{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ODXITTEVB6C5DGKVWXGJTB42VW","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":"ed81ecb74d705c73c8a84c17e0c7e362a2ba22bcdec15803130470dd5024bec2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-03T13:57:56Z","title_canon_sha256":"468f406b3d2e57113c37e68097023e6c6a09a577351a153a5475f8189a332a76"},"schema_version":"1.0","source":{"id":"1603.01101","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01101","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01101v2","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01101","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"ODXITTEVB6C5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ODXITTEVB6C5DGKV","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ODXITTEV","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:d0c9ee259f2d2b3279b2c3f2991ad0bbef3124edb016ba1fe59a5fe23f55a78c","target":"graph","created_at":"2026-05-18T01:16:09Z","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":"In the scalar case, the spectral factorization mapping $f\\to f^+$ puts a nonnegative integrable function $f$ having an integrable logarithm in correspondence with an outer analytic function $f^+$ such that $f = |f^+|^2$ almost everywhere. The main question addressed here is to what extent $\\|f^+ - g^+\\|_{H_2}$ is controlled by $\\|f-g\\|_{L_1}$ and $\\|\\log f - \\log g\\|_{L_1}$.","authors_text":"Eugene Shargorodsky, Ilya Spitkovsky, Lasha Ephremidze","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-03T13:57:56Z","title":"Quantitative results on continuity of the spectral factorization mapping in the scalar case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01101","kind":"arxiv","version":2},"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":"sha256:10eba25b0ccb6d3189005ccb82a0c44c01765e3f85f39df282a4817ece5096f0","target":"record","created_at":"2026-05-18T01:16:09Z","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":"ed81ecb74d705c73c8a84c17e0c7e362a2ba22bcdec15803130470dd5024bec2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-03T13:57:56Z","title_canon_sha256":"468f406b3d2e57113c37e68097023e6c6a09a577351a153a5475f8189a332a76"},"schema_version":"1.0","source":{"id":"1603.01101","kind":"arxiv","version":2}},"canonical_sha256":"70ee89cc950f85d19955b5cc99879aadb8d155b0bfb4b0d77707eda845641771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70ee89cc950f85d19955b5cc99879aadb8d155b0bfb4b0d77707eda845641771","first_computed_at":"2026-05-18T01:16:09.181363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:09.181363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N9Je6yP8+GM+sjhh5hfzhis8vbQynUX4aEE9ZZgDPouaQbm9dn8ZcEXF/cAXftvwiopjLIlJWcUf6chaEohNDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:09.181869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01101","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10eba25b0ccb6d3189005ccb82a0c44c01765e3f85f39df282a4817ece5096f0","sha256:d0c9ee259f2d2b3279b2c3f2991ad0bbef3124edb016ba1fe59a5fe23f55a78c"],"state_sha256":"60a0148f42d9c403cdd4e2a4822307e8793112e4425d3f5007a4d923ba160a18"}