{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6C5K2GDE3OEHEE4EX5GQ54QMC5","short_pith_number":"pith:6C5K2GDE","canonical_record":{"source":{"id":"1610.08715","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T11:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"a5e3a5a19eafa841a02061998094059ef797ad69afdd8e5b1a3e1aac51c98b5c","abstract_canon_sha256":"cd5bc94def92efbfe527be8f786f1ca87f74e1ba16401aed33348a26db1c54a8"},"schema_version":"1.0"},"canonical_sha256":"f0baad1864db88721384bf4d0ef20c1759b9496b044ee8cbbc8ece6ba9799c6c","source":{"kind":"arxiv","id":"1610.08715","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08715","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08715v2","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08715","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"pith_short_12","alias_value":"6C5K2GDE3OEH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6C5K2GDE3OEHEE4E","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6C5K2GDE","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6C5K2GDE3OEHEE4EX5GQ54QMC5","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08715","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T11:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"a5e3a5a19eafa841a02061998094059ef797ad69afdd8e5b1a3e1aac51c98b5c","abstract_canon_sha256":"cd5bc94def92efbfe527be8f786f1ca87f74e1ba16401aed33348a26db1c54a8"},"schema_version":"1.0"},"canonical_sha256":"f0baad1864db88721384bf4d0ef20c1759b9496b044ee8cbbc8ece6ba9799c6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:41.648571Z","signature_b64":"Brom0+11IHZzIkOa9Fo3TbjoYhOIeNVYFdPsQys4skm+QM2j9zxRx2VKKaMEJ7gEb947gtxxQXWlBOdjFD3yCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0baad1864db88721384bf4d0ef20c1759b9496b044ee8cbbc8ece6ba9799c6c","last_reissued_at":"2026-05-18T01:00:41.648204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:41.648204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08715","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":"2026-05-18T01:00:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nTfeEjA0qIEsp27fCJeBxUA8pu7STtPUaCXOsMQGDBXxijK14602xBMEjV1V6raMSD8Mgwk9QEII3vm6gkWjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:42:32.506773Z"},"content_sha256":"3469d4ab038f308e33c126831fe4ea60e0a4fcb28ab1553d2d64634fee7c5cca","schema_version":"1.0","event_id":"sha256:3469d4ab038f308e33c126831fe4ea60e0a4fcb28ab1553d2d64634fee7c5cca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6C5K2GDE3OEHEE4EX5GQ54QMC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The procedure of excluding of the nonlinear trend fir the models described by stochastic differential and difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Markova, V. Konakov","submitted_at":"2016-10-27T11:30:32Z","abstract_excerpt":"We consider the diffusion process and its approximation by Markov chain with nonlinear increasing trends. The usual parametrix method is not appliable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear growing trend and move to stochastic differential equation with reduced drift and diffusion coefficients. A similar procedure is considered for a Markov chain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08715","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":"2026-05-18T01:00:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mloVv4XeZGV8LMAGuZlgkH8DXY//7QOJyEq6kQQYRxKut5NPZ3z/BiDRXwTJ5vnsUFyGTl+f3f56RnH5tTfUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:42:32.507145Z"},"content_sha256":"88f17a0a3fb4734c940f9fc8262ba2fb020bd3ea7bba0abc411d86b1ac4f3795","schema_version":"1.0","event_id":"sha256:88f17a0a3fb4734c940f9fc8262ba2fb020bd3ea7bba0abc411d86b1ac4f3795"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6C5K2GDE3OEHEE4EX5GQ54QMC5/bundle.json","state_url":"https://pith.science/pith/6C5K2GDE3OEHEE4EX5GQ54QMC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6C5K2GDE3OEHEE4EX5GQ54QMC5/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":"2026-06-22T20:42:32Z","links":{"resolver":"https://pith.science/pith/6C5K2GDE3OEHEE4EX5GQ54QMC5","bundle":"https://pith.science/pith/6C5K2GDE3OEHEE4EX5GQ54QMC5/bundle.json","state":"https://pith.science/pith/6C5K2GDE3OEHEE4EX5GQ54QMC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6C5K2GDE3OEHEE4EX5GQ54QMC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6C5K2GDE3OEHEE4EX5GQ54QMC5","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":"cd5bc94def92efbfe527be8f786f1ca87f74e1ba16401aed33348a26db1c54a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T11:30:32Z","title_canon_sha256":"a5e3a5a19eafa841a02061998094059ef797ad69afdd8e5b1a3e1aac51c98b5c"},"schema_version":"1.0","source":{"id":"1610.08715","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08715","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08715v2","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08715","created_at":"2026-05-18T01:00:41Z"},{"alias_kind":"pith_short_12","alias_value":"6C5K2GDE3OEH","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6C5K2GDE3OEHEE4E","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6C5K2GDE","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:88f17a0a3fb4734c940f9fc8262ba2fb020bd3ea7bba0abc411d86b1ac4f3795","target":"graph","created_at":"2026-05-18T01:00:41Z","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 consider the diffusion process and its approximation by Markov chain with nonlinear increasing trends. The usual parametrix method is not appliable because these models have unbounded trends. We describe a procedure that allows to exclude nonlinear growing trend and move to stochastic differential equation with reduced drift and diffusion coefficients. A similar procedure is considered for a Markov chain","authors_text":"A. Markova, V. Konakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T11:30:32Z","title":"The procedure of excluding of the nonlinear trend fir the models described by stochastic differential and difference equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08715","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":"sha256:3469d4ab038f308e33c126831fe4ea60e0a4fcb28ab1553d2d64634fee7c5cca","target":"record","created_at":"2026-05-18T01:00:41Z","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":"cd5bc94def92efbfe527be8f786f1ca87f74e1ba16401aed33348a26db1c54a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-27T11:30:32Z","title_canon_sha256":"a5e3a5a19eafa841a02061998094059ef797ad69afdd8e5b1a3e1aac51c98b5c"},"schema_version":"1.0","source":{"id":"1610.08715","kind":"arxiv","version":2}},"canonical_sha256":"f0baad1864db88721384bf4d0ef20c1759b9496b044ee8cbbc8ece6ba9799c6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0baad1864db88721384bf4d0ef20c1759b9496b044ee8cbbc8ece6ba9799c6c","first_computed_at":"2026-05-18T01:00:41.648204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:41.648204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Brom0+11IHZzIkOa9Fo3TbjoYhOIeNVYFdPsQys4skm+QM2j9zxRx2VKKaMEJ7gEb947gtxxQXWlBOdjFD3yCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:41.648571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08715","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3469d4ab038f308e33c126831fe4ea60e0a4fcb28ab1553d2d64634fee7c5cca","sha256:88f17a0a3fb4734c940f9fc8262ba2fb020bd3ea7bba0abc411d86b1ac4f3795"],"state_sha256":"f397ab88b07f46e6de043e04bb8762449f346feb45beb9714f2f4bbebfcaf3ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eR69ZIBXnnCJSni4vN5nS++CgTSpK+WB+WXqU/1SBwYEG/GMu0afqcq2woLY7nUWvtECHQiSABTHGepCBAgLBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:42:32.509108Z","bundle_sha256":"59957aaaebe4ca51c000cf747b07058bb12c6a6992752ea7c87354c4c26b9d45"}}