{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4332WUSDKEIK2H4HZTAJSZTP3E","short_pith_number":"pith:4332WUSD","canonical_record":{"source":{"id":"1705.02319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-05T17:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"229e30533a1e0fd10157822b0bb8a6040dd91f10734ad39ed4928dfd0c9d926e","abstract_canon_sha256":"676f9d18fee1e28b3447159c2f4fe673a3e23f6903a89a110525788302757f22"},"schema_version":"1.0"},"canonical_sha256":"e6f7ab52435110ad1f87ccc099666fd90ece37ef4a578231586b9e221dd14a6c","source":{"kind":"arxiv","id":"1705.02319","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02319","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02319v1","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02319","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"4332WUSDKEIK","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4332WUSDKEIK2H4H","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4332WUSD","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4332WUSDKEIK2H4HZTAJSZTP3E","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-05T17:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"229e30533a1e0fd10157822b0bb8a6040dd91f10734ad39ed4928dfd0c9d926e","abstract_canon_sha256":"676f9d18fee1e28b3447159c2f4fe673a3e23f6903a89a110525788302757f22"},"schema_version":"1.0"},"canonical_sha256":"e6f7ab52435110ad1f87ccc099666fd90ece37ef4a578231586b9e221dd14a6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:58.587840Z","signature_b64":"V39jPR4ac2TFHMRYUUVTgB3+F8Mm6H9Mhi/vt0/A5rMNd2Xnv7RhX3AB6QNsSDcc5fs23R7Moy0re+pST4NmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6f7ab52435110ad1f87ccc099666fd90ece37ef4a578231586b9e221dd14a6c","last_reissued_at":"2026-05-18T00:44:58.587405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:58.587405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02319","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":"2026-05-18T00:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bCoqZ6ORKZqVQFLnmZuS0GM7OXhc7TBzEVtlLBNwE/qbjEZiuFRc78oFiQ0ohqq8mRoVGMoMgxkMqvYT3mFSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T20:34:57.451786Z"},"content_sha256":"5ea838770bf0cdd6bce735ed5fcd26b97bea0f0aea92d21b4ae55842db27a9a7","schema_version":"1.0","event_id":"sha256:5ea838770bf0cdd6bce735ed5fcd26b97bea0f0aea92d21b4ae55842db27a9a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4332WUSDKEIK2H4HZTAJSZTP3E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optical Costas loop: pull-in range estimation and hidden oscillations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"G.A. Leonov, M.V. Yuldashev, N.V. Kuznetsov, R.V. Yuldashev, S.M. Seledzhi","submitted_at":"2017-05-05T17:41:35Z","abstract_excerpt":"In this work we consider a mathematical model of the optical Costas loop. The pull-in range of the model is estimated by analytical and numerical methods. Difficulties of numerical analysis, related to the existence of so-called hidden oscillations in the phase space, are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02319","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":"2026-05-18T00:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JG+BM1FfcUrUxhXYqeGcYHimkKoSQrzKQSaCzEU6TCk6XwprmOescwnJaYwNE3TqnJTn8dx9PMjfBpd7gXXzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T20:34:57.452124Z"},"content_sha256":"c2fc1fa1b6ae1653f461e709a4b6b6dbdbfdd26d53d63343c48ec1cbf84b733b","schema_version":"1.0","event_id":"sha256:c2fc1fa1b6ae1653f461e709a4b6b6dbdbfdd26d53d63343c48ec1cbf84b733b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4332WUSDKEIK2H4HZTAJSZTP3E/bundle.json","state_url":"https://pith.science/pith/4332WUSDKEIK2H4HZTAJSZTP3E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4332WUSDKEIK2H4HZTAJSZTP3E/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":"2026-05-19T20:34:57Z","links":{"resolver":"https://pith.science/pith/4332WUSDKEIK2H4HZTAJSZTP3E","bundle":"https://pith.science/pith/4332WUSDKEIK2H4HZTAJSZTP3E/bundle.json","state":"https://pith.science/pith/4332WUSDKEIK2H4HZTAJSZTP3E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4332WUSDKEIK2H4HZTAJSZTP3E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4332WUSDKEIK2H4HZTAJSZTP3E","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":"676f9d18fee1e28b3447159c2f4fe673a3e23f6903a89a110525788302757f22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-05T17:41:35Z","title_canon_sha256":"229e30533a1e0fd10157822b0bb8a6040dd91f10734ad39ed4928dfd0c9d926e"},"schema_version":"1.0","source":{"id":"1705.02319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02319","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02319v1","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02319","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"4332WUSDKEIK","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4332WUSDKEIK2H4H","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4332WUSD","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:c2fc1fa1b6ae1653f461e709a4b6b6dbdbfdd26d53d63343c48ec1cbf84b733b","target":"graph","created_at":"2026-05-18T00:44:58Z","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 this work we consider a mathematical model of the optical Costas loop. The pull-in range of the model is estimated by analytical and numerical methods. Difficulties of numerical analysis, related to the existence of so-called hidden oscillations in the phase space, are discussed.","authors_text":"G.A. Leonov, M.V. Yuldashev, N.V. Kuznetsov, R.V. Yuldashev, S.M. Seledzhi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-05T17:41:35Z","title":"Optical Costas loop: pull-in range estimation and hidden oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02319","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":"sha256:5ea838770bf0cdd6bce735ed5fcd26b97bea0f0aea92d21b4ae55842db27a9a7","target":"record","created_at":"2026-05-18T00:44:58Z","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":"676f9d18fee1e28b3447159c2f4fe673a3e23f6903a89a110525788302757f22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-05T17:41:35Z","title_canon_sha256":"229e30533a1e0fd10157822b0bb8a6040dd91f10734ad39ed4928dfd0c9d926e"},"schema_version":"1.0","source":{"id":"1705.02319","kind":"arxiv","version":1}},"canonical_sha256":"e6f7ab52435110ad1f87ccc099666fd90ece37ef4a578231586b9e221dd14a6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6f7ab52435110ad1f87ccc099666fd90ece37ef4a578231586b9e221dd14a6c","first_computed_at":"2026-05-18T00:44:58.587405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:58.587405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V39jPR4ac2TFHMRYUUVTgB3+F8Mm6H9Mhi/vt0/A5rMNd2Xnv7RhX3AB6QNsSDcc5fs23R7Moy0re+pST4NmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:58.587840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ea838770bf0cdd6bce735ed5fcd26b97bea0f0aea92d21b4ae55842db27a9a7","sha256:c2fc1fa1b6ae1653f461e709a4b6b6dbdbfdd26d53d63343c48ec1cbf84b733b"],"state_sha256":"4f1d902bddd2997a721afdeb4ebad5181937c8affc938bc2fd5aff3c3e3375c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZP1+3yiqGN6CoLLl5SzVLG8ABkD9s2iADgj/g3tvsMPUsdZedW9YF9PTsH8DgHlJ3Rbq8EbCssGQYmDf9OBDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T20:34:57.454187Z","bundle_sha256":"491f4bd19411380e98e8c1fac082b41aa21af73625d1b52f68d86ea01c1b2d1e"}}