{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:L3BQ64SBV5JQEOC7TT3EJS6NAP","short_pith_number":"pith:L3BQ64SB","canonical_record":{"source":{"id":"1209.3435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-15T21:13:03Z","cross_cats_sorted":[],"title_canon_sha256":"2a2a537433d88d4c6c618574c5f00fa8eb3aceabaa9e6dbdcce8bfc6aa01f2df","abstract_canon_sha256":"b47d084c9cf6ced0a6f8b12af2d34292ae5a543ec3119076d770b13b6c7883f2"},"schema_version":"1.0"},"canonical_sha256":"5ec30f7241af5302385f9cf644cbcd03fd18a32fc7d0fb31eb419a522564c279","source":{"kind":"arxiv","id":"1209.3435","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3435","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3435v1","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3435","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"L3BQ64SBV5JQ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L3BQ64SBV5JQEOC7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L3BQ64SB","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:L3BQ64SBV5JQEOC7TT3EJS6NAP","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-15T21:13:03Z","cross_cats_sorted":[],"title_canon_sha256":"2a2a537433d88d4c6c618574c5f00fa8eb3aceabaa9e6dbdcce8bfc6aa01f2df","abstract_canon_sha256":"b47d084c9cf6ced0a6f8b12af2d34292ae5a543ec3119076d770b13b6c7883f2"},"schema_version":"1.0"},"canonical_sha256":"5ec30f7241af5302385f9cf644cbcd03fd18a32fc7d0fb31eb419a522564c279","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:30.981819Z","signature_b64":"G2CCIH1RTn4VzLjnYh2ThEN8eKzEk1ntFNzAV7AYka50Gdp7l0ZeVz6yzV2AomIDGSZfLwART+Iu9B31H/WlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ec30f7241af5302385f9cf644cbcd03fd18a32fc7d0fb31eb419a522564c279","last_reissued_at":"2026-05-18T03:45:30.981370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:30.981370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3435","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tP+iFikltIEyOd2QT3sTRO44svIknmwrdv8gyGfS2smQQJv601lQu8aZeuVi0v8ZLd2nKgDL4QzqmP45KmbABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:37:31.639866Z"},"content_sha256":"a990d98a17ba158bec7440b77b52fe006a5aef5d225054ee4f57e7f81db1dcc6","schema_version":"1.0","event_id":"sha256:a990d98a17ba158bec7440b77b52fe006a5aef5d225054ee4f57e7f81db1dcc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:L3BQ64SBV5JQEOC7TT3EJS6NAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On applications of the model spaces to the construction of cocyclic perturbations of the semigroup of shifts on the semiaxis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.D. Baranov, G.G. Amosov, V.V. Kapustin","submitted_at":"2012-09-15T21:13:03Z","abstract_excerpt":"We describe a construction of cocyclic perturbations of the semigroup of shifts on the semiaxis by means of the theory of model spaces. It is shown that one can choose an inner function that determines the model space so that the elements of the perturbed semigroup have a prescribed spectral type and differ from the elements of the initial semigroup by operators from the Schatten-von Neumann class $\\mathfrak{S}_p$, $p>1$. The case of the trace class $\\mathfrak{S}_1$ perturbations is considered separately."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3435","kind":"arxiv","version":1},"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":"2026-05-18T03:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LTU/+uIlkb8MIOik6q+Pg/yvn6KuSYDLFcZ/hX9COOB1pCmLl9cMfQgDkl9Q81kgHn2eOB4hC0y5bI1WCw8XDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:37:31.640589Z"},"content_sha256":"9ac90a50a7bc77328032b2a5db07ab3aa90cf8400de71af9c43d76f22c2c204e","schema_version":"1.0","event_id":"sha256:9ac90a50a7bc77328032b2a5db07ab3aa90cf8400de71af9c43d76f22c2c204e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3BQ64SBV5JQEOC7TT3EJS6NAP/bundle.json","state_url":"https://pith.science/pith/L3BQ64SBV5JQEOC7TT3EJS6NAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3BQ64SBV5JQEOC7TT3EJS6NAP/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":"2026-05-26T01:37:31Z","links":{"resolver":"https://pith.science/pith/L3BQ64SBV5JQEOC7TT3EJS6NAP","bundle":"https://pith.science/pith/L3BQ64SBV5JQEOC7TT3EJS6NAP/bundle.json","state":"https://pith.science/pith/L3BQ64SBV5JQEOC7TT3EJS6NAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3BQ64SBV5JQEOC7TT3EJS6NAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:L3BQ64SBV5JQEOC7TT3EJS6NAP","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":"b47d084c9cf6ced0a6f8b12af2d34292ae5a543ec3119076d770b13b6c7883f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-15T21:13:03Z","title_canon_sha256":"2a2a537433d88d4c6c618574c5f00fa8eb3aceabaa9e6dbdcce8bfc6aa01f2df"},"schema_version":"1.0","source":{"id":"1209.3435","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3435","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3435v1","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3435","created_at":"2026-05-18T03:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"L3BQ64SBV5JQ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L3BQ64SBV5JQEOC7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L3BQ64SB","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:9ac90a50a7bc77328032b2a5db07ab3aa90cf8400de71af9c43d76f22c2c204e","target":"graph","created_at":"2026-05-18T03:45:30Z","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 describe a construction of cocyclic perturbations of the semigroup of shifts on the semiaxis by means of the theory of model spaces. It is shown that one can choose an inner function that determines the model space so that the elements of the perturbed semigroup have a prescribed spectral type and differ from the elements of the initial semigroup by operators from the Schatten-von Neumann class $\\mathfrak{S}_p$, $p>1$. The case of the trace class $\\mathfrak{S}_1$ perturbations is considered separately.","authors_text":"A.D. Baranov, G.G. Amosov, V.V. Kapustin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-15T21:13:03Z","title":"On applications of the model spaces to the construction of cocyclic perturbations of the semigroup of shifts on the semiaxis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3435","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:a990d98a17ba158bec7440b77b52fe006a5aef5d225054ee4f57e7f81db1dcc6","target":"record","created_at":"2026-05-18T03:45:30Z","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":"b47d084c9cf6ced0a6f8b12af2d34292ae5a543ec3119076d770b13b6c7883f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-15T21:13:03Z","title_canon_sha256":"2a2a537433d88d4c6c618574c5f00fa8eb3aceabaa9e6dbdcce8bfc6aa01f2df"},"schema_version":"1.0","source":{"id":"1209.3435","kind":"arxiv","version":1}},"canonical_sha256":"5ec30f7241af5302385f9cf644cbcd03fd18a32fc7d0fb31eb419a522564c279","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ec30f7241af5302385f9cf644cbcd03fd18a32fc7d0fb31eb419a522564c279","first_computed_at":"2026-05-18T03:45:30.981370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:30.981370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G2CCIH1RTn4VzLjnYh2ThEN8eKzEk1ntFNzAV7AYka50Gdp7l0ZeVz6yzV2AomIDGSZfLwART+Iu9B31H/WlBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:30.981819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3435","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a990d98a17ba158bec7440b77b52fe006a5aef5d225054ee4f57e7f81db1dcc6","sha256:9ac90a50a7bc77328032b2a5db07ab3aa90cf8400de71af9c43d76f22c2c204e"],"state_sha256":"963731444126d66cb86eeffaef09e6fb168f7635cdf0cddae8c494fadb23de61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PsZS9k/FYtITdMn2fCltfTaPWsh3b+vQE87rfJmLdhdOhpNtAda0ch4KMfJHtA2cee3KQNxj8StgH2mVp44mCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:37:31.644417Z","bundle_sha256":"63636652c4582e91ee4458c79039e1a5d53828edab9dcdaaf49dfe2b0af54018"}}