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Union $M'$ of disjoint circles is {\\it situated} in one sphere as union $M$ of disjoint circles in the other sphere if there is a homeomorphism between these two spheres which maps $M'$ to $M$.\n  We prove (by giving an explicit example) that the answer to this problem is \""},"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":"1210.7361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-10-27T19:10:48Z","cross_cats_sorted":[],"title_canon_sha256":"a17d6bbc310f749690e81ed8017e3dbe7b3d262567b5f0294acbbe0fe33e9e60","abstract_canon_sha256":"fbd2ffd12fb6bccb04d19673e2fd6d0d3e9f7fea448ba9927fbfabaaf421faf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:46.563648Z","signature_b64":"t29n7A6KckLzvtPUa/M7Nqd5piSAxpFotLNU2FiTMCnangdNb+pLNXduSKX80knzd+S3y4esuRr2WC1zRclbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"695d4da67e6b51781c9849d02068f1df9ceb22637634d8bebb392bcf7a5e1d6a","last_reissued_at":"2026-05-18T02:32:46.563183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:46.563183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How do curved spheres intersect in 3-space?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Sergey Avvakumov","submitted_at":"2012-10-27T19:10:48Z","abstract_excerpt":"The following problem was proposed in 2010 by S. 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Union $M'$ of disjoint circles is {\\it situated} in one sphere as union $M$ of disjoint circles in the other sphere if there is a homeomorphism between these two spheres which maps $M'$ to $M$.\n  We prove (by giving an explicit example) that the answer to this problem is \""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7361","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":"1210.7361","created_at":"2026-05-18T02:32:46.563250+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.7361v2","created_at":"2026-05-18T02:32:46.563250+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7361","created_at":"2026-05-18T02:32:46.563250+00:00"},{"alias_kind":"pith_short_12","alias_value":"NFOU3JT6NNIX","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NFOU3JT6NNIXQHEY","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NFOU3JT6","created_at":"2026-05-18T12:27:16.716162+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/NFOU3JT6NNIXQHEYJHICA2HR36","json":"https://pith.science/pith/NFOU3JT6NNIXQHEYJHICA2HR36.json","graph_json":"https://pith.science/api/pith-number/NFOU3JT6NNIXQHEYJHICA2HR36/graph.json","events_json":"https://pith.science/api/pith-number/NFOU3JT6NNIXQHEYJHICA2HR36/events.json","paper":"https://pith.science/paper/NFOU3JT6"},"agent_actions":{"view_html":"https://pith.science/pith/NFOU3JT6NNIXQHEYJHICA2HR36","download_json":"https://pith.science/pith/NFOU3JT6NNIXQHEYJHICA2HR36.json","view_paper":"https://pith.science/paper/NFOU3JT6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.7361&json=true","fetch_graph":"https://pith.science/api/pith-number/NFOU3JT6NNIXQHEYJHICA2HR36/graph.json","fetch_events":"https://pith.science/api/pith-number/NFOU3JT6NNIXQHEYJHICA2HR36/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NFOU3JT6NNIXQHEYJHICA2HR36/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NFOU3JT6NNIXQHEYJHICA2HR36/action/storage_attestation","attest_author":"https://pith.science/pith/NFOU3JT6NNIXQHEYJHICA2HR36/action/author_attestation","sign_citation":"https://pith.science/pith/NFOU3JT6NNIXQHEYJHICA2HR36/action/citation_signature","submit_replication":"https://pith.science/pith/NFOU3JT6NNIXQHEYJHICA2HR36/action/replication_record"}},"created_at":"2026-05-18T02:32:46.563250+00:00","updated_at":"2026-05-18T02:32:46.563250+00:00"}