{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CQPHZASFRBFVNPRFYXBYW2URK3","short_pith_number":"pith:CQPHZASF","canonical_record":{"source":{"id":"1702.00429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-01T19:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"58c3a77e7d4800bd3eb4bc9f9a640114b30f3b390dd2ed1e243a47273f5ccfbc","abstract_canon_sha256":"53687f19014a5ee855c43be7222d36dc73b5c3f7052ff8343c4f6c9eb8d4e05d"},"schema_version":"1.0"},"canonical_sha256":"141e7c8245884b56be25c5c38b6a9156f5061e860af5d1b34339a813ec3b4855","source":{"kind":"arxiv","id":"1702.00429","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CQPHZASFRBFVNPRFYXBYW2URK3","target":"record","payload":{"canonical_record":{"source":{"id":"1702.00429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-02-01T19:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"58c3a77e7d4800bd3eb4bc9f9a640114b30f3b390dd2ed1e243a47273f5ccfbc","abstract_canon_sha256":"53687f19014a5ee855c43be7222d36dc73b5c3f7052ff8343c4f6c9eb8d4e05d"},"schema_version":"1.0"},"canonical_sha256":"141e7c8245884b56be25c5c38b6a9156f5061e860af5d1b34339a813ec3b4855","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:33.560676Z","signature_b64":"QNQAVU4a92SXg8swBz6o28AlPYSuVighWxcVlbrTvd4ZnlVA+27eGAqSc+12yZ+bUVW/gP4CNt8/AabuO72BCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"141e7c8245884b56be25c5c38b6a9156f5061e860af5d1b34339a813ec3b4855","last_reissued_at":"2026-05-18T00:51:33.560197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:33.560197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.00429","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kYHB8X8ilxwgvm3aMeRUhB4hjiT448Nx+dO7wSvYqD0Qd8fD1lPJ2mZIh3lwdJ4bOXWPUpy5ryO9314omOOEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:07:19.554273Z"},"content_sha256":"50879d15fd01ebefd057b20aa1900aed3bc2da1133b2a9317ee292291c0cfe9f","schema_version":"1.0","event_id":"sha256:50879d15fd01ebefd057b20aa1900aed3bc2da1133b2a9317ee292291c0cfe9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CQPHZASFRBFVNPRFYXBYW2URK3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On polynomially integrable convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexander Koldobsky, Alexander Merkurjev, Vladyslav Yaskin","submitted_at":"2017-02-01T19:35:06Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00429","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VYvKhKnz0zoA/iu1ESdnF9l4fTSgFMaF+sYcV5bRO5OfhL0f7DRz8pWP2lhh8/V6tV9qEPB7ku3cVi/1dEmCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:07:19.554649Z"},"content_sha256":"2e6d944d0317000f15b280cf8b3898c217f9af20b629b3de4ede6962b5450526","schema_version":"1.0","event_id":"sha256:2e6d944d0317000f15b280cf8b3898c217f9af20b629b3de4ede6962b5450526"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQPHZASFRBFVNPRFYXBYW2URK3/bundle.json","state_url":"https://pith.science/pith/CQPHZASFRBFVNPRFYXBYW2URK3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQPHZASFRBFVNPRFYXBYW2URK3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T20:07:19Z","links":{"resolver":"https://pith.science/pith/CQPHZASFRBFVNPRFYXBYW2URK3","bundle":"https://pith.science/pith/CQPHZASFRBFVNPRFYXBYW2URK3/bundle.json","state":"https://pith.science/pith/CQPHZASFRBFVNPRFYXBYW2URK3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQPHZASFRBFVNPRFYXBYW2URK3/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m2KTrrZHvsMVH3mx+VN7pmrEFkOAZ/yhfizoqaPtrZrPclhul8/T6g0e0gwSqTCrRpYmFb1czjeGwREqHkAIAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:07:19.556731Z","bundle_sha256":"4e68138d5ddfcc0b5c193a61efbf7c5eb803a32829345357a11edb0d1b4efdb2"}}