{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6VS77WN672COKOSSCI5JEM6WRZ","short_pith_number":"pith:6VS77WN6","schema_version":"1.0","canonical_sha256":"f565ffd9befe84e53a52123a9233d68e6b14db17d8ed3d61dd2d82714f3086e1","source":{"kind":"arxiv","id":"1808.08880","version":1},"attestation_state":"computed","paper":{"title":"Hilbert-Schmidtness of some finitely generated submodules in $H^2(\\mathbb{D}^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kei Ji Izuchi, Rongwei Yang, Shuaibing Luo","submitted_at":"2018-08-27T15:26:33Z","abstract_excerpt":"A closed subspace $\\mathcal{M}$ of the Hardy space $H^2(\\mathbb{D}^2)$ over the bidisk is called a submodule if it is invariant under multiplication by coordinate functions $z_1$ and $z_2$. Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem. This paper proves that every finitely generated submodule $\\mathcal{M}$ containing $z_1 - \\varphi(z_2)$ is Hilbert-Schmidt, where $\\varphi$ is any finite Blaschke product. Some other related topics such as fringe operator and Fredholm index are also discussed."},"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":"1808.08880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-27T15:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"e14cc6b01b4878d2fd6a0eb4ae8fc8a25a22166dcd7b78bfc3e8defc4faa556f","abstract_canon_sha256":"d60ae907773c04830c9670f716b6de434a7541ddadbf578d0aa302de47c55028"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:12.957382Z","signature_b64":"e5xcshejldYFF4VwCkQR3k3VPWPgRubuwHmZVAifH7DKSd3YpD/N6bvAKlZgz4EYNc1linNiRLI9k5zP7Y51Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f565ffd9befe84e53a52123a9233d68e6b14db17d8ed3d61dd2d82714f3086e1","last_reissued_at":"2026-05-18T00:07:12.956728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:12.956728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hilbert-Schmidtness of some finitely generated submodules in $H^2(\\mathbb{D}^2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Kei Ji Izuchi, Rongwei Yang, Shuaibing Luo","submitted_at":"2018-08-27T15:26:33Z","abstract_excerpt":"A closed subspace $\\mathcal{M}$ of the Hardy space $H^2(\\mathbb{D}^2)$ over the bidisk is called a submodule if it is invariant under multiplication by coordinate functions $z_1$ and $z_2$. Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem. This paper proves that every finitely generated submodule $\\mathcal{M}$ containing $z_1 - \\varphi(z_2)$ is Hilbert-Schmidt, where $\\varphi$ is any finite Blaschke product. Some other related topics such as fringe operator and Fredholm index are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08880","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":"1808.08880","created_at":"2026-05-18T00:07:12.956809+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.08880v1","created_at":"2026-05-18T00:07:12.956809+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08880","created_at":"2026-05-18T00:07:12.956809+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VS77WN672CO","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VS77WN672COKOSS","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VS77WN6","created_at":"2026-05-18T12:32:11.075285+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/6VS77WN672COKOSSCI5JEM6WRZ","json":"https://pith.science/pith/6VS77WN672COKOSSCI5JEM6WRZ.json","graph_json":"https://pith.science/api/pith-number/6VS77WN672COKOSSCI5JEM6WRZ/graph.json","events_json":"https://pith.science/api/pith-number/6VS77WN672COKOSSCI5JEM6WRZ/events.json","paper":"https://pith.science/paper/6VS77WN6"},"agent_actions":{"view_html":"https://pith.science/pith/6VS77WN672COKOSSCI5JEM6WRZ","download_json":"https://pith.science/pith/6VS77WN672COKOSSCI5JEM6WRZ.json","view_paper":"https://pith.science/paper/6VS77WN6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.08880&json=true","fetch_graph":"https://pith.science/api/pith-number/6VS77WN672COKOSSCI5JEM6WRZ/graph.json","fetch_events":"https://pith.science/api/pith-number/6VS77WN672COKOSSCI5JEM6WRZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VS77WN672COKOSSCI5JEM6WRZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VS77WN672COKOSSCI5JEM6WRZ/action/storage_attestation","attest_author":"https://pith.science/pith/6VS77WN672COKOSSCI5JEM6WRZ/action/author_attestation","sign_citation":"https://pith.science/pith/6VS77WN672COKOSSCI5JEM6WRZ/action/citation_signature","submit_replication":"https://pith.science/pith/6VS77WN672COKOSSCI5JEM6WRZ/action/replication_record"}},"created_at":"2026-05-18T00:07:12.956809+00:00","updated_at":"2026-05-18T00:07:12.956809+00:00"}