{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D7WRIEPMCBLGG5TIWTNUVH4GIV","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":"269647eca914d2248b42472504bbc1a07882253e73dc9cda7bce97b4b5245336","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-02T02:32:56Z","title_canon_sha256":"26c4fd4aa4a09a28f63d2e95e8fef196524edebd273b2f66b0ace3c33d0589af"},"schema_version":"1.0","source":{"id":"1304.0518","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0518","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0518v1","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0518","created_at":"2026-05-18T03:29:15Z"},{"alias_kind":"pith_short_12","alias_value":"D7WRIEPMCBLG","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D7WRIEPMCBLGG5TI","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D7WRIEPM","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:73dd1cbdfea1809d72632406804e6290b1c77a75bd880a58f17c0e25afc8e1f7","target":"graph","created_at":"2026-05-18T03:29:15Z","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":"We continue our study of outer elements of the noncommutative H^p spaces associated with Arveson's subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in H^p actually satisfy the stronger condition that there exist a_n in A with h a_n in Ball(A) and h a_n \\to 1 in p-norm.","authors_text":"David P. Blecher, Louis Labuschagne","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-02T02:32:56Z","title":"Outers for noncommutative H^p revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0518","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":"sha256:93ec431b2cf05983add74c49e2256529a67519240103bf2f8276ba3d6902be68","target":"record","created_at":"2026-05-18T03:29:15Z","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":"269647eca914d2248b42472504bbc1a07882253e73dc9cda7bce97b4b5245336","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-02T02:32:56Z","title_canon_sha256":"26c4fd4aa4a09a28f63d2e95e8fef196524edebd273b2f66b0ace3c33d0589af"},"schema_version":"1.0","source":{"id":"1304.0518","kind":"arxiv","version":1}},"canonical_sha256":"1fed1411ec1056637668b4db4a9f86455c8839210878ddbce1c949c5ccbb71a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fed1411ec1056637668b4db4a9f86455c8839210878ddbce1c949c5ccbb71a1","first_computed_at":"2026-05-18T03:29:15.189723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:15.189723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nwDAgedK4FusRsmgeAsmHfJ2ZPmqLI+vWauGF3ljJRz8n53bujwWrBtm2uuzYZ9fy68S51SHOImnz+0aY+NWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:15.190535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0518","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93ec431b2cf05983add74c49e2256529a67519240103bf2f8276ba3d6902be68","sha256:73dd1cbdfea1809d72632406804e6290b1c77a75bd880a58f17c0e25afc8e1f7"],"state_sha256":"e045707b952ebeaff237cc00dc85e4c2e49a938f6582ba6f889e8e36d371482f"}