{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YOWKFZBZIZET4PY4ZAK2T5BNAI","short_pith_number":"pith:YOWKFZBZ","canonical_record":{"source":{"id":"1611.01020","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-03T13:59:52Z","cross_cats_sorted":["math.CA","math.MP","math.SP"],"title_canon_sha256":"58e9a7022af5080e28ee2d6b2c70ef81ca1ef3c5e220019d59e062fa8b7f7759","abstract_canon_sha256":"c752ebb14d89c02e3a8fa7485cf5d948269b4b215dc6051f4a72019597c2c587"},"schema_version":"1.0"},"canonical_sha256":"c3aca2e43946493e3f1cc815a9f42d0238448950db6ee0ad3d1a7a1df651eb1a","source":{"kind":"arxiv","id":"1611.01020","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01020","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01020v3","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01020","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"YOWKFZBZIZET","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YOWKFZBZIZET4PY4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YOWKFZBZ","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YOWKFZBZIZET4PY4ZAK2T5BNAI","target":"record","payload":{"canonical_record":{"source":{"id":"1611.01020","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-03T13:59:52Z","cross_cats_sorted":["math.CA","math.MP","math.SP"],"title_canon_sha256":"58e9a7022af5080e28ee2d6b2c70ef81ca1ef3c5e220019d59e062fa8b7f7759","abstract_canon_sha256":"c752ebb14d89c02e3a8fa7485cf5d948269b4b215dc6051f4a72019597c2c587"},"schema_version":"1.0"},"canonical_sha256":"c3aca2e43946493e3f1cc815a9f42d0238448950db6ee0ad3d1a7a1df651eb1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.481007Z","signature_b64":"YJPFQkqJLDK0H8ifjTvGpRoF9AsKL4+vDwEunH77nnspSGSOKpnk967huQmQeeBrN+aOXBPqlAk4D5e0Bme+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3aca2e43946493e3f1cc815a9f42d0238448950db6ee0ad3d1a7a1df651eb1a","last_reissued_at":"2026-05-18T00:35:55.480612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.480612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.01020","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rv5diGr94NF/nrdS+3SYDPf/jFWlrAA2LPpeKnOz52ymfEmmCCU7dzGlVtTMKbcaRG1c2N3+ShK9/7/FMKYwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:08:56.414846Z"},"content_sha256":"f0fa5aa1e3dd2ca708bbba449cf9bf528917f6d5889c508cc4eaa8ba0e1b519d","schema_version":"1.0","event_id":"sha256:f0fa5aa1e3dd2ca708bbba449cf9bf528917f6d5889c508cc4eaa8ba0e1b519d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YOWKFZBZIZET4PY4ZAK2T5BNAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative Szeg\\H{o} asymptotics for Toeplitz determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Maurice Duits, Rostyslav Kozhan","submitted_at":"2016-11-03T13:59:52Z","abstract_excerpt":"We study the asymptotic behavior, as $n\\to\\infty$, of ratios of Toeplitz determinants $D_n(e^h d\\mu)/D_n(d\\mu)$ defined by a measure $\\mu$ on the unit circle and a sufficiently smooth function $h$. The approach we follow is based on the theory of orthogonal polynomials. We prove that the second order asymptotics depends on $h$ and only a few Verblunsky coefficients associated to $\\mu$. As a result, we establish a relative version of the Strong Szeg\\H{o} Limit Theorem for a wide class of measures $\\mu$ with essential support on a single arc. In particular, this allows the measure to have a sing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01020","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hdMSBSNKX+jAdLtzKNJTh0Wukk19A3pj2Se8cxLp6KAshh27cgxsRu+UuVnwqWXq6roQdknZeOvfqzhiN2qlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:08:56.415555Z"},"content_sha256":"a6c6f7441a519530be4cde63a5b84804fe8ad93a0533f20455543fe187908993","schema_version":"1.0","event_id":"sha256:a6c6f7441a519530be4cde63a5b84804fe8ad93a0533f20455543fe187908993"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YOWKFZBZIZET4PY4ZAK2T5BNAI/bundle.json","state_url":"https://pith.science/pith/YOWKFZBZIZET4PY4ZAK2T5BNAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YOWKFZBZIZET4PY4ZAK2T5BNAI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T21:08:56Z","links":{"resolver":"https://pith.science/pith/YOWKFZBZIZET4PY4ZAK2T5BNAI","bundle":"https://pith.science/pith/YOWKFZBZIZET4PY4ZAK2T5BNAI/bundle.json","state":"https://pith.science/pith/YOWKFZBZIZET4PY4ZAK2T5BNAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YOWKFZBZIZET4PY4ZAK2T5BNAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YOWKFZBZIZET4PY4ZAK2T5BNAI","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":"c752ebb14d89c02e3a8fa7485cf5d948269b4b215dc6051f4a72019597c2c587","cross_cats_sorted":["math.CA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-03T13:59:52Z","title_canon_sha256":"58e9a7022af5080e28ee2d6b2c70ef81ca1ef3c5e220019d59e062fa8b7f7759"},"schema_version":"1.0","source":{"id":"1611.01020","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01020","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01020v3","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01020","created_at":"2026-05-18T00:35:55Z"},{"alias_kind":"pith_short_12","alias_value":"YOWKFZBZIZET","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YOWKFZBZIZET4PY4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YOWKFZBZ","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:a6c6f7441a519530be4cde63a5b84804fe8ad93a0533f20455543fe187908993","target":"graph","created_at":"2026-05-18T00:35:55Z","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 study the asymptotic behavior, as $n\\to\\infty$, of ratios of Toeplitz determinants $D_n(e^h d\\mu)/D_n(d\\mu)$ defined by a measure $\\mu$ on the unit circle and a sufficiently smooth function $h$. The approach we follow is based on the theory of orthogonal polynomials. We prove that the second order asymptotics depends on $h$ and only a few Verblunsky coefficients associated to $\\mu$. As a result, we establish a relative version of the Strong Szeg\\H{o} Limit Theorem for a wide class of measures $\\mu$ with essential support on a single arc. In particular, this allows the measure to have a sing","authors_text":"Maurice Duits, Rostyslav Kozhan","cross_cats":["math.CA","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-03T13:59:52Z","title":"Relative Szeg\\H{o} asymptotics for Toeplitz determinants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01020","kind":"arxiv","version":3},"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:f0fa5aa1e3dd2ca708bbba449cf9bf528917f6d5889c508cc4eaa8ba0e1b519d","target":"record","created_at":"2026-05-18T00:35:55Z","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":"c752ebb14d89c02e3a8fa7485cf5d948269b4b215dc6051f4a72019597c2c587","cross_cats_sorted":["math.CA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-11-03T13:59:52Z","title_canon_sha256":"58e9a7022af5080e28ee2d6b2c70ef81ca1ef3c5e220019d59e062fa8b7f7759"},"schema_version":"1.0","source":{"id":"1611.01020","kind":"arxiv","version":3}},"canonical_sha256":"c3aca2e43946493e3f1cc815a9f42d0238448950db6ee0ad3d1a7a1df651eb1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3aca2e43946493e3f1cc815a9f42d0238448950db6ee0ad3d1a7a1df651eb1a","first_computed_at":"2026-05-18T00:35:55.480612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:55.480612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YJPFQkqJLDK0H8ifjTvGpRoF9AsKL4+vDwEunH77nnspSGSOKpnk967huQmQeeBrN+aOXBPqlAk4D5e0Bme+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:55.481007Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01020","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0fa5aa1e3dd2ca708bbba449cf9bf528917f6d5889c508cc4eaa8ba0e1b519d","sha256:a6c6f7441a519530be4cde63a5b84804fe8ad93a0533f20455543fe187908993"],"state_sha256":"1c1fb02d4adb7c6776060d3cf745c8ec5d665a85b6fbd9a25011af9eb7ea8e21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wk/qdicdduWHl3DhDXE7GEjZBKCBszHSou2tmOb1y60lJ1+RmpmDpaT+kLNcQh8gZywarhpV6FRp2esGk8HDBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:08:56.420362Z","bundle_sha256":"0f8b9db8b7e96c2dd121544ee38f541e2c4fad3a389dbc39eb4909bb9b40bb03"}}