{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NBDQVWDJ6FCJZSIZGSPKPJ5QVF","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":"9b473274adaa84f887c69872b4dfbed24730f621a2f8059113f1f51cc84a6b0b","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-01T11:23:56Z","title_canon_sha256":"80c5a0acf0a8990a61d3f4508ef79014a6f728fc86a8df9bd5b5604e021c1557"},"schema_version":"1.0","source":{"id":"1606.00230","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00230","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00230v3","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00230","created_at":"2026-05-18T00:48:32Z"},{"alias_kind":"pith_short_12","alias_value":"NBDQVWDJ6FCJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NBDQVWDJ6FCJZSIZ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NBDQVWDJ","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:b33dc316c1af047ee876f29017f8c4dc456e2b398cde829b3161350267182a0e","target":"graph","created_at":"2026-05-18T00:48:32Z","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 show that any sufficiently (finitely) smooth $\\mathbb Z_2$-symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid, i.e. all deformations among domains in the same class which preserve the length of all periodic orbits of the associated billiard flow must necessarily be isometric deformations. This gives a partial answer to a question of P. Sarnak.","authors_text":"Jacopo De Simoi, Qiaoling Wei, Vadim Kaloshin, with an appendix joint with Hamid Hezari","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-01T11:23:56Z","title":"Dynamical Spectral rigidity among $\\mathbb Z_2$-symmetric strictly convex domains close to a circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00230","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":"sha256:05c66891eaa255ec4c607f41a93c24ac653cbe469a48501a1833ef4853832451","target":"record","created_at":"2026-05-18T00:48:32Z","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":"9b473274adaa84f887c69872b4dfbed24730f621a2f8059113f1f51cc84a6b0b","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-01T11:23:56Z","title_canon_sha256":"80c5a0acf0a8990a61d3f4508ef79014a6f728fc86a8df9bd5b5604e021c1557"},"schema_version":"1.0","source":{"id":"1606.00230","kind":"arxiv","version":3}},"canonical_sha256":"68470ad869f1449cc919349ea7a7b0a976bba340fa6946068fba08c2766c9f78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68470ad869f1449cc919349ea7a7b0a976bba340fa6946068fba08c2766c9f78","first_computed_at":"2026-05-18T00:48:32.901098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:32.901098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cPVp/oL7I3aOeffdYVG+0d84vy52hKkeTNN1Ysh6GPoxly9P784Cu00GU/unkVbSduB8rZyfErLwjOJtQqQaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:32.901736Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00230","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05c66891eaa255ec4c607f41a93c24ac653cbe469a48501a1833ef4853832451","sha256:b33dc316c1af047ee876f29017f8c4dc456e2b398cde829b3161350267182a0e"],"state_sha256":"a37d0933ff91d62c0c8d8f13a13a32cb698506b069fff0ecae8af2c803b2882c"}