{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SFTMX3DBPS5V563G3DQNEO2DNK","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":"bb2531847f482e915e90cb1fdcecc3b4e184122fc6375c7dcd0e5e63c378028d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-02T18:33:14Z","title_canon_sha256":"44197aef779c0868e0c721fd688dd1f11f8a5b094b23bf449bbd4f50d1b3746f"},"schema_version":"1.0","source":{"id":"1109.0517","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0517","created_at":"2026-05-18T02:45:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0517v3","created_at":"2026-05-18T02:45:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0517","created_at":"2026-05-18T02:45:56Z"},{"alias_kind":"pith_short_12","alias_value":"SFTMX3DBPS5V","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SFTMX3DBPS5V563G","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SFTMX3DB","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:4bc68f4e768b84c850a5e9da3b647dd458d5d86070b2b1c42e9303462c934a25","target":"graph","created_at":"2026-05-18T02:45:56Z","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 construct an explicit family of arithmetic Teichm\\\"uller curves $\\mathcal{C}_{2k}$, $k\\in\\mathbb{N}$, supporting $\\textrm{SL}(2,\\mathbb{R})$-invariant probabilities $\\mu_{2k}$ such that the associated $\\textrm{SL}(2,\\mathbb{R})$-representation on $L^2(\\mathcal{C}_{2k}, \\mu_{2k})$ has complementary series for every $k\\geq 3$. Actually, the size of the spectral gap along this family goes to zero. In particular, the Teichm\\\"uller geodesic flow restricted to these explicit arithmetic Teichm\\\"uller curves $\\mathcal{C}_{2k}$ has arbitrarily slow rate of exponential mixing.","authors_text":"Carlos Matheus, Gabriela Weitze-Schmith\\\"usen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-02T18:33:14Z","title":"Explicit Teichm\\\"uller curves with complemetary series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0517","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:f649c27c42954c3e1255d716ce9718aa35aa826ff99620bf1f7175c1f30dbff7","target":"record","created_at":"2026-05-18T02:45:56Z","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":"bb2531847f482e915e90cb1fdcecc3b4e184122fc6375c7dcd0e5e63c378028d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-02T18:33:14Z","title_canon_sha256":"44197aef779c0868e0c721fd688dd1f11f8a5b094b23bf449bbd4f50d1b3746f"},"schema_version":"1.0","source":{"id":"1109.0517","kind":"arxiv","version":3}},"canonical_sha256":"9166cbec617cbb5efb66d8e0d23b436aa6e18193f1900386bd01f095e127611c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9166cbec617cbb5efb66d8e0d23b436aa6e18193f1900386bd01f095e127611c","first_computed_at":"2026-05-18T02:45:56.164274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:56.164274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MbyuG5RVeH7g0YBpKBncCl9ldvtThBwXb/YdhXm1gA2KmhphMGPVXz80h4Bywov4rNTaobyIYLy6dluPkKeMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:56.164900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0517","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f649c27c42954c3e1255d716ce9718aa35aa826ff99620bf1f7175c1f30dbff7","sha256:4bc68f4e768b84c850a5e9da3b647dd458d5d86070b2b1c42e9303462c934a25"],"state_sha256":"efec1b998e9a8744dc196ef63538a65d8de762ba356ef4bf60b802942be97239"}