{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IZJNMUJO4FCIJY543BHSVCHYVT","short_pith_number":"pith:IZJNMUJO","schema_version":"1.0","canonical_sha256":"4652d6512ee14484e3bcd84f2a88f8acc3ea3eaa0e9048cf4735d953f31eb054","source":{"kind":"arxiv","id":"2606.09680","version":1},"attestation_state":"computed","paper":{"title":"On de Branges--Rovnyak Kernels Admitting a Complete Pick Factor","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Haripada Sau","submitted_at":"2026-06-08T16:00:28Z","abstract_excerpt":"For a contractive multiplier $\\varphi$ in the multiplier algebra $M(k)$ of a kernel $k$, the associated de Branges--Rovnyak kernel is given by $k^\\varphi(x,y) = (1-\\varphi(x)\\overline{\\varphi(y)})k(x,y)$. Motivated by recent developments clarifying the structural and geometric features of reproducing kernel Hilbert spaces associated with kernels admitting a complete Pick factor, we investigate the precise conditions for a general de Branges-Rovnyak kernel to admit a complete Pick factor, thereby extending the framework introduced by Ahmed, Das and Panja (\\textit{J. Geom. Anal.}, 2025). In this"},"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":"2606.09680","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2026-06-08T16:00:28Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ba3d364c90fec2a4b13a97cd472b4e5b5e0b85c90e8542407dcdf87d8cd1c59e","abstract_canon_sha256":"1e28c1300710ffd421bea7f7a8ce126c96845b398073cdabda45b2a3238e71f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:09:03.494029Z","signature_b64":"Tv2Mcw+bY69CZuR+J3lw9HqmAsIrvJ+R0lw/u5t5Y/uUwP2++9/6ix4HUX10P8yaLtFQbAPPPddU51xiYC5sAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4652d6512ee14484e3bcd84f2a88f8acc3ea3eaa0e9048cf4735d953f31eb054","last_reissued_at":"2026-06-09T02:09:03.493259Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:09:03.493259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On de Branges--Rovnyak Kernels Admitting a Complete Pick Factor","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Haripada Sau","submitted_at":"2026-06-08T16:00:28Z","abstract_excerpt":"For a contractive multiplier $\\varphi$ in the multiplier algebra $M(k)$ of a kernel $k$, the associated de Branges--Rovnyak kernel is given by $k^\\varphi(x,y) = (1-\\varphi(x)\\overline{\\varphi(y)})k(x,y)$. Motivated by recent developments clarifying the structural and geometric features of reproducing kernel Hilbert spaces associated with kernels admitting a complete Pick factor, we investigate the precise conditions for a general de Branges-Rovnyak kernel to admit a complete Pick factor, thereby extending the framework introduced by Ahmed, Das and Panja (\\textit{J. Geom. Anal.}, 2025). In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09680","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/2606.09680/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":"2606.09680","created_at":"2026-06-09T02:09:03.493392+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.09680v1","created_at":"2026-06-09T02:09:03.493392+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09680","created_at":"2026-06-09T02:09:03.493392+00:00"},{"alias_kind":"pith_short_12","alias_value":"IZJNMUJO4FCI","created_at":"2026-06-09T02:09:03.493392+00:00"},{"alias_kind":"pith_short_16","alias_value":"IZJNMUJO4FCIJY54","created_at":"2026-06-09T02:09:03.493392+00:00"},{"alias_kind":"pith_short_8","alias_value":"IZJNMUJO","created_at":"2026-06-09T02:09:03.493392+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/IZJNMUJO4FCIJY543BHSVCHYVT","json":"https://pith.science/pith/IZJNMUJO4FCIJY543BHSVCHYVT.json","graph_json":"https://pith.science/api/pith-number/IZJNMUJO4FCIJY543BHSVCHYVT/graph.json","events_json":"https://pith.science/api/pith-number/IZJNMUJO4FCIJY543BHSVCHYVT/events.json","paper":"https://pith.science/paper/IZJNMUJO"},"agent_actions":{"view_html":"https://pith.science/pith/IZJNMUJO4FCIJY543BHSVCHYVT","download_json":"https://pith.science/pith/IZJNMUJO4FCIJY543BHSVCHYVT.json","view_paper":"https://pith.science/paper/IZJNMUJO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.09680&json=true","fetch_graph":"https://pith.science/api/pith-number/IZJNMUJO4FCIJY543BHSVCHYVT/graph.json","fetch_events":"https://pith.science/api/pith-number/IZJNMUJO4FCIJY543BHSVCHYVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IZJNMUJO4FCIJY543BHSVCHYVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IZJNMUJO4FCIJY543BHSVCHYVT/action/storage_attestation","attest_author":"https://pith.science/pith/IZJNMUJO4FCIJY543BHSVCHYVT/action/author_attestation","sign_citation":"https://pith.science/pith/IZJNMUJO4FCIJY543BHSVCHYVT/action/citation_signature","submit_replication":"https://pith.science/pith/IZJNMUJO4FCIJY543BHSVCHYVT/action/replication_record"}},"created_at":"2026-06-09T02:09:03.493392+00:00","updated_at":"2026-06-09T02:09:03.493392+00:00"}