{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:6EDNU7I2VGKUYUMTIS6OYARIDL","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":"0a40d636986800a241749b07d2916c1ed6d5b0fde34412f3f7390922607ec485","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-09-16T13:07:56Z","title_canon_sha256":"8d1a2703d55bc4182864d25b6db9d46f31d3f62b19f7bc96c98462e1970dceb9"},"schema_version":"1.0","source":{"id":"2109.07952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.07952","created_at":"2026-07-05T03:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"2109.07952v1","created_at":"2026-07-05T03:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.07952","created_at":"2026-07-05T03:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"6EDNU7I2VGKU","created_at":"2026-07-05T03:15:02Z"},{"alias_kind":"pith_short_16","alias_value":"6EDNU7I2VGKUYUMT","created_at":"2026-07-05T03:15:02Z"},{"alias_kind":"pith_short_8","alias_value":"6EDNU7I2","created_at":"2026-07-05T03:15:02Z"}],"graph_snapshots":[{"event_id":"sha256:d16688db3c732e654201f4d8b56ac36b2934ca39d4143290efed8bf9ad4309e1","target":"graph","created_at":"2026-07-05T03:15:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.07952/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This note is devoted to several results about frequency localized functions and associated Bernstein inequalities for higher order operators. In particular, we construct some counterexamples for the frequency-localized Bernstein inequalities for higher order Laplacians. We show also that the heat semi-group associated to powers larger than one of the laplacian does not satisfy the strict maximum principle in general. Finally, in a suitable range we provide several positive results.","authors_text":"Dong Li, Yannick Sire","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-09-16T13:07:56Z","title":"Remarks on the Bernstein inequality for higher order operators and related results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.07952","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":"sha256:03ac1222ede77b268e46dcfc3b7e6193f55328428fcbb372cd5bb566111c3401","target":"record","created_at":"2026-07-05T03:15:02Z","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":"0a40d636986800a241749b07d2916c1ed6d5b0fde34412f3f7390922607ec485","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-09-16T13:07:56Z","title_canon_sha256":"8d1a2703d55bc4182864d25b6db9d46f31d3f62b19f7bc96c98462e1970dceb9"},"schema_version":"1.0","source":{"id":"2109.07952","kind":"arxiv","version":1}},"canonical_sha256":"f106da7d1aa9954c519344bcec02281ada77a12a2555fc774910ed090ee85408","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f106da7d1aa9954c519344bcec02281ada77a12a2555fc774910ed090ee85408","first_computed_at":"2026-07-05T03:15:02.844473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:15:02.844473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z4lBx/a5ygPLSc0LSvODKSc/XWB6bxSn2ArPsq5SNKxwiT6QUek2aor1jwIyyOFQEBbFopRS1auRXgig+KtzDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:15:02.844938Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.07952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03ac1222ede77b268e46dcfc3b7e6193f55328428fcbb372cd5bb566111c3401","sha256:d16688db3c732e654201f4d8b56ac36b2934ca39d4143290efed8bf9ad4309e1"],"state_sha256":"891b5ab150e8e1f51217fbdfe3755ca461d905c6d59d8066a33b384d84424516"}