{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CJA4WEZFAGONYLOWQUACH2AFHG","short_pith_number":"pith:CJA4WEZF","schema_version":"1.0","canonical_sha256":"1241cb1325019cdc2dd6850023e80539adbe25af49f0cf384cf8ed64a8e6571c","source":{"kind":"arxiv","id":"1111.1110","version":2},"attestation_state":"computed","paper":{"title":"Conchoid surfaces of spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Gruber, Juana Sendra, Martin Peternell","submitted_at":"2011-11-04T12:38:14Z","abstract_excerpt":"The conchoid of a surface $F$ with respect to given fixed point $O$ is roughly speaking the surface obtained by increasing the radius function with respect to $O$ by a constant. This paper studies {\\it conchoid surfaces of spheres} and shows that these surfaces admit rational parameterizations. Explicit parameterizations of these surfaces are constructed using the relations to pencils of quadrics in $\\R^3$ and $\\R^4$. Moreover we point to remarkable geometric properties of these surfaces and their construction."},"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":"1111.1110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-04T12:38:14Z","cross_cats_sorted":[],"title_canon_sha256":"b444f72a98a124ae915bc4f976ffb54f992ee10dd12fa374fef07e305603a1be","abstract_canon_sha256":"15ad30af4f1acf21da7e9f8536c7af00d003650ed4613c748bcbca77644904d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:57.557945Z","signature_b64":"dcJ3qBR4yPmPSsQIWaSrq8i9IBaksn92n7pueoHGEOltwevP162HUk62tFJDZQ52wpHKZ3GF8PF3oL5JNGJLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1241cb1325019cdc2dd6850023e80539adbe25af49f0cf384cf8ed64a8e6571c","last_reissued_at":"2026-05-18T03:02:57.557452Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:57.557452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conchoid surfaces of spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Gruber, Juana Sendra, Martin Peternell","submitted_at":"2011-11-04T12:38:14Z","abstract_excerpt":"The conchoid of a surface $F$ with respect to given fixed point $O$ is roughly speaking the surface obtained by increasing the radius function with respect to $O$ by a constant. This paper studies {\\it conchoid surfaces of spheres} and shows that these surfaces admit rational parameterizations. Explicit parameterizations of these surfaces are constructed using the relations to pencils of quadrics in $\\R^3$ and $\\R^4$. Moreover we point to remarkable geometric properties of these surfaces and their construction."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1110","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":"1111.1110","created_at":"2026-05-18T03:02:57.557530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.1110v2","created_at":"2026-05-18T03:02:57.557530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1110","created_at":"2026-05-18T03:02:57.557530+00:00"},{"alias_kind":"pith_short_12","alias_value":"CJA4WEZFAGON","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CJA4WEZFAGONYLOW","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CJA4WEZF","created_at":"2026-05-18T12:26:26.731475+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/CJA4WEZFAGONYLOWQUACH2AFHG","json":"https://pith.science/pith/CJA4WEZFAGONYLOWQUACH2AFHG.json","graph_json":"https://pith.science/api/pith-number/CJA4WEZFAGONYLOWQUACH2AFHG/graph.json","events_json":"https://pith.science/api/pith-number/CJA4WEZFAGONYLOWQUACH2AFHG/events.json","paper":"https://pith.science/paper/CJA4WEZF"},"agent_actions":{"view_html":"https://pith.science/pith/CJA4WEZFAGONYLOWQUACH2AFHG","download_json":"https://pith.science/pith/CJA4WEZFAGONYLOWQUACH2AFHG.json","view_paper":"https://pith.science/paper/CJA4WEZF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.1110&json=true","fetch_graph":"https://pith.science/api/pith-number/CJA4WEZFAGONYLOWQUACH2AFHG/graph.json","fetch_events":"https://pith.science/api/pith-number/CJA4WEZFAGONYLOWQUACH2AFHG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CJA4WEZFAGONYLOWQUACH2AFHG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CJA4WEZFAGONYLOWQUACH2AFHG/action/storage_attestation","attest_author":"https://pith.science/pith/CJA4WEZFAGONYLOWQUACH2AFHG/action/author_attestation","sign_citation":"https://pith.science/pith/CJA4WEZFAGONYLOWQUACH2AFHG/action/citation_signature","submit_replication":"https://pith.science/pith/CJA4WEZFAGONYLOWQUACH2AFHG/action/replication_record"}},"created_at":"2026-05-18T03:02:57.557530+00:00","updated_at":"2026-05-18T03:02:57.557530+00:00"}