{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:AWBNFOABPAX6MPWHW5LIHJZLXW","short_pith_number":"pith:AWBNFOAB","schema_version":"1.0","canonical_sha256":"0582d2b801782fe63ec7b75683a72bbdb025b9203454689176f0764d8010764d","source":{"kind":"arxiv","id":"1302.0807","version":1},"attestation_state":"computed","paper":{"title":"Non-compactness of the Neumann operator for the Kohn Laplacian on the Heisenberg ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Robert K. Hladky","submitted_at":"2013-02-04T19:34:52Z","abstract_excerpt":"For $1\\leq q \\leq n-2$, we provide explicit examples to demonstrate non-compactness of the Neumann operator for the Kohn Laplacian acting on $L^2$ $(0,q)$-forms on the unit ball in $(2n+1)$-dimensional Heisenberg space."},"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":"1302.0807","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-04T19:34:52Z","cross_cats_sorted":["math.AP","math.DG"],"title_canon_sha256":"08a24812d55593cd03d4deb349e83a9f0ddb5cf9f796926c72e9c7af634fac02","abstract_canon_sha256":"317b46c38973f444508978e4922c3733921b26b57baa258868e70ac55637c49c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:36.257869Z","signature_b64":"XwPL2fPb8FRqerDuPwCIN6SGSifzFSFtwlwoCGkwfGDa3pee1dgYbbW1su7L72+N+ZIzjiofK9la+cNdxvG5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0582d2b801782fe63ec7b75683a72bbdb025b9203454689176f0764d8010764d","last_reissued_at":"2026-05-18T03:34:36.257425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:36.257425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-compactness of the Neumann operator for the Kohn Laplacian on the Heisenberg ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.CV","authors_text":"Robert K. Hladky","submitted_at":"2013-02-04T19:34:52Z","abstract_excerpt":"For $1\\leq q \\leq n-2$, we provide explicit examples to demonstrate non-compactness of the Neumann operator for the Kohn Laplacian acting on $L^2$ $(0,q)$-forms on the unit ball in $(2n+1)$-dimensional Heisenberg space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0807","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":"1302.0807","created_at":"2026-05-18T03:34:36.257489+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.0807v1","created_at":"2026-05-18T03:34:36.257489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0807","created_at":"2026-05-18T03:34:36.257489+00:00"},{"alias_kind":"pith_short_12","alias_value":"AWBNFOABPAX6","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"AWBNFOABPAX6MPWH","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"AWBNFOAB","created_at":"2026-05-18T12:27:38.830355+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/AWBNFOABPAX6MPWHW5LIHJZLXW","json":"https://pith.science/pith/AWBNFOABPAX6MPWHW5LIHJZLXW.json","graph_json":"https://pith.science/api/pith-number/AWBNFOABPAX6MPWHW5LIHJZLXW/graph.json","events_json":"https://pith.science/api/pith-number/AWBNFOABPAX6MPWHW5LIHJZLXW/events.json","paper":"https://pith.science/paper/AWBNFOAB"},"agent_actions":{"view_html":"https://pith.science/pith/AWBNFOABPAX6MPWHW5LIHJZLXW","download_json":"https://pith.science/pith/AWBNFOABPAX6MPWHW5LIHJZLXW.json","view_paper":"https://pith.science/paper/AWBNFOAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.0807&json=true","fetch_graph":"https://pith.science/api/pith-number/AWBNFOABPAX6MPWHW5LIHJZLXW/graph.json","fetch_events":"https://pith.science/api/pith-number/AWBNFOABPAX6MPWHW5LIHJZLXW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AWBNFOABPAX6MPWHW5LIHJZLXW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AWBNFOABPAX6MPWHW5LIHJZLXW/action/storage_attestation","attest_author":"https://pith.science/pith/AWBNFOABPAX6MPWHW5LIHJZLXW/action/author_attestation","sign_citation":"https://pith.science/pith/AWBNFOABPAX6MPWHW5LIHJZLXW/action/citation_signature","submit_replication":"https://pith.science/pith/AWBNFOABPAX6MPWHW5LIHJZLXW/action/replication_record"}},"created_at":"2026-05-18T03:34:36.257489+00:00","updated_at":"2026-05-18T03:34:36.257489+00:00"}