{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5XVTNP3V4L6QGJDOIKOAZWH45W","short_pith_number":"pith:5XVTNP3V","canonical_record":{"source":{"id":"1303.4161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-18T05:54:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3d2f41447c7131862e97b40374e52c6be744cf0f51635e7761e77bbb92d76422","abstract_canon_sha256":"3ba6a80d0bf317b05f6e53375c0e2055b8e25f2ec60f9e2c8b6f023a6ee6e753"},"schema_version":"1.0"},"canonical_sha256":"edeb36bf75e2fd03246e429c0cd8fced94a99cc3a9577523369916a7b2d24ef4","source":{"kind":"arxiv","id":"1303.4161","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4161","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4161v2","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4161","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"5XVTNP3V4L6Q","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5XVTNP3V4L6QGJDO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5XVTNP3V","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5XVTNP3V4L6QGJDOIKOAZWH45W","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4161","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-18T05:54:31Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3d2f41447c7131862e97b40374e52c6be744cf0f51635e7761e77bbb92d76422","abstract_canon_sha256":"3ba6a80d0bf317b05f6e53375c0e2055b8e25f2ec60f9e2c8b6f023a6ee6e753"},"schema_version":"1.0"},"canonical_sha256":"edeb36bf75e2fd03246e429c0cd8fced94a99cc3a9577523369916a7b2d24ef4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:42.325669Z","signature_b64":"e7wdDEZRAMLMIM1RuS/pA8YvlucHbet4OIw9WBEiO1bZvFv4blDTawNAXnUTvkX6iicUNVX6LSNIyqoWvR2mBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edeb36bf75e2fd03246e429c0cd8fced94a99cc3a9577523369916a7b2d24ef4","last_reissued_at":"2026-05-18T03:18:42.325090Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:42.325090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4161","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:18:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qoXJQFZStYqWMd0+NqNuYVsQY9Nr4aGvV7v5kAy8lUH6SyPWnRaUV71x29dV8vTKFiru3TIilGF21ZsPZMvVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:58:11.415215Z"},"content_sha256":"fb8a6472debcbea8f520a6281dd97421701a9c655b058b8a2413fa7bf12ff7e4","schema_version":"1.0","event_id":"sha256:fb8a6472debcbea8f520a6281dd97421701a9c655b058b8a2413fa7bf12ff7e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5XVTNP3V4L6QGJDOIKOAZWH45W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Square-summable variation and absolutely continuous spectrum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Milivoje Lukic","submitted_at":"2013-03-18T05:54:31Z","abstract_excerpt":"Recent results of Denisov and Kaluzhny-Shamis describe the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an l^2 bounded variation condition with step p and are asymptotically periodic. We extend these results to orthogonal polynomials on the unit circle. We also replace the asymptotic periodicity condition by the weaker condition of convergence to an isospectral torus and, for p=1 and p=2, we remove even that condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4161","kind":"arxiv","version":2},"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":"2026-05-18T03:18:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5JrkAST6P2dotTQ8ZyPGHDK/WB9RIjJvG/0AcPs7rToQyf2hreUbjrTtvwfP2FwYoYkU7MMQYN+xktj2IewBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:58:11.415568Z"},"content_sha256":"29734b003b19f3d816bccefb24888600af9b818cea9f74c580235b666d3ef806","schema_version":"1.0","event_id":"sha256:29734b003b19f3d816bccefb24888600af9b818cea9f74c580235b666d3ef806"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5XVTNP3V4L6QGJDOIKOAZWH45W/bundle.json","state_url":"https://pith.science/pith/5XVTNP3V4L6QGJDOIKOAZWH45W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5XVTNP3V4L6QGJDOIKOAZWH45W/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":"2026-07-03T11:58:11Z","links":{"resolver":"https://pith.science/pith/5XVTNP3V4L6QGJDOIKOAZWH45W","bundle":"https://pith.science/pith/5XVTNP3V4L6QGJDOIKOAZWH45W/bundle.json","state":"https://pith.science/pith/5XVTNP3V4L6QGJDOIKOAZWH45W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5XVTNP3V4L6QGJDOIKOAZWH45W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5XVTNP3V4L6QGJDOIKOAZWH45W","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":"3ba6a80d0bf317b05f6e53375c0e2055b8e25f2ec60f9e2c8b6f023a6ee6e753","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-18T05:54:31Z","title_canon_sha256":"3d2f41447c7131862e97b40374e52c6be744cf0f51635e7761e77bbb92d76422"},"schema_version":"1.0","source":{"id":"1303.4161","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4161","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4161v2","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4161","created_at":"2026-05-18T03:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"5XVTNP3V4L6Q","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5XVTNP3V4L6QGJDO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5XVTNP3V","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:29734b003b19f3d816bccefb24888600af9b818cea9f74c580235b666d3ef806","target":"graph","created_at":"2026-05-18T03:18:42Z","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":"Recent results of Denisov and Kaluzhny-Shamis describe the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an l^2 bounded variation condition with step p and are asymptotically periodic. We extend these results to orthogonal polynomials on the unit circle. We also replace the asymptotic periodicity condition by the weaker condition of convergence to an isospectral torus and, for p=1 and p=2, we remove even that condition.","authors_text":"Milivoje Lukic","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-18T05:54:31Z","title":"Square-summable variation and absolutely continuous spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4161","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:fb8a6472debcbea8f520a6281dd97421701a9c655b058b8a2413fa7bf12ff7e4","target":"record","created_at":"2026-05-18T03:18:42Z","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":"3ba6a80d0bf317b05f6e53375c0e2055b8e25f2ec60f9e2c8b6f023a6ee6e753","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-18T05:54:31Z","title_canon_sha256":"3d2f41447c7131862e97b40374e52c6be744cf0f51635e7761e77bbb92d76422"},"schema_version":"1.0","source":{"id":"1303.4161","kind":"arxiv","version":2}},"canonical_sha256":"edeb36bf75e2fd03246e429c0cd8fced94a99cc3a9577523369916a7b2d24ef4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edeb36bf75e2fd03246e429c0cd8fced94a99cc3a9577523369916a7b2d24ef4","first_computed_at":"2026-05-18T03:18:42.325090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:42.325090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e7wdDEZRAMLMIM1RuS/pA8YvlucHbet4OIw9WBEiO1bZvFv4blDTawNAXnUTvkX6iicUNVX6LSNIyqoWvR2mBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:42.325669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4161","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb8a6472debcbea8f520a6281dd97421701a9c655b058b8a2413fa7bf12ff7e4","sha256:29734b003b19f3d816bccefb24888600af9b818cea9f74c580235b666d3ef806"],"state_sha256":"b80b33fb73917444f4f68376b923e98fe305e00bf652d40140d870e8db523713"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+KKZMDkS29F3r7rrI7y2LKssUagu3QkJN0Pskxs1JGYo0Qj8M4h8poxyMt10x0YotS/de8oM8SqJmH7S+ky7BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T11:58:11.417420Z","bundle_sha256":"bc03c85625453a505ee1c44af94e9d12a826faf977210944f8c8a62ad57dc408"}}