{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BP7XOAGJ66CI6IEAIJ2YHZ4ER4","short_pith_number":"pith:BP7XOAGJ","schema_version":"1.0","canonical_sha256":"0bff7700c9f7848f2080427583e7848f37b3d8f08c91d45d7576f412862d8d14","source":{"kind":"arxiv","id":"2606.08174","version":1},"attestation_state":"computed","paper":{"title":"Superdirectivity as a Spectral-Collision RKHS Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hong Yang","submitted_at":"2026-06-06T13:39:48Z","abstract_excerpt":"We develop a reproducing-kernel Hilbert space interpretation of array superdirectivity based on spectral-collision limits and polynomial jet geometry. As the spacing of an $M$-element linear array tends to zero, the exponential family generated by a linear array undergoes a spectral collision, and the associated finite-dimensional subspaces converge in reproducing kernel to a polynomial jet space. Array gain equals the diagonal evaluation of the reproducing kernel, and the $M^2$ endfire law emerges from endpoint asymptotics of the Christoffel-Darboux kernel. Unlike classical derivations that r"},"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":"2606.08174","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-06-06T13:39:48Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3b5390fcb37087fb7642fa8c74b86af9f2598f97a923729058c28eebd2e2a300","abstract_canon_sha256":"217d9f000edf3f4099ca3a1e4e1b4d1307a2a2a2f5c30b3b83a99a092f2253e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:29.044631Z","signature_b64":"DgNUIEMssCfZ5y5iDwCg6JXQJwu/qLDCxcMQAxAww1BGUSi7waL1yhc4/V7G0kJgkoB5r27Q6bKsLuSiXjGUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bff7700c9f7848f2080427583e7848f37b3d8f08c91d45d7576f412862d8d14","last_reissued_at":"2026-06-09T01:05:29.044051Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:29.044051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Superdirectivity as a Spectral-Collision RKHS Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Hong Yang","submitted_at":"2026-06-06T13:39:48Z","abstract_excerpt":"We develop a reproducing-kernel Hilbert space interpretation of array superdirectivity based on spectral-collision limits and polynomial jet geometry. As the spacing of an $M$-element linear array tends to zero, the exponential family generated by a linear array undergoes a spectral collision, and the associated finite-dimensional subspaces converge in reproducing kernel to a polynomial jet space. Array gain equals the diagonal evaluation of the reproducing kernel, and the $M^2$ endfire law emerges from endpoint asymptotics of the Christoffel-Darboux kernel. Unlike classical derivations that r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08174","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/2606.08174/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":"2606.08174","created_at":"2026-06-09T01:05:29.044127+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.08174v1","created_at":"2026-06-09T01:05:29.044127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08174","created_at":"2026-06-09T01:05:29.044127+00:00"},{"alias_kind":"pith_short_12","alias_value":"BP7XOAGJ66CI","created_at":"2026-06-09T01:05:29.044127+00:00"},{"alias_kind":"pith_short_16","alias_value":"BP7XOAGJ66CI6IEA","created_at":"2026-06-09T01:05:29.044127+00:00"},{"alias_kind":"pith_short_8","alias_value":"BP7XOAGJ","created_at":"2026-06-09T01:05:29.044127+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/BP7XOAGJ66CI6IEAIJ2YHZ4ER4","json":"https://pith.science/pith/BP7XOAGJ66CI6IEAIJ2YHZ4ER4.json","graph_json":"https://pith.science/api/pith-number/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/graph.json","events_json":"https://pith.science/api/pith-number/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/events.json","paper":"https://pith.science/paper/BP7XOAGJ"},"agent_actions":{"view_html":"https://pith.science/pith/BP7XOAGJ66CI6IEAIJ2YHZ4ER4","download_json":"https://pith.science/pith/BP7XOAGJ66CI6IEAIJ2YHZ4ER4.json","view_paper":"https://pith.science/paper/BP7XOAGJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.08174&json=true","fetch_graph":"https://pith.science/api/pith-number/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/graph.json","fetch_events":"https://pith.science/api/pith-number/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/action/storage_attestation","attest_author":"https://pith.science/pith/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/action/author_attestation","sign_citation":"https://pith.science/pith/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/action/citation_signature","submit_replication":"https://pith.science/pith/BP7XOAGJ66CI6IEAIJ2YHZ4ER4/action/replication_record"}},"created_at":"2026-06-09T01:05:29.044127+00:00","updated_at":"2026-06-09T01:05:29.044127+00:00"}