{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:BANCTQGJDKJE7O72EKOAO7KQLD","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":"841b3d792ac577eb213ec8372dd18d6b75f69b81da34b2c38149217c75921108","cross_cats_sorted":["math.DG","math.DS"],"license":"","primary_cat":"math.SP","submitted_at":"2006-12-10T04:29:09Z","title_canon_sha256":"ae8e708f9eceb6e97cdb6db89f037cb194bdee43365a2e917d94d8b3f4914b00"},"schema_version":"1.0","source":{"id":"math/0612250","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612250","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612250v3","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612250","created_at":"2026-05-18T04:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"BANCTQGJDKJE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"BANCTQGJDKJE7O72","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"BANCTQGJ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d161799b6f632fae667432178a02ce6a05f0286681e144bc24a32d6a18fac671","target":"graph","created_at":"2026-05-18T04:08:53Z","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 obtain an estimate from below for the remainder in Weyl's law on negatively curved surfaces. In the constant curvature case, such a bound was proved independently by Hejhal and Randol in 1976 using the Selberg zeta function techniques. Our approach works in arbitrary negative curvature, and is based on wave trace asymptotics for long times, equidistribution of closed geodesics and small-scale microlocalization.","authors_text":"Dmitry Jakobson, Iosif Polterovich, John A. Toth","cross_cats":["math.DG","math.DS"],"headline":"","license":"","primary_cat":"math.SP","submitted_at":"2006-12-10T04:29:09Z","title":"A lower bound for the remainder in Weyl's law on negatively curved surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612250","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":"sha256:8d756026e92d814382686e8b050e32ce6ddd6d7e097690c37b423ceca421d084","target":"record","created_at":"2026-05-18T04:08:53Z","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":"841b3d792ac577eb213ec8372dd18d6b75f69b81da34b2c38149217c75921108","cross_cats_sorted":["math.DG","math.DS"],"license":"","primary_cat":"math.SP","submitted_at":"2006-12-10T04:29:09Z","title_canon_sha256":"ae8e708f9eceb6e97cdb6db89f037cb194bdee43365a2e917d94d8b3f4914b00"},"schema_version":"1.0","source":{"id":"math/0612250","kind":"arxiv","version":3}},"canonical_sha256":"081a29c0c91a924fbbfa229c077d5058ef381bd2cc0b8d3d410650172129291b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"081a29c0c91a924fbbfa229c077d5058ef381bd2cc0b8d3d410650172129291b","first_computed_at":"2026-05-18T04:08:53.086128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:53.086128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RRk0OieqM5daehKpWJcba8t4VjvBjYdpRzPoCjKJBG6NqaQfjzKtrVAKdNy7hMB4JNY5nSy6umEfJf/u3oAiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:53.086614Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612250","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d756026e92d814382686e8b050e32ce6ddd6d7e097690c37b423ceca421d084","sha256:d161799b6f632fae667432178a02ce6a05f0286681e144bc24a32d6a18fac671"],"state_sha256":"e9041fbf513baf533059016a9ebd42a6ac19df13e1bd2e59d8b47379e3819385"}