{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:Z2JZGXEWJOSXYGKB2FMDEQWIJJ","short_pith_number":"pith:Z2JZGXEW","schema_version":"1.0","canonical_sha256":"ce93935c964ba57c1941d1583242c84a5de0f64127730d393e6268ceaa6156d8","source":{"kind":"arxiv","id":"2004.13647","version":1},"attestation_state":"computed","paper":{"title":"Special eccentricities of rational four-dimensional ellipsoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dan Cristofaro-Gardiner","submitted_at":"2020-04-28T16:44:40Z","abstract_excerpt":"A striking result of McDuff and Schlenk asserts that in determining when a four-dimensional symplectic ellipsoid can be symplectically embedded into a four-dimensional symplectic ball, the answer is governed by an \"infinite staircase\" determined by the odd-index Fibonacci numbers and the Golden Mean. Here we study embeddings of one four-dimensional symplectic ellipsoid into another, and we show that if the target is rational, then the infinite staircase phenomenon found by McDuff and Schlenk is quite rare. Specifically, in the rational case, there is an infinite staircase in precisely three ca"},"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":"2004.13647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-04-28T16:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"30cde659c091b82ba610227e2c4c098847348ac609ba4d7902e12f26a840c134","abstract_canon_sha256":"0aa30612ef789fa1874ba5b69bcbcd1d5e3e11c537fe1e70b9c13ae81ddac1c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:12:06.985769Z","signature_b64":"XHO3eB7tFllXoM8ZZAQ7pLDhDVGlyNN6JcT5FxzJpIZlaSBh2LdQAo8YnK6gsNWmtL1oyf7LHRtgcNBXOjegCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce93935c964ba57c1941d1583242c84a5de0f64127730d393e6268ceaa6156d8","last_reissued_at":"2026-07-05T05:12:06.985324Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:12:06.985324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Special eccentricities of rational four-dimensional ellipsoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dan Cristofaro-Gardiner","submitted_at":"2020-04-28T16:44:40Z","abstract_excerpt":"A striking result of McDuff and Schlenk asserts that in determining when a four-dimensional symplectic ellipsoid can be symplectically embedded into a four-dimensional symplectic ball, the answer is governed by an \"infinite staircase\" determined by the odd-index Fibonacci numbers and the Golden Mean. Here we study embeddings of one four-dimensional symplectic ellipsoid into another, and we show that if the target is rational, then the infinite staircase phenomenon found by McDuff and Schlenk is quite rare. Specifically, in the rational case, there is an infinite staircase in precisely three ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.13647","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.13647/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2004.13647","created_at":"2026-07-05T05:12:06.985393+00:00"},{"alias_kind":"arxiv_version","alias_value":"2004.13647v1","created_at":"2026-07-05T05:12:06.985393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.13647","created_at":"2026-07-05T05:12:06.985393+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2JZGXEWJOSX","created_at":"2026-07-05T05:12:06.985393+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2JZGXEWJOSXYGKB","created_at":"2026-07-05T05:12:06.985393+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2JZGXEW","created_at":"2026-07-05T05:12:06.985393+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.12729","citing_title":"Quadrilateral mutations and symplectic embeddings","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ","json":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ.json","graph_json":"https://pith.science/api/pith-number/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/graph.json","events_json":"https://pith.science/api/pith-number/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/events.json","paper":"https://pith.science/paper/Z2JZGXEW"},"agent_actions":{"view_html":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ","download_json":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ.json","view_paper":"https://pith.science/paper/Z2JZGXEW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2004.13647&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/action/storage_attestation","attest_author":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/action/author_attestation","sign_citation":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/action/citation_signature","submit_replication":"https://pith.science/pith/Z2JZGXEWJOSXYGKB2FMDEQWIJJ/action/replication_record"}},"created_at":"2026-07-05T05:12:06.985393+00:00","updated_at":"2026-07-05T05:12:06.985393+00:00"}