{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4ZGJQBPKNI5U4M7GTLO26GCQ2P","short_pith_number":"pith:4ZGJQBPK","schema_version":"1.0","canonical_sha256":"e64c9805ea6a3b4e33e69addaf1850d3faeb3edd27b9c3d6f1a8255018c23121","source":{"kind":"arxiv","id":"1201.4505","version":2},"attestation_state":"computed","paper":{"title":"Limit Points Badly Approximable by Horoballs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.MG","authors_text":"Dustin Mayeda, Keith Merrill","submitted_at":"2012-01-21T20:08:40Z","abstract_excerpt":"For a proper, geodesic, Gromov hyperbolic metric space X, a discrete subgroup of isometries \\Gamma whose limit set is uniformly perfect, and a disjoint collection of horoballs {H_j}, we show that the set of limit points badly approximable by {H_j} is absolutely winning in the limit set. As an application, we deduce that for a geometrically finite Kleinian group acting on H^{n+1}, the limit points badly approximable by parabolics is absolutely winning, generalizing previous results of Dani and McMullen. As a consequence of winning, we show that the set of badly approximable limit points has dim"},"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":"1201.4505","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-01-21T20:08:40Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"e7b893f42536443ebf320a2ee303196836c2d2b8e9fa1059b3cb5c388f560766","abstract_canon_sha256":"7925adb14f68fe6041b329ffc5dd26168a054f6472df333233496678a0f4c730"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:40.833891Z","signature_b64":"BJzWkTCG+QPPhWARel4GLLYENZ+YI/CVNPw2FTLc3ECKezthQe8E0rJAOREPA9YSd9XR8KrrMbPYUXQZOCyPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e64c9805ea6a3b4e33e69addaf1850d3faeb3edd27b9c3d6f1a8255018c23121","last_reissued_at":"2026-05-18T03:29:40.833235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:40.833235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limit Points Badly Approximable by Horoballs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.MG","authors_text":"Dustin Mayeda, Keith Merrill","submitted_at":"2012-01-21T20:08:40Z","abstract_excerpt":"For a proper, geodesic, Gromov hyperbolic metric space X, a discrete subgroup of isometries \\Gamma whose limit set is uniformly perfect, and a disjoint collection of horoballs {H_j}, we show that the set of limit points badly approximable by {H_j} is absolutely winning in the limit set. As an application, we deduce that for a geometrically finite Kleinian group acting on H^{n+1}, the limit points badly approximable by parabolics is absolutely winning, generalizing previous results of Dani and McMullen. As a consequence of winning, we show that the set of badly approximable limit points has dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4505","kind":"arxiv","version":2},"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":"1201.4505","created_at":"2026-05-18T03:29:40.833348+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.4505v2","created_at":"2026-05-18T03:29:40.833348+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4505","created_at":"2026-05-18T03:29:40.833348+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ZGJQBPKNI5U","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ZGJQBPKNI5U4M7G","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ZGJQBPK","created_at":"2026-05-18T12:26:53.410803+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/4ZGJQBPKNI5U4M7GTLO26GCQ2P","json":"https://pith.science/pith/4ZGJQBPKNI5U4M7GTLO26GCQ2P.json","graph_json":"https://pith.science/api/pith-number/4ZGJQBPKNI5U4M7GTLO26GCQ2P/graph.json","events_json":"https://pith.science/api/pith-number/4ZGJQBPKNI5U4M7GTLO26GCQ2P/events.json","paper":"https://pith.science/paper/4ZGJQBPK"},"agent_actions":{"view_html":"https://pith.science/pith/4ZGJQBPKNI5U4M7GTLO26GCQ2P","download_json":"https://pith.science/pith/4ZGJQBPKNI5U4M7GTLO26GCQ2P.json","view_paper":"https://pith.science/paper/4ZGJQBPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.4505&json=true","fetch_graph":"https://pith.science/api/pith-number/4ZGJQBPKNI5U4M7GTLO26GCQ2P/graph.json","fetch_events":"https://pith.science/api/pith-number/4ZGJQBPKNI5U4M7GTLO26GCQ2P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ZGJQBPKNI5U4M7GTLO26GCQ2P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ZGJQBPKNI5U4M7GTLO26GCQ2P/action/storage_attestation","attest_author":"https://pith.science/pith/4ZGJQBPKNI5U4M7GTLO26GCQ2P/action/author_attestation","sign_citation":"https://pith.science/pith/4ZGJQBPKNI5U4M7GTLO26GCQ2P/action/citation_signature","submit_replication":"https://pith.science/pith/4ZGJQBPKNI5U4M7GTLO26GCQ2P/action/replication_record"}},"created_at":"2026-05-18T03:29:40.833348+00:00","updated_at":"2026-05-18T03:29:40.833348+00:00"}