{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WWFMALHWM4RNW57P5YCQK75PQH","short_pith_number":"pith:WWFMALHW","schema_version":"1.0","canonical_sha256":"b58ac02cf66722db77efee05057faf81c1625f699345891d72c155964b23c6e8","source":{"kind":"arxiv","id":"1012.6006","version":3},"attestation_state":"computed","paper":{"title":"Locally Divergent Orbits on Hilbert Modular Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"George Tomanov","submitted_at":"2010-12-29T19:16:36Z","abstract_excerpt":"We describe the closures of locally divergent orbitsunder the action of tori on Hilbert modular spaces of rank r = 2. In particular, we prove that if D is a maximal R-split torus acting on a real Hilbert modular space then every locally divergent non-closed orbit is dense for r > 2 and its closure is a finite union of tori orbits for r = 2. Our results confirm an orbit rigidity conjecture of Margulis in all cases except for (i) r = 2 and, (ii) r > 2 and the Hilbert modular space corresponds to a CM-field; in the cases (i) and (ii) our results contradict the conjecture. As an application, we de"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.6006","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-29T19:16:36Z","cross_cats_sorted":[],"title_canon_sha256":"483f0f0e98c96988b7e939d6ab474f7bba5b493c94c1dde3dd0c8b431a5303c0","abstract_canon_sha256":"8a8a62d15d8a9bb3b22e3423066c2a54829124ef93e17ce5b9be7187ac5c83f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:38.366775Z","signature_b64":"3KwPJZuOKdP9VydOiT0CRC5O0DgTUxJ9L+FhVI4hMwzs9VXIB+mP6oyGv92Y8aoUOQmDLV9seHVOLFftZBZaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b58ac02cf66722db77efee05057faf81c1625f699345891d72c155964b23c6e8","last_reissued_at":"2026-05-18T03:58:38.366146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:38.366146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locally Divergent Orbits on Hilbert Modular Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"George Tomanov","submitted_at":"2010-12-29T19:16:36Z","abstract_excerpt":"We describe the closures of locally divergent orbitsunder the action of tori on Hilbert modular spaces of rank r = 2. In particular, we prove that if D is a maximal R-split torus acting on a real Hilbert modular space then every locally divergent non-closed orbit is dense for r > 2 and its closure is a finite union of tori orbits for r = 2. Our results confirm an orbit rigidity conjecture of Margulis in all cases except for (i) r = 2 and, (ii) r > 2 and the Hilbert modular space corresponds to a CM-field; in the cases (i) and (ii) our results contradict the conjecture. As an application, we de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.6006","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.6006","created_at":"2026-05-18T03:58:38.366251+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.6006v3","created_at":"2026-05-18T03:58:38.366251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.6006","created_at":"2026-05-18T03:58:38.366251+00:00"},{"alias_kind":"pith_short_12","alias_value":"WWFMALHWM4RN","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"WWFMALHWM4RNW57P","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"WWFMALHW","created_at":"2026-05-18T12:26:17.028572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH","json":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH.json","graph_json":"https://pith.science/api/pith-number/WWFMALHWM4RNW57P5YCQK75PQH/graph.json","events_json":"https://pith.science/api/pith-number/WWFMALHWM4RNW57P5YCQK75PQH/events.json","paper":"https://pith.science/paper/WWFMALHW"},"agent_actions":{"view_html":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH","download_json":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH.json","view_paper":"https://pith.science/paper/WWFMALHW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.6006&json=true","fetch_graph":"https://pith.science/api/pith-number/WWFMALHWM4RNW57P5YCQK75PQH/graph.json","fetch_events":"https://pith.science/api/pith-number/WWFMALHWM4RNW57P5YCQK75PQH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH/action/storage_attestation","attest_author":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH/action/author_attestation","sign_citation":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH/action/citation_signature","submit_replication":"https://pith.science/pith/WWFMALHWM4RNW57P5YCQK75PQH/action/replication_record"}},"created_at":"2026-05-18T03:58:38.366251+00:00","updated_at":"2026-05-18T03:58:38.366251+00:00"}