{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:P74FBD3ZQHKY6BPD2X6ZLSLP4O","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":"9458da3c6177d16e061b3321e632663a79e4a3bbe6609b8f08cf11c83cfe5e57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-04T17:20:17Z","title_canon_sha256":"b4ab62ebd08aac1df97b6412152ff3920c78375e9a49f7a5dce5c3df5dacb8fa"},"schema_version":"1.0","source":{"id":"1410.1065","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1065","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1065v2","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1065","created_at":"2026-05-18T01:23:13Z"},{"alias_kind":"pith_short_12","alias_value":"P74FBD3ZQHKY","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P74FBD3ZQHKY6BPD","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P74FBD3Z","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:073041bec74e3bee2610769002b24a62e246966d52d7679d4e69c7ce8b41845f","target":"graph","created_at":"2026-05-18T01:23:13Z","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":"Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g. random Schr\\\"odinger operators and control theory.\n  We review recent results and announce new ones regarding quantitative unique continuation principles for partial differential equations with an underlying multiscale structure. They concern Schr\\\"odinger and second order elliptic operators. An important feature is that the estimates are scale free and with quantitative dependence on parameters. These unique continuation principles apply to functions satisfying cert","authors_text":"Christian Rose, Denis Borisov, Ivan Veseli\\'c, Ivica Naki\\'c, Martin Tautenhahn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-04T17:20:17Z","title":"Multiscale unique continuation properties of eigenfunctions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1065","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:f2a2620548098cf638cc423858bb696e7666a22e19919dfeff49f2c0b902f48b","target":"record","created_at":"2026-05-18T01:23:13Z","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":"9458da3c6177d16e061b3321e632663a79e4a3bbe6609b8f08cf11c83cfe5e57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-04T17:20:17Z","title_canon_sha256":"b4ab62ebd08aac1df97b6412152ff3920c78375e9a49f7a5dce5c3df5dacb8fa"},"schema_version":"1.0","source":{"id":"1410.1065","kind":"arxiv","version":2}},"canonical_sha256":"7ff8508f7981d58f05e3d5fd95c96fe3ba4792d1236d8555e0111b0a06f4b1cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ff8508f7981d58f05e3d5fd95c96fe3ba4792d1236d8555e0111b0a06f4b1cf","first_computed_at":"2026-05-18T01:23:13.094741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:13.094741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7MbR94p6fo86cs18q+sL2DLurV+N8kE1Pgl3tOxEIMvRuF9RH+uKSfrgWBIlmMow8EKVasogPj+aBGfP0buQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:13.095236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1065","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2a2620548098cf638cc423858bb696e7666a22e19919dfeff49f2c0b902f48b","sha256:073041bec74e3bee2610769002b24a62e246966d52d7679d4e69c7ce8b41845f"],"state_sha256":"b1d3c0f7f059be9e5f68289a0f76a76392a3fd8527c22192f3614a3d385ebafb"}