{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZKEUYW3WNJOZNLYEBWVA7E5U6Q","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":"2db4fea81f53062bedf461515849244b31b2a31bd913a00180bd1ddd8f3b76fa","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-08-07T16:22:37Z","title_canon_sha256":"ac7c550f58140e38bbc67018c09500f192b61ab79a16d27b98aa12152d673548"},"schema_version":"1.0","source":{"id":"1608.02238","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02238","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02238v3","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02238","created_at":"2026-05-18T00:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"ZKEUYW3WNJOZ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZKEUYW3WNJOZNLYE","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZKEUYW3W","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:931e7f01c8eb2bf5b20917a4c47b6f2a12a6db579cad7da67a150b77e37ef337","target":"graph","created_at":"2026-05-18T00:45:01Z","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 study eigenvalues of quantum open baker's maps with trapped sets given by linear arithmetic Cantor sets of dimensions $\\delta\\in (0,1)$. We show that the size of the spectral gap is strictly greater than the standard bound $\\max(0,{1\\over 2}-\\delta)$ for all values of $\\delta$, which is the first result of this kind. The size of the improvement is determined from a fractal uncertainty principle and can be computed for any given Cantor set. We next show a fractal Weyl upper bound for the number of eigenvalues in annuli, with exponent which depends on the inner radius of the annulus.","authors_text":"Long Jin, Semyon Dyatlov","cross_cats":["math-ph","math.AP","math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-08-07T16:22:37Z","title":"Resonances for open quantum maps and a fractal uncertainty principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02238","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:dafc11bb3c500bc5944107b2b051adfd99e698ab4181abcdf0c2781ed224c640","target":"record","created_at":"2026-05-18T00:45:01Z","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":"2db4fea81f53062bedf461515849244b31b2a31bd913a00180bd1ddd8f3b76fa","cross_cats_sorted":["math-ph","math.AP","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-08-07T16:22:37Z","title_canon_sha256":"ac7c550f58140e38bbc67018c09500f192b61ab79a16d27b98aa12152d673548"},"schema_version":"1.0","source":{"id":"1608.02238","kind":"arxiv","version":3}},"canonical_sha256":"ca894c5b766a5d96af040daa0f93b4f424fa06865ef4bd93cb5defb7b2efd5ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca894c5b766a5d96af040daa0f93b4f424fa06865ef4bd93cb5defb7b2efd5ca","first_computed_at":"2026-05-18T00:45:01.560276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:01.560276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SwwZG+MnQ3NoNcZRa3issM2PoJtJfNbILv9HXf8dKhyEs5aprUW0ccKs1NoCrVRMGRqA3528WNOXtm4WJQDSAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:01.560660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02238","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dafc11bb3c500bc5944107b2b051adfd99e698ab4181abcdf0c2781ed224c640","sha256:931e7f01c8eb2bf5b20917a4c47b6f2a12a6db579cad7da67a150b77e37ef337"],"state_sha256":"5e8ca39cd2c502c0b35f2b295d2242919d6576470278f26ec25b12dfbbe04c0c"}