{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:X3IRBFERFNYW7Q73Z4BKTUE37F","short_pith_number":"pith:X3IRBFER","schema_version":"1.0","canonical_sha256":"bed11094912b716fc3fbcf02a9d09bf95586bc892af9de0cc830ff172bae9379","source":{"kind":"arxiv","id":"1803.03843","version":3},"attestation_state":"computed","paper":{"title":"The intersection of three spheres in a sphere and a new application of the Sato-Levine invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eiji Ogasa","submitted_at":"2018-03-10T17:37:59Z","abstract_excerpt":"Take transverse immersions f from a disjoint unin of the three 4-spheres $S^4_1$, $S^4_2$, and $S^4_3$ into $S^6$ with the following properties:\n  (1) The restriction of $f$ to $S^4_i$ is an embedding,\n  (2) The intersection of $f(S^4_i)$ and $f(S^4_j)$ is not empty and connected,\n  (3)The intersection among $f(S^4_1)$, $f(S^4_2)$, and $f(S^4_3)$ is not empty.\n  Then we obtain three surface-links $L_i=(S^4_i\\cap S^4_j, S^4_i\\cap S^4_k)$ in $S^4_i$, where $(i,j,k)=(1,2,3), (2,3,1), (3,1,2).$ We prove that, we have the equality $\\beta(L_1)+\\beta(L_2)+\\beta(L_3)=0$, where $\\beta(L_i)$ is the Sato"},"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":"1803.03843","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-03-10T17:37:59Z","cross_cats_sorted":[],"title_canon_sha256":"e6ed3ba11d9b27d3cad2268f4af051957f12914f464fceeb06b4023fda99ae50","abstract_canon_sha256":"3a904ed9da13df89b9060b2682a183fc69bdfe3a3b42607eb22426ccee467eec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:21.630434Z","signature_b64":"vAZL5pax3UYBMQyQiXV26Nd2VBxB5bV/pU3x1c6lSVzMmHT46U8y5igTPVunXs0hBZCfQ1rSgP4EWUb5Z/2GAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bed11094912b716fc3fbcf02a9d09bf95586bc892af9de0cc830ff172bae9379","last_reissued_at":"2026-05-18T00:14:21.629604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:21.629604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The intersection of three spheres in a sphere and a new application of the Sato-Levine invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eiji Ogasa","submitted_at":"2018-03-10T17:37:59Z","abstract_excerpt":"Take transverse immersions f from a disjoint unin of the three 4-spheres $S^4_1$, $S^4_2$, and $S^4_3$ into $S^6$ with the following properties:\n  (1) The restriction of $f$ to $S^4_i$ is an embedding,\n  (2) The intersection of $f(S^4_i)$ and $f(S^4_j)$ is not empty and connected,\n  (3)The intersection among $f(S^4_1)$, $f(S^4_2)$, and $f(S^4_3)$ is not empty.\n  Then we obtain three surface-links $L_i=(S^4_i\\cap S^4_j, S^4_i\\cap S^4_k)$ in $S^4_i$, where $(i,j,k)=(1,2,3), (2,3,1), (3,1,2).$ We prove that, we have the equality $\\beta(L_1)+\\beta(L_2)+\\beta(L_3)=0$, where $\\beta(L_i)$ is the Sato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03843","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":"1803.03843","created_at":"2026-05-18T00:14:21.629740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.03843v3","created_at":"2026-05-18T00:14:21.629740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03843","created_at":"2026-05-18T00:14:21.629740+00:00"},{"alias_kind":"pith_short_12","alias_value":"X3IRBFERFNYW","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"X3IRBFERFNYW7Q73","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"X3IRBFER","created_at":"2026-05-18T12:33:01.666342+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/X3IRBFERFNYW7Q73Z4BKTUE37F","json":"https://pith.science/pith/X3IRBFERFNYW7Q73Z4BKTUE37F.json","graph_json":"https://pith.science/api/pith-number/X3IRBFERFNYW7Q73Z4BKTUE37F/graph.json","events_json":"https://pith.science/api/pith-number/X3IRBFERFNYW7Q73Z4BKTUE37F/events.json","paper":"https://pith.science/paper/X3IRBFER"},"agent_actions":{"view_html":"https://pith.science/pith/X3IRBFERFNYW7Q73Z4BKTUE37F","download_json":"https://pith.science/pith/X3IRBFERFNYW7Q73Z4BKTUE37F.json","view_paper":"https://pith.science/paper/X3IRBFER","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.03843&json=true","fetch_graph":"https://pith.science/api/pith-number/X3IRBFERFNYW7Q73Z4BKTUE37F/graph.json","fetch_events":"https://pith.science/api/pith-number/X3IRBFERFNYW7Q73Z4BKTUE37F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X3IRBFERFNYW7Q73Z4BKTUE37F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X3IRBFERFNYW7Q73Z4BKTUE37F/action/storage_attestation","attest_author":"https://pith.science/pith/X3IRBFERFNYW7Q73Z4BKTUE37F/action/author_attestation","sign_citation":"https://pith.science/pith/X3IRBFERFNYW7Q73Z4BKTUE37F/action/citation_signature","submit_replication":"https://pith.science/pith/X3IRBFERFNYW7Q73Z4BKTUE37F/action/replication_record"}},"created_at":"2026-05-18T00:14:21.629740+00:00","updated_at":"2026-05-18T00:14:21.629740+00:00"}