{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:H5URN4XNVLQZ3L7U56NP6MAV43","short_pith_number":"pith:H5URN4XN","schema_version":"1.0","canonical_sha256":"3f6916f2edaae19daff4ef9aff3015e6effb203bcd6cbf71e53acb94a3f35b32","source":{"kind":"arxiv","id":"1210.2266","version":1},"attestation_state":"computed","paper":{"title":"Symplectic embeddings of 4-dimensional ellipsoids into cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"David Frenkel, Dorothee M\\\"uller","submitted_at":"2012-10-08T13:08:56Z","abstract_excerpt":"Recently, McDuff and Schlenk determined the function c_{EB}(a) whose value at a is the infimum of the size of a 4-ball into which the ellipsoid E(1,a) symplectically embeds (here, a >= 1 is the ratio of the area of the large axis to that of the smaller axis of the ellipsoid). In this paper we look at embeddings into four-dimensional cubes instead, and determine the function c_{EC}(a) whose value at a is the infimum of the size of a 4-cube C^{4}(A) = D^{2}(A) times D^{2}(A) into which the ellipsoid E(1,a) symplectically embeds (where D^{2}(A) denotes the disc in mathbb{R}^{2} of area A). As in "},"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":"1210.2266","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-10-08T13:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"6a6e941302b0d89548ca671912b7743ba27d57c7f6369d06e5f1e47007e1bc0a","abstract_canon_sha256":"294d9b4b3363506f9f8b99ab47d4688f6f141c7457df082fa49901b561724074"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:50.656098Z","signature_b64":"TM744uIwPAL/o/hG+pLEc9Ruz6Txd3LXP8of5ugjPaHizWVyvGGUI8n7G5/9+kUZXCTFuX4dfAIAOF3LaBLFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f6916f2edaae19daff4ef9aff3015e6effb203bcd6cbf71e53acb94a3f35b32","last_reissued_at":"2026-05-18T03:43:50.655067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:50.655067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symplectic embeddings of 4-dimensional ellipsoids into cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"David Frenkel, Dorothee M\\\"uller","submitted_at":"2012-10-08T13:08:56Z","abstract_excerpt":"Recently, McDuff and Schlenk determined the function c_{EB}(a) whose value at a is the infimum of the size of a 4-ball into which the ellipsoid E(1,a) symplectically embeds (here, a >= 1 is the ratio of the area of the large axis to that of the smaller axis of the ellipsoid). In this paper we look at embeddings into four-dimensional cubes instead, and determine the function c_{EC}(a) whose value at a is the infimum of the size of a 4-cube C^{4}(A) = D^{2}(A) times D^{2}(A) into which the ellipsoid E(1,a) symplectically embeds (where D^{2}(A) denotes the disc in mathbb{R}^{2} of area A). As in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2266","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":"1210.2266","created_at":"2026-05-18T03:43:50.655243+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2266v1","created_at":"2026-05-18T03:43:50.655243+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2266","created_at":"2026-05-18T03:43:50.655243+00:00"},{"alias_kind":"pith_short_12","alias_value":"H5URN4XNVLQZ","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"H5URN4XNVLQZ3L7U","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"H5URN4XN","created_at":"2026-05-18T12:27:06.952714+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/H5URN4XNVLQZ3L7U56NP6MAV43","json":"https://pith.science/pith/H5URN4XNVLQZ3L7U56NP6MAV43.json","graph_json":"https://pith.science/api/pith-number/H5URN4XNVLQZ3L7U56NP6MAV43/graph.json","events_json":"https://pith.science/api/pith-number/H5URN4XNVLQZ3L7U56NP6MAV43/events.json","paper":"https://pith.science/paper/H5URN4XN"},"agent_actions":{"view_html":"https://pith.science/pith/H5URN4XNVLQZ3L7U56NP6MAV43","download_json":"https://pith.science/pith/H5URN4XNVLQZ3L7U56NP6MAV43.json","view_paper":"https://pith.science/paper/H5URN4XN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2266&json=true","fetch_graph":"https://pith.science/api/pith-number/H5URN4XNVLQZ3L7U56NP6MAV43/graph.json","fetch_events":"https://pith.science/api/pith-number/H5URN4XNVLQZ3L7U56NP6MAV43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H5URN4XNVLQZ3L7U56NP6MAV43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H5URN4XNVLQZ3L7U56NP6MAV43/action/storage_attestation","attest_author":"https://pith.science/pith/H5URN4XNVLQZ3L7U56NP6MAV43/action/author_attestation","sign_citation":"https://pith.science/pith/H5URN4XNVLQZ3L7U56NP6MAV43/action/citation_signature","submit_replication":"https://pith.science/pith/H5URN4XNVLQZ3L7U56NP6MAV43/action/replication_record"}},"created_at":"2026-05-18T03:43:50.655243+00:00","updated_at":"2026-05-18T03:43:50.655243+00:00"}