{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:24JGFW3754TKO37DODWSFHKC3M","short_pith_number":"pith:24JGFW37","canonical_record":{"source":{"id":"1803.00199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-01T03:58:14Z","cross_cats_sorted":[],"title_canon_sha256":"a5901b1046fc49ed5ace802e3ddaa4490d96e83609ec541010d8afaa91c35e2f","abstract_canon_sha256":"66f4dfbfabd7c02bed0809bab76f78e07fad916d6d4da8a3c09360165324a50b"},"schema_version":"1.0"},"canonical_sha256":"d71262db7fef26a76fe370ed229d42db28aa35abda2ff57937a67aa219c4b7e4","source":{"kind":"arxiv","id":"1803.00199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00199","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00199v1","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00199","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"24JGFW3754TK","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"24JGFW3754TKO37D","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"24JGFW37","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:24JGFW3754TKO37DODWSFHKC3M","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-01T03:58:14Z","cross_cats_sorted":[],"title_canon_sha256":"a5901b1046fc49ed5ace802e3ddaa4490d96e83609ec541010d8afaa91c35e2f","abstract_canon_sha256":"66f4dfbfabd7c02bed0809bab76f78e07fad916d6d4da8a3c09360165324a50b"},"schema_version":"1.0"},"canonical_sha256":"d71262db7fef26a76fe370ed229d42db28aa35abda2ff57937a67aa219c4b7e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:13.033141Z","signature_b64":"SYhGbQ+jB9nAHk6esoeKLttU89VIZGb3HTYHKL8TzbH3+6lae6wVqAhYPQMl0CIkMF3Zbr57/tgv0/WGd2tCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d71262db7fef26a76fe370ed229d42db28aa35abda2ff57937a67aa219c4b7e4","last_reissued_at":"2026-05-18T00:22:13.032527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:13.032527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00199","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":"2026-05-18T00:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WH+TTNbN1/F8zrIi8Pqm3XkDU/sKXIiiGpT927hl9rwjvjzs8pjDn2ruV+z74YEvgFrTqM+2u5ElHzMazEr0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:14:44.913972Z"},"content_sha256":"cab76f42f321f46d7f42202fe728b26bc80d929f9fd28c19f50bf429936cdad8","schema_version":"1.0","event_id":"sha256:cab76f42f321f46d7f42202fe728b26bc80d929f9fd28c19f50bf429936cdad8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:24JGFW3754TKO37DODWSFHKC3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An extension of polynomial integrability to dual quermassintegrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Vladyslav Yaskin","submitted_at":"2018-03-01T03:58:14Z","abstract_excerpt":"A body $K$ is called polynomially integrable if its parallel section function $V_{n-1}(K\\cap\\{\\xi^\\perp+t\\xi\\})$ is a polynomial of $t$ (on its support) for every $\\xi$. A complete characterization of such bodies was given recently. Here we obtain a generalization of these results in the setting of dual quermassintegrals. We also address the associated smoothness issues."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00199","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":"2026-05-18T00:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ocHI8A1IIGsfgbmoZFoxfVdbtpvbGWQ0F7KP7TwihFMtHVmErNEwehjUtPKA7rgs/Zh7ZTIGghLoei35OrCiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:14:44.914349Z"},"content_sha256":"67d4abb8fe691df129c2329f35c5cc2566d0854f2f5492c47c96a590a00f8408","schema_version":"1.0","event_id":"sha256:67d4abb8fe691df129c2329f35c5cc2566d0854f2f5492c47c96a590a00f8408"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/bundle.json","state_url":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24JGFW3754TKO37DODWSFHKC3M/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":"2026-06-01T00:14:44Z","links":{"resolver":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M","bundle":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/bundle.json","state":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24JGFW3754TKO37DODWSFHKC3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:24JGFW3754TKO37DODWSFHKC3M","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":"66f4dfbfabd7c02bed0809bab76f78e07fad916d6d4da8a3c09360165324a50b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-01T03:58:14Z","title_canon_sha256":"a5901b1046fc49ed5ace802e3ddaa4490d96e83609ec541010d8afaa91c35e2f"},"schema_version":"1.0","source":{"id":"1803.00199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00199","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00199v1","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00199","created_at":"2026-05-18T00:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"24JGFW3754TK","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"24JGFW3754TKO37D","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"24JGFW37","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:67d4abb8fe691df129c2329f35c5cc2566d0854f2f5492c47c96a590a00f8408","target":"graph","created_at":"2026-05-18T00:22:13Z","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":"A body $K$ is called polynomially integrable if its parallel section function $V_{n-1}(K\\cap\\{\\xi^\\perp+t\\xi\\})$ is a polynomial of $t$ (on its support) for every $\\xi$. A complete characterization of such bodies was given recently. Here we obtain a generalization of these results in the setting of dual quermassintegrals. We also address the associated smoothness issues.","authors_text":"Vladyslav Yaskin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-01T03:58:14Z","title":"An extension of polynomial integrability to dual quermassintegrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00199","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:cab76f42f321f46d7f42202fe728b26bc80d929f9fd28c19f50bf429936cdad8","target":"record","created_at":"2026-05-18T00:22:13Z","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":"66f4dfbfabd7c02bed0809bab76f78e07fad916d6d4da8a3c09360165324a50b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-03-01T03:58:14Z","title_canon_sha256":"a5901b1046fc49ed5ace802e3ddaa4490d96e83609ec541010d8afaa91c35e2f"},"schema_version":"1.0","source":{"id":"1803.00199","kind":"arxiv","version":1}},"canonical_sha256":"d71262db7fef26a76fe370ed229d42db28aa35abda2ff57937a67aa219c4b7e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d71262db7fef26a76fe370ed229d42db28aa35abda2ff57937a67aa219c4b7e4","first_computed_at":"2026-05-18T00:22:13.032527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:13.032527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SYhGbQ+jB9nAHk6esoeKLttU89VIZGb3HTYHKL8TzbH3+6lae6wVqAhYPQMl0CIkMF3Zbr57/tgv0/WGd2tCCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:13.033141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cab76f42f321f46d7f42202fe728b26bc80d929f9fd28c19f50bf429936cdad8","sha256:67d4abb8fe691df129c2329f35c5cc2566d0854f2f5492c47c96a590a00f8408"],"state_sha256":"593e09afd2484c54698db52101f4d9d5d8a9ca2ff46c1249beaf0093a9662bfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vIk6aRC7uYOROy0ERIkRHmZyhDOjrVZCoLXYdp4Myac8N3j5P+y3NE6igxVNuaT/xu2n/fBqlcDoQUAGAgwEBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:14:44.916632Z","bundle_sha256":"d25c8543def6d658a37aefd4c25e091e3d90bebec83db539fd187dca78c94fe5"}}