{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7NMGQNOZUXYHFFMUQL3FVUV2S4","short_pith_number":"pith:7NMGQNOZ","schema_version":"1.0","canonical_sha256":"fb586835d9a5f072959482f65ad2ba971d7a10926f10529cd580f8e63652a695","source":{"kind":"arxiv","id":"1110.6792","version":1},"attestation_state":"computed","paper":{"title":"On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Eyvindur Palsson, Mihalis Mourgoglou","submitted_at":"2011-10-31T13:41:54Z","abstract_excerpt":"We prove that if the Hausdorff dimension of a compact subset of ${\\mathbb R}^d$ is greater than $\\frac{d+1}{2}$, then the set of angles determined by triples of points from this set has positive Lebesgue measure. Sobolev bounds for bi-linear analogs of generalized Radon transforms and the method of stationary phase play a key role. These results complement those of V. Harangi, T. Keleti, G. Kiss, P. Maga, P. Mattila and B. Stenner in (\\cite{HKKMMS10}). We also obtain new upper bounds for the number of times an angle can occur among $N$ points in ${\\mathbb R}^d$, $d \\ge 4$, motivated by the res"},"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":"1110.6792","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-31T13:41:54Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9c2435ac5bbf48e47a3036938178be7e022caf8665ec53e7f77ae7264ec1f5c9","abstract_canon_sha256":"689231380cee570956cffc51728707a18d97a7a69143a4b452808428208352c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:54.186164Z","signature_b64":"oSUicbkTX5af93CbnNfg23GONUH/MDFWCG5H5GGyNbEaR5+mw91NazUhF9todpgJo6J1hZJh6bMOIPbuL6XYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb586835d9a5f072959482f65ad2ba971d7a10926f10529cd580f8e63652a695","last_reissued_at":"2026-05-18T04:09:54.185733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:54.185733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Alex Iosevich, Eyvindur Palsson, Mihalis Mourgoglou","submitted_at":"2011-10-31T13:41:54Z","abstract_excerpt":"We prove that if the Hausdorff dimension of a compact subset of ${\\mathbb R}^d$ is greater than $\\frac{d+1}{2}$, then the set of angles determined by triples of points from this set has positive Lebesgue measure. Sobolev bounds for bi-linear analogs of generalized Radon transforms and the method of stationary phase play a key role. These results complement those of V. Harangi, T. Keleti, G. Kiss, P. Maga, P. Mattila and B. Stenner in (\\cite{HKKMMS10}). We also obtain new upper bounds for the number of times an angle can occur among $N$ points in ${\\mathbb R}^d$, $d \\ge 4$, motivated by the res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6792","kind":"arxiv","version":1},"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":"1110.6792","created_at":"2026-05-18T04:09:54.185797+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.6792v1","created_at":"2026-05-18T04:09:54.185797+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6792","created_at":"2026-05-18T04:09:54.185797+00:00"},{"alias_kind":"pith_short_12","alias_value":"7NMGQNOZUXYH","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7NMGQNOZUXYHFFMU","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7NMGQNOZ","created_at":"2026-05-18T12:26:22.705136+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/7NMGQNOZUXYHFFMUQL3FVUV2S4","json":"https://pith.science/pith/7NMGQNOZUXYHFFMUQL3FVUV2S4.json","graph_json":"https://pith.science/api/pith-number/7NMGQNOZUXYHFFMUQL3FVUV2S4/graph.json","events_json":"https://pith.science/api/pith-number/7NMGQNOZUXYHFFMUQL3FVUV2S4/events.json","paper":"https://pith.science/paper/7NMGQNOZ"},"agent_actions":{"view_html":"https://pith.science/pith/7NMGQNOZUXYHFFMUQL3FVUV2S4","download_json":"https://pith.science/pith/7NMGQNOZUXYHFFMUQL3FVUV2S4.json","view_paper":"https://pith.science/paper/7NMGQNOZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.6792&json=true","fetch_graph":"https://pith.science/api/pith-number/7NMGQNOZUXYHFFMUQL3FVUV2S4/graph.json","fetch_events":"https://pith.science/api/pith-number/7NMGQNOZUXYHFFMUQL3FVUV2S4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7NMGQNOZUXYHFFMUQL3FVUV2S4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7NMGQNOZUXYHFFMUQL3FVUV2S4/action/storage_attestation","attest_author":"https://pith.science/pith/7NMGQNOZUXYHFFMUQL3FVUV2S4/action/author_attestation","sign_citation":"https://pith.science/pith/7NMGQNOZUXYHFFMUQL3FVUV2S4/action/citation_signature","submit_replication":"https://pith.science/pith/7NMGQNOZUXYHFFMUQL3FVUV2S4/action/replication_record"}},"created_at":"2026-05-18T04:09:54.185797+00:00","updated_at":"2026-05-18T04:09:54.185797+00:00"}