{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U6NLCGPP3YGRUJP2UY63VLKNQ6","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":"085ab2007bb3f33398b9cafc474f0f2439d3b4d4bddb4c6eca693e475dcfefe8","cross_cats_sorted":["math.AP","math.DS","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-29T04:21:08Z","title_canon_sha256":"891a843895f85fef398fe4e5e6dda8c02e09fd6abbf3bcc4f8c5fb5893c2aa80"},"schema_version":"1.0","source":{"id":"1810.11949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.11949","created_at":"2026-05-18T00:02:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.11949v1","created_at":"2026-05-18T00:02:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11949","created_at":"2026-05-18T00:02:06Z"},{"alias_kind":"pith_short_12","alias_value":"U6NLCGPP3YGR","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U6NLCGPP3YGRUJP2","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U6NLCGPP","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:4e0264c5e5ec28bc86db5a31729157f1dd11635bd8517456e2e8f44faae9351d","target":"graph","created_at":"2026-05-18T00:02:06Z","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 this series, we investigate quantum ergodicity at small scales for linear hyperbolic maps of the torus (\"cat maps\"). In Part I of the series, we prove quantum ergodicity at various scales. Let $N=1/h$, in which $h$ is the Planck constant. First, for all integers $N\\in\\mathbb{N}$, we show quantum ergodicity at logarithmical scales $|\\log h|^{-\\alpha}$ for some $\\alpha>0$. Second, we show quantum ergodicity at polynomial scales $h^\\alpha$ for some $\\alpha>0$, in two special cases: $N\\in S(\\mathbb{N})$ of a full density subset $S(\\mathbb{N})$ of integers and Hecke eigenbasis for all integers.","authors_text":"Xiaolong Han","cross_cats":["math.AP","math.DS","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-29T04:21:08Z","title":"Small scale quantum ergodicity in cat maps. I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11949","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":"sha256:93807eeb8b0f9de2749851224b58e0755303cda39296336bb862269ea2d729c5","target":"record","created_at":"2026-05-18T00:02:06Z","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":"085ab2007bb3f33398b9cafc474f0f2439d3b4d4bddb4c6eca693e475dcfefe8","cross_cats_sorted":["math.AP","math.DS","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-29T04:21:08Z","title_canon_sha256":"891a843895f85fef398fe4e5e6dda8c02e09fd6abbf3bcc4f8c5fb5893c2aa80"},"schema_version":"1.0","source":{"id":"1810.11949","kind":"arxiv","version":1}},"canonical_sha256":"a79ab119efde0d1a25faa63dbaad4d87acc36fa7c3957f48ca144f3844c90e8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a79ab119efde0d1a25faa63dbaad4d87acc36fa7c3957f48ca144f3844c90e8a","first_computed_at":"2026-05-18T00:02:06.931010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:06.931010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sdM7PbSf3GuWcB90OU/rNHe2i3IALuHQ1hQfp70kuqpEEauw5UcarR3UA08UUFZ2uMZ4VEEjGLVFgJm/lHCxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:06.931609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.11949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93807eeb8b0f9de2749851224b58e0755303cda39296336bb862269ea2d729c5","sha256:4e0264c5e5ec28bc86db5a31729157f1dd11635bd8517456e2e8f44faae9351d"],"state_sha256":"148c15a586d7dcaf098cdf397dba54d1167685f1049a965abbbaeddd7e0a69b4"}