{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:3N7SNNT3QT4F3FHJGCI7DA4D3L","short_pith_number":"pith:3N7SNNT3","schema_version":"1.0","canonical_sha256":"db7f26b67b84f85d94e93091f18383dad9ac71859025534137023c2732893f07","source":{"kind":"arxiv","id":"1807.08371","version":1},"attestation_state":"computed","paper":{"title":"Column extreme multipliers of the Free Hardy space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Michael T. Jury, Robert T.W. Martin","submitted_at":"2018-07-22T21:31:07Z","abstract_excerpt":"The full Fock space over $\\mathbb C ^d$ can be identified with the free Hardy space, $H^2 (\\mathbb B ^d _\\mathbb N)$ - the unique non-commutative reproducing kernel Hilbert space corresponding to a non-commutative Szeg\\\"{o} kernel on the non-commutative, multi-variable open unit ball $\\mathbb B ^d _\\mathbb N := \\bigsqcup _{n=1} ^\\infty \\left( \\mathbb C^{n\\times n} \\otimes \\mathbb C ^d \\right) _1$.\n  Elements of this space are free or non-commutative functions on $\\mathbb B ^d _\\mathbb N$. Under this identification, the full Fock space is the canonical non-commutative and several-variable analo"},"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":"1807.08371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-07-22T21:31:07Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"25e760243d75d3cd329ca1f213d841cd016cab77d7aef21d70ba70476b5e851a","abstract_canon_sha256":"58097036c3a20d9704d539d1f65057c88be7634766af03e7140f94552af361c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:04.858557Z","signature_b64":"srJ+bv2qQp69Cgy3vUsRpnEutZqxoXXuTeWqv3db3BANABcngv4/vzD3ExbOf2BquG3GFCmbvSp+RW4KvK0TDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db7f26b67b84f85d94e93091f18383dad9ac71859025534137023c2732893f07","last_reissued_at":"2026-05-17T23:43:04.858047Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:04.858047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Column extreme multipliers of the Free Hardy space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Michael T. Jury, Robert T.W. Martin","submitted_at":"2018-07-22T21:31:07Z","abstract_excerpt":"The full Fock space over $\\mathbb C ^d$ can be identified with the free Hardy space, $H^2 (\\mathbb B ^d _\\mathbb N)$ - the unique non-commutative reproducing kernel Hilbert space corresponding to a non-commutative Szeg\\\"{o} kernel on the non-commutative, multi-variable open unit ball $\\mathbb B ^d _\\mathbb N := \\bigsqcup _{n=1} ^\\infty \\left( \\mathbb C^{n\\times n} \\otimes \\mathbb C ^d \\right) _1$.\n  Elements of this space are free or non-commutative functions on $\\mathbb B ^d _\\mathbb N$. Under this identification, the full Fock space is the canonical non-commutative and several-variable analo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08371","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":"1807.08371","created_at":"2026-05-17T23:43:04.858127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08371v1","created_at":"2026-05-17T23:43:04.858127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08371","created_at":"2026-05-17T23:43:04.858127+00:00"},{"alias_kind":"pith_short_12","alias_value":"3N7SNNT3QT4F","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"3N7SNNT3QT4F3FHJ","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"3N7SNNT3","created_at":"2026-05-18T12:32:02.567920+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/3N7SNNT3QT4F3FHJGCI7DA4D3L","json":"https://pith.science/pith/3N7SNNT3QT4F3FHJGCI7DA4D3L.json","graph_json":"https://pith.science/api/pith-number/3N7SNNT3QT4F3FHJGCI7DA4D3L/graph.json","events_json":"https://pith.science/api/pith-number/3N7SNNT3QT4F3FHJGCI7DA4D3L/events.json","paper":"https://pith.science/paper/3N7SNNT3"},"agent_actions":{"view_html":"https://pith.science/pith/3N7SNNT3QT4F3FHJGCI7DA4D3L","download_json":"https://pith.science/pith/3N7SNNT3QT4F3FHJGCI7DA4D3L.json","view_paper":"https://pith.science/paper/3N7SNNT3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08371&json=true","fetch_graph":"https://pith.science/api/pith-number/3N7SNNT3QT4F3FHJGCI7DA4D3L/graph.json","fetch_events":"https://pith.science/api/pith-number/3N7SNNT3QT4F3FHJGCI7DA4D3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3N7SNNT3QT4F3FHJGCI7DA4D3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3N7SNNT3QT4F3FHJGCI7DA4D3L/action/storage_attestation","attest_author":"https://pith.science/pith/3N7SNNT3QT4F3FHJGCI7DA4D3L/action/author_attestation","sign_citation":"https://pith.science/pith/3N7SNNT3QT4F3FHJGCI7DA4D3L/action/citation_signature","submit_replication":"https://pith.science/pith/3N7SNNT3QT4F3FHJGCI7DA4D3L/action/replication_record"}},"created_at":"2026-05-17T23:43:04.858127+00:00","updated_at":"2026-05-17T23:43:04.858127+00:00"}