{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:BCSNREGOWNOVYMQMDCGTAIXUJC","short_pith_number":"pith:BCSNREGO","schema_version":"1.0","canonical_sha256":"08a4d890ceb35d5c320c188d3022f448a15db70c2ee24a858e406d48b11f9f88","source":{"kind":"arxiv","id":"0808.1788","version":3},"attestation_state":"computed","paper":{"title":"Some extensions of the class of convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Vladimir Golubyatnikov, Vladimir Rovenski","submitted_at":"2008-08-13T06:53:12Z","abstract_excerpt":"We introduce and study a new class of $\\eps$-convex bodies (extending the class of convex bodies) in metric and normed linear spaces. We analyze relations between characteristic properties of convex bodies, demonstrate how $\\eps$-convex bodies connect with some classical results of Convex Geometry, as Helly theorem, and find applications to geometric tomography. We introduce the notion of a circular projection and investigate the problem of determination of $\\eps$-convex bodies by their projection-type images. The results generalize corresponding stability theorems by H. Groemer."},"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":"0808.1788","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-08-13T06:53:12Z","cross_cats_sorted":[],"title_canon_sha256":"6e3ac9779d098f757e8a9a8245778b9d5beacac195969d3c0ad0dad9269d594d","abstract_canon_sha256":"5b52a7f45016fa24b584f758795262df47e8575399ae217dd3e5617772249d74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:33.093824Z","signature_b64":"qEDAx+y+d1RTdY6BgYCmdayLrbv0PyGYGAawkbhIu1HS7BSYMAUlOFWBfTyHjJOKzCl0IZZywhuqHhNt9OtFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08a4d890ceb35d5c320c188d3022f448a15db70c2ee24a858e406d48b11f9f88","last_reissued_at":"2026-05-18T01:21:33.093161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:33.093161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some extensions of the class of convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Vladimir Golubyatnikov, Vladimir Rovenski","submitted_at":"2008-08-13T06:53:12Z","abstract_excerpt":"We introduce and study a new class of $\\eps$-convex bodies (extending the class of convex bodies) in metric and normed linear spaces. We analyze relations between characteristic properties of convex bodies, demonstrate how $\\eps$-convex bodies connect with some classical results of Convex Geometry, as Helly theorem, and find applications to geometric tomography. We introduce the notion of a circular projection and investigate the problem of determination of $\\eps$-convex bodies by their projection-type images. The results generalize corresponding stability theorems by H. Groemer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1788","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":"0808.1788","created_at":"2026-05-18T01:21:33.093268+00:00"},{"alias_kind":"arxiv_version","alias_value":"0808.1788v3","created_at":"2026-05-18T01:21:33.093268+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1788","created_at":"2026-05-18T01:21:33.093268+00:00"},{"alias_kind":"pith_short_12","alias_value":"BCSNREGOWNOV","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"BCSNREGOWNOVYMQM","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"BCSNREGO","created_at":"2026-05-18T12:25:56.245647+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/BCSNREGOWNOVYMQMDCGTAIXUJC","json":"https://pith.science/pith/BCSNREGOWNOVYMQMDCGTAIXUJC.json","graph_json":"https://pith.science/api/pith-number/BCSNREGOWNOVYMQMDCGTAIXUJC/graph.json","events_json":"https://pith.science/api/pith-number/BCSNREGOWNOVYMQMDCGTAIXUJC/events.json","paper":"https://pith.science/paper/BCSNREGO"},"agent_actions":{"view_html":"https://pith.science/pith/BCSNREGOWNOVYMQMDCGTAIXUJC","download_json":"https://pith.science/pith/BCSNREGOWNOVYMQMDCGTAIXUJC.json","view_paper":"https://pith.science/paper/BCSNREGO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0808.1788&json=true","fetch_graph":"https://pith.science/api/pith-number/BCSNREGOWNOVYMQMDCGTAIXUJC/graph.json","fetch_events":"https://pith.science/api/pith-number/BCSNREGOWNOVYMQMDCGTAIXUJC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BCSNREGOWNOVYMQMDCGTAIXUJC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BCSNREGOWNOVYMQMDCGTAIXUJC/action/storage_attestation","attest_author":"https://pith.science/pith/BCSNREGOWNOVYMQMDCGTAIXUJC/action/author_attestation","sign_citation":"https://pith.science/pith/BCSNREGOWNOVYMQMDCGTAIXUJC/action/citation_signature","submit_replication":"https://pith.science/pith/BCSNREGOWNOVYMQMDCGTAIXUJC/action/replication_record"}},"created_at":"2026-05-18T01:21:33.093268+00:00","updated_at":"2026-05-18T01:21:33.093268+00:00"}