{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KGS7G3WO5LJJQ4ZJ2WE6S7HMEE","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":"12dd83bff4dcaf43f3dd2eabdf39ee03a8d904d1806c980b2780878eb7d5a00d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-18T18:23:34Z","title_canon_sha256":"79fb08d6cdd833d7fd2224924f9189426e7d7c0ea267b1881c95d91493342207"},"schema_version":"1.0","source":{"id":"1409.5397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5397","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5397v2","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5397","created_at":"2026-05-18T01:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"KGS7G3WO5LJJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KGS7G3WO5LJJQ4ZJ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KGS7G3WO","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:da12f1cf0ac22001425c10104c7b44dd1b9b139279716fa1903ba6945f0abd8b","target":"graph","created_at":"2026-05-18T01:11:57Z","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":"Nikol'skii inequalities for various sets of functions, domains and weights will be discussed. Much of the work is dedicated to the class of algebraic polynomials of total degree $n$ on a bounded convex domain $D$. That is, we study $\\sigma:= \\sigma(D,d)$ for which \\[ \\|P\\|_{L_q(D)}\\le c n^{\\sigma(\\frac1p-\\frac1q)}\\|P\\|_{L_p(D)},\\quad 0<p\\le q\\le\\infty, \\] where $P$ is a polynomial of total degree $n$. We use geometric properties of the boundary of $D$ to determine $\\sigma(D,n)$ with the aid of comparison between domains. Computing the asymptotics of the Christoffel function of various domains ","authors_text":"A. Prymak, Z. Ditzian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-18T18:23:34Z","title":"On Nikol'skii inequalities for domains in $R^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5397","kind":"arxiv","version":2},"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:f24050bcead776816ac9c02e0fa30263e2b629d7fb52782e71c7aa85b5a0acb7","target":"record","created_at":"2026-05-18T01:11:57Z","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":"12dd83bff4dcaf43f3dd2eabdf39ee03a8d904d1806c980b2780878eb7d5a00d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-09-18T18:23:34Z","title_canon_sha256":"79fb08d6cdd833d7fd2224924f9189426e7d7c0ea267b1881c95d91493342207"},"schema_version":"1.0","source":{"id":"1409.5397","kind":"arxiv","version":2}},"canonical_sha256":"51a5f36eceead2987329d589e97cec213aa0bc1f0be66da0f5b408475751d932","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51a5f36eceead2987329d589e97cec213aa0bc1f0be66da0f5b408475751d932","first_computed_at":"2026-05-18T01:11:57.921844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:57.921844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Xkrw42AWJlfnSEggz3pN+Q9ic20tEYdqna8d6EPKDg3kZTyLUMp4OHPlAt+lngmbyEtU+18TkFd/6bIVFLEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:57.922281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f24050bcead776816ac9c02e0fa30263e2b629d7fb52782e71c7aa85b5a0acb7","sha256:da12f1cf0ac22001425c10104c7b44dd1b9b139279716fa1903ba6945f0abd8b"],"state_sha256":"45373165d3ef178834f0382161d0053a2e2fe2384dc39101efa858dabbd64695"}