cf301aa43fee8471f4290eee0f4421115c38c74","cross_cats_sorted":["math.NT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-09-05T23:26:59Z","title_canon_sha256":"6ebdd9a1efd1fa18f4410fcb92034b975492d4f6dae1b49d8607f9f936df0c6e"},"schema_version":"1.0","source":{"id":"1609.06172","kind":"arxiv","version":2}},"canonical_sha256":"31a39bbc5b8fb0508ab9189c65853f859253b0c3c4def84c2967c984461cc512","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31a39bbc5b8fb0508ab9189c65853f859253b0c3c4def84c2967c984461cc512","first_computed_at":"2026-05-18T00:35:55.570328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.570328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kpWxaocynT9N2E8oK+nS63S6tdSzLn96NaqLY7IDfae9IcLA4l+dQfFgL/T05b3UWO5rih9cyW/EER+OJrHTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.570725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06172","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d27946dc04f72d0c13796f26e97f8783bca255161ec35223d54058869d0d3b9","sha256:aed0756adaa21dfdf3f3d619bde3baf6dd29fdf8950b973bf4689587d14c22ea"],"state_sha256":"70f26ecbb9ebd0dd71e258dec73977ae7cb83f9ca9f1a356b1fe98afae47223f"}