{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:24JGFW3754TKO37DODWSFHKC3M","short_pith_number":"pith:24JGFW37","schema_version":"1.0","canonical_sha256":"d71262db7fef26a76fe370ed229d42db28aa35abda2ff57937a67aa219c4b7e4","source":{"kind":"arxiv","id":"1803.00199","version":1},"attestation_state":"computed","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."},"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":"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.00199","created_at":"2026-05-18T00:22:13.032606+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.00199v1","created_at":"2026-05-18T00:22:13.032606+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00199","created_at":"2026-05-18T00:22:13.032606+00:00"},{"alias_kind":"pith_short_12","alias_value":"24JGFW3754TK","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"24JGFW3754TKO37D","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"24JGFW37","created_at":"2026-05-18T12:31:59.375834+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/24JGFW3754TKO37DODWSFHKC3M","json":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M.json","graph_json":"https://pith.science/api/pith-number/24JGFW3754TKO37DODWSFHKC3M/graph.json","events_json":"https://pith.science/api/pith-number/24JGFW3754TKO37DODWSFHKC3M/events.json","paper":"https://pith.science/paper/24JGFW37"},"agent_actions":{"view_html":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M","download_json":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M.json","view_paper":"https://pith.science/paper/24JGFW37","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.00199&json=true","fetch_graph":"https://pith.science/api/pith-number/24JGFW3754TKO37DODWSFHKC3M/graph.json","fetch_events":"https://pith.science/api/pith-number/24JGFW3754TKO37DODWSFHKC3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/action/storage_attestation","attest_author":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/action/author_attestation","sign_citation":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/action/citation_signature","submit_replication":"https://pith.science/pith/24JGFW3754TKO37DODWSFHKC3M/action/replication_record"}},"created_at":"2026-05-18T00:22:13.032606+00:00","updated_at":"2026-05-18T00:22:13.032606+00:00"}