{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MEPXLIMXVQH33T4ULZMIWSZ22G","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":"9af04b1ba747b6da016b560806d37628a9b8d4eff01776d7f9ee21b5c3530f02","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-11-02T14:58:59Z","title_canon_sha256":"d80dea97f50c741dfed02a448c1e6d03a0978ad6ad711ce030b8cf2abb2ae3f5"},"schema_version":"1.0","source":{"id":"0911.0329","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0329","created_at":"2026-05-18T04:41:44Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0329v2","created_at":"2026-05-18T04:41:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0329","created_at":"2026-05-18T04:41:44Z"},{"alias_kind":"pith_short_12","alias_value":"MEPXLIMXVQH3","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MEPXLIMXVQH33T4U","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MEPXLIMX","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:46c74eb417c538929cf5ce501b6421f9b3795c87756b86d0633a7fbc4c501f04","target":"graph","created_at":"2026-05-18T04:41:44Z","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":"Let $\\calM=\\Gamma\\bs \\calH^{(n)}$, where $\\calH^{(n)}$ is a product of $n+1$ hyperbolic planes and $\\Gamma\\subset\\PSL(2,\\bbR)^{n+1}$ is an irreducible cocompact lattice. We consider closed geodesics on $\\calM$ that propagate locally only in one factor. We show that, as the length tends to infinity, the holonomy rotations attached to these geodesics become equidistributed in $\\PSO(2)^n$ with respect to a certain measure. For the special case of lattices derived from quaternion algebras, we can give another interpretation of the holonomy angles under which this measure arises naturally.","authors_text":"Dubi Kelmer","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-11-02T14:58:59Z","title":"Distribution of holonomy about closed geodesics in a product of hyperbolic planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0329","kind":"arxiv","version":2},"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:a0beb32ef7d524a32dabd0559d39b6a4cbd3e19184f1438fa905d2c170c4ce49","target":"record","created_at":"2026-05-18T04:41:44Z","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":"9af04b1ba747b6da016b560806d37628a9b8d4eff01776d7f9ee21b5c3530f02","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-11-02T14:58:59Z","title_canon_sha256":"d80dea97f50c741dfed02a448c1e6d03a0978ad6ad711ce030b8cf2abb2ae3f5"},"schema_version":"1.0","source":{"id":"0911.0329","kind":"arxiv","version":2}},"canonical_sha256":"611f75a197ac0fbdcf945e588b4b3ad1a438ae93233326e313f341049ac3734b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"611f75a197ac0fbdcf945e588b4b3ad1a438ae93233326e313f341049ac3734b","first_computed_at":"2026-05-18T04:41:44.057024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:44.057024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CfDvkNdaCoEkwa/4AfuzK9cSyS6+11HLXcrgarbmcssikQ5/M7W4XoBJJXuEwyA2dOiqOJRae3Qhtvy6PS1yAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:44.057410Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0329","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0beb32ef7d524a32dabd0559d39b6a4cbd3e19184f1438fa905d2c170c4ce49","sha256:46c74eb417c538929cf5ce501b6421f9b3795c87756b86d0633a7fbc4c501f04"],"state_sha256":"8eddf8fd43f079b1c715611faf2ffddac5fabb2fe8b7bd05b321f33eaa976bfc"}