{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:B6JXZ5GYDB4XDLIVWXFC7JAQYY","short_pith_number":"pith:B6JXZ5GY","schema_version":"1.0","canonical_sha256":"0f937cf4d8187971ad15b5ca2fa410c62053aec80d1eb3723c602c622846f4bb","source":{"kind":"arxiv","id":"1608.08113","version":1},"attestation_state":"computed","paper":{"title":"Module tensor product of subnormal modules need not be subnormal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Akash Anand, Sameer Chavan","submitted_at":"2016-08-29T15:46:41Z","abstract_excerpt":"Let $\\kappa : \\mathbb D \\times \\mathbb D \\to \\mathbb C$ be a diagonal positive definite kernel and let $\\mathscr H_{\\kappa}$ denote the associated reproducing kernel Hilbert space of holomorphic functions on the open unit disc $\\mathbb D$. Assume that $zf \\in \\mathscr H$ whenever $f \\in \\mathscr H.$ Then $\\mathscr H$ is a Hilbert module over the polynomial ring $\\mathbb C[z]$ with module action $p \\cdot f \\mapsto pf$. We say that $\\mathscr H_{\\kappa}$ is a subnormal Hilbert module if the operator $\\mathscr M_{z}$ of multiplication by the coordinate function $z$ on $\\mathscr H_{\\kappa}$ is subn"},"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":"1608.08113","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-29T15:46:41Z","cross_cats_sorted":[],"title_canon_sha256":"7ca1c42e8f72d5fac107e458daba8e82e06a77db622fb1a7a9679c711cb84e98","abstract_canon_sha256":"6e5fa2f0890fe56144b91f0cdad3280456614bec1c0d13d58aba7d66084423cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:48.653797Z","signature_b64":"QfCkGK6DPwLHP+0SmgCampSREX2sz54myoWB1BwLoIaLPV2KCtjqDqKb28pCUosN92dNI++fOjEZA9dhBot2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f937cf4d8187971ad15b5ca2fa410c62053aec80d1eb3723c602c622846f4bb","last_reissued_at":"2026-05-18T01:07:48.653341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:48.653341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Module tensor product of subnormal modules need not be subnormal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Akash Anand, Sameer Chavan","submitted_at":"2016-08-29T15:46:41Z","abstract_excerpt":"Let $\\kappa : \\mathbb D \\times \\mathbb D \\to \\mathbb C$ be a diagonal positive definite kernel and let $\\mathscr H_{\\kappa}$ denote the associated reproducing kernel Hilbert space of holomorphic functions on the open unit disc $\\mathbb D$. Assume that $zf \\in \\mathscr H$ whenever $f \\in \\mathscr H.$ Then $\\mathscr H$ is a Hilbert module over the polynomial ring $\\mathbb C[z]$ with module action $p \\cdot f \\mapsto pf$. We say that $\\mathscr H_{\\kappa}$ is a subnormal Hilbert module if the operator $\\mathscr M_{z}$ of multiplication by the coordinate function $z$ on $\\mathscr H_{\\kappa}$ is subn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08113","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":"1608.08113","created_at":"2026-05-18T01:07:48.653410+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.08113v1","created_at":"2026-05-18T01:07:48.653410+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08113","created_at":"2026-05-18T01:07:48.653410+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6JXZ5GYDB4X","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6JXZ5GYDB4XDLIV","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6JXZ5GY","created_at":"2026-05-18T12:30:07.202191+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/B6JXZ5GYDB4XDLIVWXFC7JAQYY","json":"https://pith.science/pith/B6JXZ5GYDB4XDLIVWXFC7JAQYY.json","graph_json":"https://pith.science/api/pith-number/B6JXZ5GYDB4XDLIVWXFC7JAQYY/graph.json","events_json":"https://pith.science/api/pith-number/B6JXZ5GYDB4XDLIVWXFC7JAQYY/events.json","paper":"https://pith.science/paper/B6JXZ5GY"},"agent_actions":{"view_html":"https://pith.science/pith/B6JXZ5GYDB4XDLIVWXFC7JAQYY","download_json":"https://pith.science/pith/B6JXZ5GYDB4XDLIVWXFC7JAQYY.json","view_paper":"https://pith.science/paper/B6JXZ5GY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.08113&json=true","fetch_graph":"https://pith.science/api/pith-number/B6JXZ5GYDB4XDLIVWXFC7JAQYY/graph.json","fetch_events":"https://pith.science/api/pith-number/B6JXZ5GYDB4XDLIVWXFC7JAQYY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6JXZ5GYDB4XDLIVWXFC7JAQYY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6JXZ5GYDB4XDLIVWXFC7JAQYY/action/storage_attestation","attest_author":"https://pith.science/pith/B6JXZ5GYDB4XDLIVWXFC7JAQYY/action/author_attestation","sign_citation":"https://pith.science/pith/B6JXZ5GYDB4XDLIVWXFC7JAQYY/action/citation_signature","submit_replication":"https://pith.science/pith/B6JXZ5GYDB4XDLIVWXFC7JAQYY/action/replication_record"}},"created_at":"2026-05-18T01:07:48.653410+00:00","updated_at":"2026-05-18T01:07:48.653410+00:00"}