{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CQPHZASFRBFVNPRFYXBYW2URK3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"53687f19014a5ee855c43be7222d36dc73b5c3f7052ff8343c4f6c9eb8d4e05d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-01T19:35:06Z","title_canon_sha256":"58c3a77e7d4800bd3eb4bc9f9a640114b30f3b390dd2ed1e243a47273f5ccfbc"},"schema_version":"1.0","source":{"id":"1702.00429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00429","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00429v1","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00429","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"pith_short_12","alias_value":"CQPHZASFRBFV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CQPHZASFRBFVNPRF","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CQPHZASF","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:2e6d944d0317000f15b280cf8b3898c217f9af20b629b3de4ede6962b5450526","target":"graph","created_at":"2026-05-18T00:51:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"An infinitely smooth convex body in $\\mathbb R^n$ is called polynomially integrable of degree $N$ if its parallel section functions are polynomials of degree $N$. We prove that the only smooth convex bodies with this property in odd dimensions are ellipsoids, if $N\\ge n-1$. This is in contrast with the case of even dimensions and the case of odd dimensions with $N<n-1$, where such bodies do not exist, as it was recently shown by Agranovsky.","authors_text":"Alexander Koldobsky, Alexander Merkurjev, Vladyslav Yaskin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-01T19:35:06Z","title":"On polynomially integrable convex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00429","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:50879d15fd01ebefd057b20aa1900aed3bc2da1133b2a9317ee292291c0cfe9f","target":"record","created_at":"2026-05-18T00:51:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"53687f19014a5ee855c43be7222d36dc73b5c3f7052ff8343c4f6c9eb8d4e05d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-01T19:35:06Z","title_canon_sha256":"58c3a77e7d4800bd3eb4bc9f9a640114b30f3b390dd2ed1e243a47273f5ccfbc"},"schema_version":"1.0","source":{"id":"1702.00429","kind":"arxiv","version":1}},"canonical_sha256":"141e7c8245884b56be25c5c38b6a9156f5061e860af5d1b34339a813ec3b4855","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"141e7c8245884b56be25c5c38b6a9156f5061e860af5d1b34339a813ec3b4855","first_computed_at":"2026-05-18T00:51:33.560197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:33.560197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QNQAVU4a92SXg8swBz6o28AlPYSuVighWxcVlbrTvd4ZnlVA+27eGAqSc+12yZ+bUVW/gP4CNt8/AabuO72BCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:33.560676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50879d15fd01ebefd057b20aa1900aed3bc2da1133b2a9317ee292291c0cfe9f","sha256:2e6d944d0317000f15b280cf8b3898c217f9af20b629b3de4ede6962b5450526"],"state_sha256":"fcaa96a09d68daedb5c80e6ef346d6ca49e107e6dadd8bd10a4d424d1c34b0c4"}