{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MBYPQAUD6ILX4KO5FU573FZOQK","short_pith_number":"pith:MBYPQAUD","schema_version":"1.0","canonical_sha256":"6070f80283f2177e29dd2d3bfd972e82b407b73d7fdc43a26eb7b1993a0b3ac2","source":{"kind":"arxiv","id":"2605.24404","version":1},"attestation_state":"computed","paper":{"title":"On higher order Morrey's inequalities over RCD{\\boldmath$(K,N)$}-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jun Kitagawa, Kazuhiro Kuwae","submitted_at":"2026-05-23T05:20:18Z","abstract_excerpt":"In this paper, we establish a higher order Morrey's inequality in the framework of %non-collapsed $\\mathsf{RCD}(K,N)$-spaces for $K\\in\\mathbb{R}$ and $N\\in\\mathbb{N}$. We do so by first introducing an alternate version of the second order Sobolev space $W^{2, p}(X)$, which contains amply many functions even when $p>N$."},"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":"2605.24404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-05-23T05:20:18Z","cross_cats_sorted":[],"title_canon_sha256":"4d838f2949296282cf9db629e6559eba75b15fcb7b4c0ebc5bc887b13b44ce14","abstract_canon_sha256":"479c4b4fe80d009c13f1ebbb52c44e86ebd81e6d1ae8cb2df629a323f6811da9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:37.746332Z","signature_b64":"h87+j7s+4/Zo73kcNn7IgxmTYb4B9KZ06qVBeRcFqWDy3AO0/wcu8Mw81ZZSgO+M4DzwHZFwXSMz/n+X0E4MDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6070f80283f2177e29dd2d3bfd972e82b407b73d7fdc43a26eb7b1993a0b3ac2","last_reissued_at":"2026-05-26T01:03:37.745504Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:37.745504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On higher order Morrey's inequalities over RCD{\\boldmath$(K,N)$}-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Jun Kitagawa, Kazuhiro Kuwae","submitted_at":"2026-05-23T05:20:18Z","abstract_excerpt":"In this paper, we establish a higher order Morrey's inequality in the framework of %non-collapsed $\\mathsf{RCD}(K,N)$-spaces for $K\\in\\mathbb{R}$ and $N\\in\\mathbb{N}$. We do so by first introducing an alternate version of the second order Sobolev space $W^{2, p}(X)$, which contains amply many functions even when $p>N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24404","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24404/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.24404","created_at":"2026-05-26T01:03:37.745614+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.24404v1","created_at":"2026-05-26T01:03:37.745614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24404","created_at":"2026-05-26T01:03:37.745614+00:00"},{"alias_kind":"pith_short_12","alias_value":"MBYPQAUD6ILX","created_at":"2026-05-26T01:03:37.745614+00:00"},{"alias_kind":"pith_short_16","alias_value":"MBYPQAUD6ILX4KO5","created_at":"2026-05-26T01:03:37.745614+00:00"},{"alias_kind":"pith_short_8","alias_value":"MBYPQAUD","created_at":"2026-05-26T01:03:37.745614+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/MBYPQAUD6ILX4KO5FU573FZOQK","json":"https://pith.science/pith/MBYPQAUD6ILX4KO5FU573FZOQK.json","graph_json":"https://pith.science/api/pith-number/MBYPQAUD6ILX4KO5FU573FZOQK/graph.json","events_json":"https://pith.science/api/pith-number/MBYPQAUD6ILX4KO5FU573FZOQK/events.json","paper":"https://pith.science/paper/MBYPQAUD"},"agent_actions":{"view_html":"https://pith.science/pith/MBYPQAUD6ILX4KO5FU573FZOQK","download_json":"https://pith.science/pith/MBYPQAUD6ILX4KO5FU573FZOQK.json","view_paper":"https://pith.science/paper/MBYPQAUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.24404&json=true","fetch_graph":"https://pith.science/api/pith-number/MBYPQAUD6ILX4KO5FU573FZOQK/graph.json","fetch_events":"https://pith.science/api/pith-number/MBYPQAUD6ILX4KO5FU573FZOQK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MBYPQAUD6ILX4KO5FU573FZOQK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MBYPQAUD6ILX4KO5FU573FZOQK/action/storage_attestation","attest_author":"https://pith.science/pith/MBYPQAUD6ILX4KO5FU573FZOQK/action/author_attestation","sign_citation":"https://pith.science/pith/MBYPQAUD6ILX4KO5FU573FZOQK/action/citation_signature","submit_replication":"https://pith.science/pith/MBYPQAUD6ILX4KO5FU573FZOQK/action/replication_record"}},"created_at":"2026-05-26T01:03:37.745614+00:00","updated_at":"2026-05-26T01:03:37.745614+00:00"}