{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:662KVUKVBIIKKM4PVOG5L5MSP7","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":"4937ca6627b7764bb5d04c373d1040e3441f9630ba716e1f17e740d2a37bd87a","cross_cats_sorted":["math.DS","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-23T23:23:38Z","title_canon_sha256":"a98b1056601fd0eeba35428130febf1d6b3c13c44e5ec503a9f303bfa153b693"},"schema_version":"1.0","source":{"id":"1304.6440","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6440","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6440v3","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6440","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"662KVUKVBIIK","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"662KVUKVBIIKKM4P","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"662KVUKV","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:0280d179686be475251311d6ea7bee13737338e9b56bf0451f2a32858c27b635","target":"graph","created_at":"2026-05-18T02:48:17Z","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":"The celebrated Hardy-Landau lower bound for the error term in the Gauss's circle problem can be viewed as an estimate from below for the remainder in Weyl's law on a square, with either Dirichlet or Neumann boundary conditions. We prove an analogous estimate for smooth star-shaped planar domains admitting an appropriate one-parameter family of periodic billiard trajectories. Examples include ellipses and smooth domains of constant width. Our results confirm a prediction of P. Sarnak who proved a similar statement for surfaces without boundary. We also obtain lower bounds on the error term in h","authors_text":"Iosif Polterovich, John A. Toth, Suresh Eswarathasan","cross_cats":["math.DS","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-23T23:23:38Z","title":"Smooth billiards with a large Weyl remainder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6440","kind":"arxiv","version":3},"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":"sha256:34de7fe69ae5d46235741e623ec8ab78bf48de077daa47cbcd1a96ad1fe8eab6","target":"record","created_at":"2026-05-18T02:48:17Z","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":"4937ca6627b7764bb5d04c373d1040e3441f9630ba716e1f17e740d2a37bd87a","cross_cats_sorted":["math.DS","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-23T23:23:38Z","title_canon_sha256":"a98b1056601fd0eeba35428130febf1d6b3c13c44e5ec503a9f303bfa153b693"},"schema_version":"1.0","source":{"id":"1304.6440","kind":"arxiv","version":3}},"canonical_sha256":"f7b4aad1550a10a5338fab8dd5f5927fd6da5cf27d820d4717e9efb9ca0b6344","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7b4aad1550a10a5338fab8dd5f5927fd6da5cf27d820d4717e9efb9ca0b6344","first_computed_at":"2026-05-18T02:48:17.792581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:17.792581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"otwZwovfmqygv/rFnTGU8ou83VBf7QY0Cg7U5Sh+IXlDnOMhpyVeB0UQdAdRAcuJc3moKzec3br0oRYcr3nSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:17.793053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6440","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34de7fe69ae5d46235741e623ec8ab78bf48de077daa47cbcd1a96ad1fe8eab6","sha256:0280d179686be475251311d6ea7bee13737338e9b56bf0451f2a32858c27b635"],"state_sha256":"7dea51c4c597dc2dff4893b42647b2543ac13d199e494b29abb5a8bbabd6c25a"}