{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3N7SNNT3QT4F3FHJGCI7DA4D3L","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"58097036c3a20d9704d539d1f65057c88be7634766af03e7140f94552af361c8","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-07-22T21:31:07Z","title_canon_sha256":"25e760243d75d3cd329ca1f213d841cd016cab77d7aef21d70ba70476b5e851a"},"schema_version":"1.0","source":{"id":"1807.08371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08371","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08371v1","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08371","created_at":"2026-05-17T23:43:04Z"},{"alias_kind":"pith_short_12","alias_value":"3N7SNNT3QT4F","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3N7SNNT3QT4F3FHJ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3N7SNNT3","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:df2f9013c816ea29e68ed5a4c5a9ea736a46ecf0d085b5b07d71b99a007a4967","target":"graph","created_at":"2026-05-17T23:43:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Michael T. Jury, Robert T.W. Martin","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-07-22T21:31:07Z","title":"Column extreme multipliers of the Free Hardy space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08371","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ba3d48aa4e221462fec6e4e545a9cf4bae229928c1c6b3911b76ced0831ce987","target":"record","created_at":"2026-05-17T23:43:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"58097036c3a20d9704d539d1f65057c88be7634766af03e7140f94552af361c8","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-07-22T21:31:07Z","title_canon_sha256":"25e760243d75d3cd329ca1f213d841cd016cab77d7aef21d70ba70476b5e851a"},"schema_version":"1.0","source":{"id":"1807.08371","kind":"arxiv","version":1}},"canonical_sha256":"db7f26b67b84f85d94e93091f18383dad9ac71859025534137023c2732893f07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db7f26b67b84f85d94e93091f18383dad9ac71859025534137023c2732893f07","first_computed_at":"2026-05-17T23:43:04.858047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:04.858047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"srJ+bv2qQp69Cgy3vUsRpnEutZqxoXXuTeWqv3db3BANABcngv4/vzD3ExbOf2BquG3GFCmbvSp+RW4KvK0TDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:04.858557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba3d48aa4e221462fec6e4e545a9cf4bae229928c1c6b3911b76ced0831ce987","sha256:df2f9013c816ea29e68ed5a4c5a9ea736a46ecf0d085b5b07d71b99a007a4967"],"state_sha256":"67988adaec496d2f8934f5aab0fc01f36e1a5c5c20e2519e5938f93a946f9ceb"}