{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5RMFLJVTBBS4S4AGG4PN7X3USS","short_pith_number":"pith:5RMFLJVT","canonical_record":{"source":{"id":"1506.00241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-31T14:36:33Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a8eca17ce23c8660bf23d33c3ba1f6ec274b6067ebaea91b36f15e4dcc3fc9c8","abstract_canon_sha256":"6088fc99fe461d3ab879eb4ab0bf0d815db1ac3b25af1c3600d2405e4cb9cb81"},"schema_version":"1.0"},"canonical_sha256":"ec5855a6b30865c97006371edfdf7494856291c9dad9877dc3433df5213a9263","source":{"kind":"arxiv","id":"1506.00241","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00241","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00241v2","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00241","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"5RMFLJVTBBS4","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5RMFLJVTBBS4S4AG","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5RMFLJVT","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5RMFLJVTBBS4S4AGG4PN7X3USS","target":"record","payload":{"canonical_record":{"source":{"id":"1506.00241","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-31T14:36:33Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a8eca17ce23c8660bf23d33c3ba1f6ec274b6067ebaea91b36f15e4dcc3fc9c8","abstract_canon_sha256":"6088fc99fe461d3ab879eb4ab0bf0d815db1ac3b25af1c3600d2405e4cb9cb81"},"schema_version":"1.0"},"canonical_sha256":"ec5855a6b30865c97006371edfdf7494856291c9dad9877dc3433df5213a9263","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:38.212106Z","signature_b64":"r+ezpUkzn4V2JIofmsLCT+nxe2tHO9GxPNjHL6qAYk0WMQ13yN+DNXI/hGerBs5gvUhWlfjhzrBpNOmtjVL5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec5855a6b30865c97006371edfdf7494856291c9dad9877dc3433df5213a9263","last_reissued_at":"2026-05-18T01:29:38.211372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:38.211372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.00241","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":"2026-05-18T01:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eMnT+s4Yx6yYLE9kufVZzk18CWSFkV70idgz/C9oMLlWnhmjabnX5oiSTAEHc5nndq4zY0ntzZd0s6mR/faMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T14:49:21.680308Z"},"content_sha256":"aeaa208386c8b8a5419f0d56a4441b7e95f391e6ad5ea26e7838f027acb1074b","schema_version":"1.0","event_id":"sha256:aeaa208386c8b8a5419f0d56a4441b7e95f391e6ad5ea26e7838f027acb1074b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5RMFLJVTBBS4S4AGG4PN7X3USS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Favard separation method for almost periodic stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Wenhe Wang, Zhenxin Liu","submitted_at":"2015-05-31T14:36:33Z","abstract_excerpt":"Favard separation method is an important means to study almost periodic solutions to linear differential equations; later, Amerio applied Favard's idea to nonlinear differential equations. In this paper, by appropriate choosing separation and almost periodicity in distribution sense, we obtain the Favard and Amerio type theorems for stochastic differential equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00241","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":"2026-05-18T01:29:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZjIOC56VnShBG1IUtJyxfiQwESSLHMcOQAcSn7ugg7PWedwPLrQJagdsQ1Wv/ns8ilxBtR0Qv4x7C7Yei+eaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T14:49:21.680663Z"},"content_sha256":"d1575d561e3d1c6d830d2b426598ce19e21c877d048058cc1aaf2a450ef7e970","schema_version":"1.0","event_id":"sha256:d1575d561e3d1c6d830d2b426598ce19e21c877d048058cc1aaf2a450ef7e970"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RMFLJVTBBS4S4AGG4PN7X3USS/bundle.json","state_url":"https://pith.science/pith/5RMFLJVTBBS4S4AGG4PN7X3USS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RMFLJVTBBS4S4AGG4PN7X3USS/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":"2026-07-02T14:49:21Z","links":{"resolver":"https://pith.science/pith/5RMFLJVTBBS4S4AGG4PN7X3USS","bundle":"https://pith.science/pith/5RMFLJVTBBS4S4AGG4PN7X3USS/bundle.json","state":"https://pith.science/pith/5RMFLJVTBBS4S4AGG4PN7X3USS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RMFLJVTBBS4S4AGG4PN7X3USS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5RMFLJVTBBS4S4AGG4PN7X3USS","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":"6088fc99fe461d3ab879eb4ab0bf0d815db1ac3b25af1c3600d2405e4cb9cb81","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-31T14:36:33Z","title_canon_sha256":"a8eca17ce23c8660bf23d33c3ba1f6ec274b6067ebaea91b36f15e4dcc3fc9c8"},"schema_version":"1.0","source":{"id":"1506.00241","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00241","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00241v2","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00241","created_at":"2026-05-18T01:29:38Z"},{"alias_kind":"pith_short_12","alias_value":"5RMFLJVTBBS4","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5RMFLJVTBBS4S4AG","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5RMFLJVT","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:d1575d561e3d1c6d830d2b426598ce19e21c877d048058cc1aaf2a450ef7e970","target":"graph","created_at":"2026-05-18T01:29:38Z","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":"Favard separation method is an important means to study almost periodic solutions to linear differential equations; later, Amerio applied Favard's idea to nonlinear differential equations. In this paper, by appropriate choosing separation and almost periodicity in distribution sense, we obtain the Favard and Amerio type theorems for stochastic differential equations.","authors_text":"Wenhe Wang, Zhenxin Liu","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-31T14:36:33Z","title":"Favard separation method for almost periodic stochastic differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00241","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:aeaa208386c8b8a5419f0d56a4441b7e95f391e6ad5ea26e7838f027acb1074b","target":"record","created_at":"2026-05-18T01:29:38Z","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":"6088fc99fe461d3ab879eb4ab0bf0d815db1ac3b25af1c3600d2405e4cb9cb81","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-31T14:36:33Z","title_canon_sha256":"a8eca17ce23c8660bf23d33c3ba1f6ec274b6067ebaea91b36f15e4dcc3fc9c8"},"schema_version":"1.0","source":{"id":"1506.00241","kind":"arxiv","version":2}},"canonical_sha256":"ec5855a6b30865c97006371edfdf7494856291c9dad9877dc3433df5213a9263","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec5855a6b30865c97006371edfdf7494856291c9dad9877dc3433df5213a9263","first_computed_at":"2026-05-18T01:29:38.211372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:38.211372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r+ezpUkzn4V2JIofmsLCT+nxe2tHO9GxPNjHL6qAYk0WMQ13yN+DNXI/hGerBs5gvUhWlfjhzrBpNOmtjVL5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:38.212106Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00241","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeaa208386c8b8a5419f0d56a4441b7e95f391e6ad5ea26e7838f027acb1074b","sha256:d1575d561e3d1c6d830d2b426598ce19e21c877d048058cc1aaf2a450ef7e970"],"state_sha256":"cbe0a0953f5cb01cf9fc12cd901a67d978341cd409a351f8dbde05dedc27211e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6rBNpXyUMrp3Ry3bSBrAqrP9FbKKJgNLbwAz8w/mVrHhJ4vWh7EiZPpPr4YwU0HNH7yHt663lSEGfEk8OIFAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T14:49:21.683055Z","bundle_sha256":"8d458cee98c4a269e2208cc52eaeef2d23c754fb1c59ff03ce7e13817d1ebd63"}}