{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HHLGCFYZJ55BEDJJPYAQNP3Z3H","short_pith_number":"pith:HHLGCFYZ","schema_version":"1.0","canonical_sha256":"39d66117194f7a120d297e0106bf79d9e95853654a1f9a04e63a5c448f5b451a","source":{"kind":"arxiv","id":"1705.06063","version":2},"attestation_state":"computed","paper":{"title":"On algebraically integrable domains in Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Mark Agranovsky","submitted_at":"2017-05-17T09:26:19Z","abstract_excerpt":"Let $D$ be a bounded domain $D$ in $\\mathbb R^n $ with infinitely smooth boundary and $n$ is odd. We prove that if the volume cut off from the domain by a hyperplane is an algebraic function of the hyperplane, free of real singular points, then the domain is an ellipsoid. This partially answers a question of V.I. Arnold: whether odd-dimensional ellipsoids are the only algebraically integrable domains?"},"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":"1705.06063","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-05-17T09:26:19Z","cross_cats_sorted":[],"title_canon_sha256":"87964b163d079a9dac990dffdf1e91a6bd78a11811fee23a87c767e9068d973a","abstract_canon_sha256":"22fc5990fec08d0a5a9f6dc50fb9283adb998304574a88933fb585bd9b904d5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:06.573354Z","signature_b64":"SVGsMq27iq2iEccQmpn7QK4jdoKrMKkL46rmXD+5YTFNDT5fw9AVf1DunSLrRTl8wz7bQu+HQLotdrqlLPOoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39d66117194f7a120d297e0106bf79d9e95853654a1f9a04e63a5c448f5b451a","last_reissued_at":"2026-05-18T00:44:06.572870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:06.572870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On algebraically integrable domains in Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Mark Agranovsky","submitted_at":"2017-05-17T09:26:19Z","abstract_excerpt":"Let $D$ be a bounded domain $D$ in $\\mathbb R^n $ with infinitely smooth boundary and $n$ is odd. We prove that if the volume cut off from the domain by a hyperplane is an algebraic function of the hyperplane, free of real singular points, then the domain is an ellipsoid. This partially answers a question of V.I. Arnold: whether odd-dimensional ellipsoids are the only algebraically integrable domains?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06063","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":"1705.06063","created_at":"2026-05-18T00:44:06.572937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.06063v2","created_at":"2026-05-18T00:44:06.572937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06063","created_at":"2026-05-18T00:44:06.572937+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHLGCFYZJ55B","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHLGCFYZJ55BEDJJ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHLGCFYZ","created_at":"2026-05-18T12:31:18.294218+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/HHLGCFYZJ55BEDJJPYAQNP3Z3H","json":"https://pith.science/pith/HHLGCFYZJ55BEDJJPYAQNP3Z3H.json","graph_json":"https://pith.science/api/pith-number/HHLGCFYZJ55BEDJJPYAQNP3Z3H/graph.json","events_json":"https://pith.science/api/pith-number/HHLGCFYZJ55BEDJJPYAQNP3Z3H/events.json","paper":"https://pith.science/paper/HHLGCFYZ"},"agent_actions":{"view_html":"https://pith.science/pith/HHLGCFYZJ55BEDJJPYAQNP3Z3H","download_json":"https://pith.science/pith/HHLGCFYZJ55BEDJJPYAQNP3Z3H.json","view_paper":"https://pith.science/paper/HHLGCFYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.06063&json=true","fetch_graph":"https://pith.science/api/pith-number/HHLGCFYZJ55BEDJJPYAQNP3Z3H/graph.json","fetch_events":"https://pith.science/api/pith-number/HHLGCFYZJ55BEDJJPYAQNP3Z3H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHLGCFYZJ55BEDJJPYAQNP3Z3H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHLGCFYZJ55BEDJJPYAQNP3Z3H/action/storage_attestation","attest_author":"https://pith.science/pith/HHLGCFYZJ55BEDJJPYAQNP3Z3H/action/author_attestation","sign_citation":"https://pith.science/pith/HHLGCFYZJ55BEDJJPYAQNP3Z3H/action/citation_signature","submit_replication":"https://pith.science/pith/HHLGCFYZJ55BEDJJPYAQNP3Z3H/action/replication_record"}},"created_at":"2026-05-18T00:44:06.572937+00:00","updated_at":"2026-05-18T00:44:06.572937+00:00"}