{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KD4VG2VZRNK7247QAOK3J27JXQ","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":"3959cc4a57c331b25dc6b2196e3cdf1842c8e2ec7788515d143b7676d74f2918","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-26T07:57:09Z","title_canon_sha256":"d71c76658db117bc9420af284f4658d42e7f22d403a752f42eeb20c387142fc0"},"schema_version":"1.0","source":{"id":"1003.5061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5061","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5061v1","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5061","created_at":"2026-05-18T04:13:55Z"},{"alias_kind":"pith_short_12","alias_value":"KD4VG2VZRNK7","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KD4VG2VZRNK7247Q","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KD4VG2VZ","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:4b2a0f624560b24c00a7bd3629e74be9d70d2a90e5818aafb7bde766692ba94e","target":"graph","created_at":"2026-05-18T04:13:55Z","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":"In the case of a linear symplectic map A of the 2d-torus, semiclassical measures are A-invariant probability measures associated to sequences of high energy quantum states. Our main result is an explicit lower bound on the entropy of any semiclassical measure of a given quantizable matrix A in Sp(2d,Z). In particular, our result implies that if A has an eigenvalue outside the unit circle, then a semiclassical measure cannot be carried by a closed orbit of A.","authors_text":"Gabriel Riviere (CMLS-EcolePolytechnique)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-26T07:57:09Z","title":"Entropy of quantum limits for symplectic linear maps of the multidimensional torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5061","kind":"arxiv","version":1},"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":"sha256:40c8e4a853325965bf45deaaced9770d18e8574c0f77ed2a1ea67be0ceaf1a6d","target":"record","created_at":"2026-05-18T04:13:55Z","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":"3959cc4a57c331b25dc6b2196e3cdf1842c8e2ec7788515d143b7676d74f2918","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-03-26T07:57:09Z","title_canon_sha256":"d71c76658db117bc9420af284f4658d42e7f22d403a752f42eeb20c387142fc0"},"schema_version":"1.0","source":{"id":"1003.5061","kind":"arxiv","version":1}},"canonical_sha256":"50f9536ab98b55fd73f00395b4ebe9bc010dfe47fca3c530ba3314586ced56e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50f9536ab98b55fd73f00395b4ebe9bc010dfe47fca3c530ba3314586ced56e9","first_computed_at":"2026-05-18T04:13:55.326293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:55.326293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W6y+J6KBXpe2dpyzzJO22DdGB6YBKeE90roURJugkK59fQ8WEVr0MDgW7+lcDbXKlWKWBYz/ID2lUrr9tCe4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:55.326859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40c8e4a853325965bf45deaaced9770d18e8574c0f77ed2a1ea67be0ceaf1a6d","sha256:4b2a0f624560b24c00a7bd3629e74be9d70d2a90e5818aafb7bde766692ba94e"],"state_sha256":"afa185378ccfeaa9ece881160675c9bca3e1085c3f6d99cc84c5b29d0b7428ef"}