{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PYBGH34HSYJUKWOX2XLHJRW245","short_pith_number":"pith:PYBGH34H","schema_version":"1.0","canonical_sha256":"7e0263ef8796134559d7d5d674c6dae76db45dd2ff1dfa283defee1998cbd6a1","source":{"kind":"arxiv","id":"2605.29690","version":1},"attestation_state":"computed","paper":{"title":"A priori bounds for energy-bounded solutions of critical polyharmonic equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno Premoselli, Lorenzo Carletti","submitted_at":"2026-05-28T09:52:37Z","abstract_excerpt":"We investigate critical polyharmonic equations of the following type: $$ Lu = |u|^{2^\\sharp-2} u \\quad \\text{ in } \\Omega $$ with Dirichlet boundary conditions, in a smooth bounded domain $\\Omega$ of $\\mathbb{R}^n$. Here $L$ is an elliptic differential operator of even integer order $2 \\le 2k < n$ whose leading order term is $(-\\Delta)^k$ and $2^\\sharp = \\frac{2n}{n-2k}$ is the critical Sobolev exponent. Our main result establishes, in large dimensions, uniform \\emph{a priori} bounds on bounded-energy solutions of this problem under a coercivity assumption of sorts on the lower-order terms of "},"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":"2605.29690","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-28T09:52:37Z","cross_cats_sorted":[],"title_canon_sha256":"b47d370d913f09d383c65cf378f180a065efefd7c854996bfdd8e05aa10e9847","abstract_canon_sha256":"c3a4400afe3648174917952b135bdc1ef5b0aceaec6a2ccfb8c645abdc2d35b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:05:55.846342Z","signature_b64":"jYEq8AHENKrx1U6RuDu1O62Zohzyy2/pI9pYxqLf3x2ukXzvSEPcmtXu65HHhl4/+K6h2usW/bjNaK9UBRLSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e0263ef8796134559d7d5d674c6dae76db45dd2ff1dfa283defee1998cbd6a1","last_reissued_at":"2026-05-29T01:05:55.845824Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:05:55.845824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A priori bounds for energy-bounded solutions of critical polyharmonic equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bruno Premoselli, Lorenzo Carletti","submitted_at":"2026-05-28T09:52:37Z","abstract_excerpt":"We investigate critical polyharmonic equations of the following type: $$ Lu = |u|^{2^\\sharp-2} u \\quad \\text{ in } \\Omega $$ with Dirichlet boundary conditions, in a smooth bounded domain $\\Omega$ of $\\mathbb{R}^n$. Here $L$ is an elliptic differential operator of even integer order $2 \\le 2k < n$ whose leading order term is $(-\\Delta)^k$ and $2^\\sharp = \\frac{2n}{n-2k}$ is the critical Sobolev exponent. Our main result establishes, in large dimensions, uniform \\emph{a priori} bounds on bounded-energy solutions of this problem under a coercivity assumption of sorts on the lower-order terms of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29690","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/2605.29690/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":"2605.29690","created_at":"2026-05-29T01:05:55.845895+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.29690v1","created_at":"2026-05-29T01:05:55.845895+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29690","created_at":"2026-05-29T01:05:55.845895+00:00"},{"alias_kind":"pith_short_12","alias_value":"PYBGH34HSYJU","created_at":"2026-05-29T01:05:55.845895+00:00"},{"alias_kind":"pith_short_16","alias_value":"PYBGH34HSYJUKWOX","created_at":"2026-05-29T01:05:55.845895+00:00"},{"alias_kind":"pith_short_8","alias_value":"PYBGH34H","created_at":"2026-05-29T01:05:55.845895+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/PYBGH34HSYJUKWOX2XLHJRW245","json":"https://pith.science/pith/PYBGH34HSYJUKWOX2XLHJRW245.json","graph_json":"https://pith.science/api/pith-number/PYBGH34HSYJUKWOX2XLHJRW245/graph.json","events_json":"https://pith.science/api/pith-number/PYBGH34HSYJUKWOX2XLHJRW245/events.json","paper":"https://pith.science/paper/PYBGH34H"},"agent_actions":{"view_html":"https://pith.science/pith/PYBGH34HSYJUKWOX2XLHJRW245","download_json":"https://pith.science/pith/PYBGH34HSYJUKWOX2XLHJRW245.json","view_paper":"https://pith.science/paper/PYBGH34H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.29690&json=true","fetch_graph":"https://pith.science/api/pith-number/PYBGH34HSYJUKWOX2XLHJRW245/graph.json","fetch_events":"https://pith.science/api/pith-number/PYBGH34HSYJUKWOX2XLHJRW245/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PYBGH34HSYJUKWOX2XLHJRW245/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PYBGH34HSYJUKWOX2XLHJRW245/action/storage_attestation","attest_author":"https://pith.science/pith/PYBGH34HSYJUKWOX2XLHJRW245/action/author_attestation","sign_citation":"https://pith.science/pith/PYBGH34HSYJUKWOX2XLHJRW245/action/citation_signature","submit_replication":"https://pith.science/pith/PYBGH34HSYJUKWOX2XLHJRW245/action/replication_record"}},"created_at":"2026-05-29T01:05:55.845895+00:00","updated_at":"2026-05-29T01:05:55.845895+00:00"}