{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IQTEOSHW3WBWKDQ3GV6DT5DRTN","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":"aa8aa3218582d5a6c9a3e2bd28453738ff7d57a6d89aecca3abcaf6612fb46ce","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-28T23:35:03Z","title_canon_sha256":"0deef117d9a35e3b5ea5e3b8b62f7f39abecf33d7741addc5afcd9c99c7abba1"},"schema_version":"1.0","source":{"id":"1803.00134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00134","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00134v1","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00134","created_at":"2026-05-18T00:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"IQTEOSHW3WBW","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IQTEOSHW3WBWKDQ3","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IQTEOSHW","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:c8b43484d9d43acf33be4c892ec69837f6bb1911840fdd801b450e4199b22f7a","target":"graph","created_at":"2026-05-18T00:22:11Z","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":"Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider in this paper the reverse: for a positive matrix in the Hardy space of the unit disc we consider which measures, if any, yield a boundary representation of the positive matrix. We prove a characterization of those representing measures via a matrix identity by introducing a new operator product called the Abel Product.","authors_text":"Eric S. Weber, John E. Herr, Palle E.T. Jorgensen","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-28T23:35:03Z","title":"A Characterization of Boundary Representations of Positive Matrices in the Hardy Space via the Abel Product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00134","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:fa0b0a6a8a5383655c197a70991820b2b3c2d20cadf52e6db51263f713f1c65f","target":"record","created_at":"2026-05-18T00:22:11Z","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":"aa8aa3218582d5a6c9a3e2bd28453738ff7d57a6d89aecca3abcaf6612fb46ce","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-28T23:35:03Z","title_canon_sha256":"0deef117d9a35e3b5ea5e3b8b62f7f39abecf33d7741addc5afcd9c99c7abba1"},"schema_version":"1.0","source":{"id":"1803.00134","kind":"arxiv","version":1}},"canonical_sha256":"44264748f6dd83650e1b357c39f4719b74f4ce17ba80a42d5a0b0f3e8a79f90c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44264748f6dd83650e1b357c39f4719b74f4ce17ba80a42d5a0b0f3e8a79f90c","first_computed_at":"2026-05-18T00:22:11.809342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:11.809342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/QXBKt/lq9FZNm+RAv3GUipjWDM5pXYKigP/J/LO58UNQA0JYVFAK7cYnwgHWB78L997rcTDiJ4E+hpsu8YyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:11.809863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa0b0a6a8a5383655c197a70991820b2b3c2d20cadf52e6db51263f713f1c65f","sha256:c8b43484d9d43acf33be4c892ec69837f6bb1911840fdd801b450e4199b22f7a"],"state_sha256":"3e25f58edb9eea598865e4a1c74253ee137a3ef4afbf6cea961b826746475518"}