{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZBZYSJHZUZGCIJO77ZDRF3XFD4","short_pith_number":"pith:ZBZYSJHZ","schema_version":"1.0","canonical_sha256":"c8738924f9a64c2425dffe4712eee51f00e2860f5a123b307f47db57356a5dc8","source":{"kind":"arxiv","id":"1403.7015","version":2},"attestation_state":"computed","paper":{"title":"Dimension Functions on the Spectrum over Bounded Geodesics and Applications to Diophantine Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.NT"],"primary_cat":"math.DS","authors_text":"Steffen Weil","submitted_at":"2014-03-27T13:14:43Z","abstract_excerpt":"The set B of geodesic rays avoiding a suitable obstacle in a complete negatively curved Riemannian manifold determines a spectrum S. While various properties of this spectrum are known, we define and study dimension functions on S in terms of the Hausdorff-dimension of suitable subsets of the set of bounded geodesic rays. We establish estimates on the Hausdorff-dimension of these subsets and thereby obtain non-trivial bounds for the dimension functions. Moreover we discuss the property of B being an absolute winning set, therefore satisfying a remarkable rigidity. Finally, we apply the obtaine"},"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":"1403.7015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-27T13:14:43Z","cross_cats_sorted":["math.MG","math.NT"],"title_canon_sha256":"028130eae343486a20c72831b68d552e7c766ac3fcf9e976bcb229cb827d183b","abstract_canon_sha256":"48d8e4bce6774ea4258fbf22fe3aea227f2818252c41ca0e5c53dec723a4c43a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:26.049584Z","signature_b64":"vLFaVI3QTssYWWOTdIaMUaTGdGKCRQW3NllM/TCmx17ldbASDbdcOsjvRTD9paZzvGBHW3/Z2/WP69GKmRKgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8738924f9a64c2425dffe4712eee51f00e2860f5a123b307f47db57356a5dc8","last_reissued_at":"2026-05-18T02:43:26.048868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:26.048868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dimension Functions on the Spectrum over Bounded Geodesics and Applications to Diophantine Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.NT"],"primary_cat":"math.DS","authors_text":"Steffen Weil","submitted_at":"2014-03-27T13:14:43Z","abstract_excerpt":"The set B of geodesic rays avoiding a suitable obstacle in a complete negatively curved Riemannian manifold determines a spectrum S. While various properties of this spectrum are known, we define and study dimension functions on S in terms of the Hausdorff-dimension of suitable subsets of the set of bounded geodesic rays. We establish estimates on the Hausdorff-dimension of these subsets and thereby obtain non-trivial bounds for the dimension functions. Moreover we discuss the property of B being an absolute winning set, therefore satisfying a remarkable rigidity. Finally, we apply the obtaine"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7015","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":"1403.7015","created_at":"2026-05-18T02:43:26.048979+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.7015v2","created_at":"2026-05-18T02:43:26.048979+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7015","created_at":"2026-05-18T02:43:26.048979+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZBZYSJHZUZGC","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZBZYSJHZUZGCIJO7","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZBZYSJHZ","created_at":"2026-05-18T12:28:59.999130+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/ZBZYSJHZUZGCIJO77ZDRF3XFD4","json":"https://pith.science/pith/ZBZYSJHZUZGCIJO77ZDRF3XFD4.json","graph_json":"https://pith.science/api/pith-number/ZBZYSJHZUZGCIJO77ZDRF3XFD4/graph.json","events_json":"https://pith.science/api/pith-number/ZBZYSJHZUZGCIJO77ZDRF3XFD4/events.json","paper":"https://pith.science/paper/ZBZYSJHZ"},"agent_actions":{"view_html":"https://pith.science/pith/ZBZYSJHZUZGCIJO77ZDRF3XFD4","download_json":"https://pith.science/pith/ZBZYSJHZUZGCIJO77ZDRF3XFD4.json","view_paper":"https://pith.science/paper/ZBZYSJHZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.7015&json=true","fetch_graph":"https://pith.science/api/pith-number/ZBZYSJHZUZGCIJO77ZDRF3XFD4/graph.json","fetch_events":"https://pith.science/api/pith-number/ZBZYSJHZUZGCIJO77ZDRF3XFD4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZBZYSJHZUZGCIJO77ZDRF3XFD4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZBZYSJHZUZGCIJO77ZDRF3XFD4/action/storage_attestation","attest_author":"https://pith.science/pith/ZBZYSJHZUZGCIJO77ZDRF3XFD4/action/author_attestation","sign_citation":"https://pith.science/pith/ZBZYSJHZUZGCIJO77ZDRF3XFD4/action/citation_signature","submit_replication":"https://pith.science/pith/ZBZYSJHZUZGCIJO77ZDRF3XFD4/action/replication_record"}},"created_at":"2026-05-18T02:43:26.048979+00:00","updated_at":"2026-05-18T02:43:26.048979+00:00"}