{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:W44TZA3MAMCRZUDMKNLW2E5FWN","short_pith_number":"pith:W44TZA3M","canonical_record":{"source":{"id":"1508.02847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-12T08:40:02Z","cross_cats_sorted":[],"title_canon_sha256":"0072ea772c2c257737fc57e28ae4569436d85170bcace21c86c591f911a33fb0","abstract_canon_sha256":"385477408400df2a3fb22e9233f3e19e9a13e39c252db302990c76ba3f5e6715"},"schema_version":"1.0"},"canonical_sha256":"b7393c836c03051cd06c53576d13a5b35284d888f17730b1d0f9a5c08238a122","source":{"kind":"arxiv","id":"1508.02847","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02847","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02847v1","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02847","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"pith_short_12","alias_value":"W44TZA3MAMCR","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W44TZA3MAMCRZUDM","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W44TZA3M","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:W44TZA3MAMCRZUDMKNLW2E5FWN","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-12T08:40:02Z","cross_cats_sorted":[],"title_canon_sha256":"0072ea772c2c257737fc57e28ae4569436d85170bcace21c86c591f911a33fb0","abstract_canon_sha256":"385477408400df2a3fb22e9233f3e19e9a13e39c252db302990c76ba3f5e6715"},"schema_version":"1.0"},"canonical_sha256":"b7393c836c03051cd06c53576d13a5b35284d888f17730b1d0f9a5c08238a122","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:23.670815Z","signature_b64":"ZJCUJisE99pRQRKqNP6R8ObdDAWHU9CQubawJUBjSQYnzL9CZougFUqyFhoUaloavRQzV3paTGnWunH1GLZDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7393c836c03051cd06c53576d13a5b35284d888f17730b1d0f9a5c08238a122","last_reissued_at":"2026-05-18T01:35:23.670184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:23.670184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02847","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":"2026-05-18T01:35:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Zx/21uIy8VWg2HejtN8gXdDmido0m6jjNo6V9T7HPGVcw3DP71Nuk9Q2R0woYVXjJ5CF/bZjD2oz7IQEKQxCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:01:34.724279Z"},"content_sha256":"7a9259902f25acdc7c63cba445b54e557bfe7fc3eb352385fa1e2ad1936ab9da","schema_version":"1.0","event_id":"sha256:7a9259902f25acdc7c63cba445b54e557bfe7fc3eb352385fa1e2ad1936ab9da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:W44TZA3MAMCRZUDMKNLW2E5FWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast $L_2$-approximation of integral-type functionals of Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Iurii Ganychenko","submitted_at":"2015-08-12T08:40:02Z","abstract_excerpt":"In this paper, we provide strong $L_2$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its transition probability density, we get the accuracy that coincides with that obtained in [3] for a one-dimensional diffusion process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02847","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":"2026-05-18T01:35:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/C+BlvvC302xlPLea/B0NeFKh6/JMMjwfZw1dP98hrJWcsQ70QetcH5+2aa85BU9Fh1tGc15Pl3/DEoqaPyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:01:34.724633Z"},"content_sha256":"fad4c66ef6ab33c008b8b5fdb49f1a44062bf2931e38189c0407b7d53a9b979c","schema_version":"1.0","event_id":"sha256:fad4c66ef6ab33c008b8b5fdb49f1a44062bf2931e38189c0407b7d53a9b979c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W44TZA3MAMCRZUDMKNLW2E5FWN/bundle.json","state_url":"https://pith.science/pith/W44TZA3MAMCRZUDMKNLW2E5FWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W44TZA3MAMCRZUDMKNLW2E5FWN/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":"2026-06-26T23:01:34Z","links":{"resolver":"https://pith.science/pith/W44TZA3MAMCRZUDMKNLW2E5FWN","bundle":"https://pith.science/pith/W44TZA3MAMCRZUDMKNLW2E5FWN/bundle.json","state":"https://pith.science/pith/W44TZA3MAMCRZUDMKNLW2E5FWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W44TZA3MAMCRZUDMKNLW2E5FWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W44TZA3MAMCRZUDMKNLW2E5FWN","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":"385477408400df2a3fb22e9233f3e19e9a13e39c252db302990c76ba3f5e6715","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-12T08:40:02Z","title_canon_sha256":"0072ea772c2c257737fc57e28ae4569436d85170bcace21c86c591f911a33fb0"},"schema_version":"1.0","source":{"id":"1508.02847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02847","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02847v1","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02847","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"pith_short_12","alias_value":"W44TZA3MAMCR","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W44TZA3MAMCRZUDM","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W44TZA3M","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:fad4c66ef6ab33c008b8b5fdb49f1a44062bf2931e38189c0407b7d53a9b979c","target":"graph","created_at":"2026-05-18T01:35:23Z","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 paper, we provide strong $L_2$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its transition probability density, we get the accuracy that coincides with that obtained in [3] for a one-dimensional diffusion process.","authors_text":"Iurii Ganychenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-12T08:40:02Z","title":"Fast $L_2$-approximation of integral-type functionals of Markov processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02847","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":"sha256:7a9259902f25acdc7c63cba445b54e557bfe7fc3eb352385fa1e2ad1936ab9da","target":"record","created_at":"2026-05-18T01:35:23Z","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":"385477408400df2a3fb22e9233f3e19e9a13e39c252db302990c76ba3f5e6715","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-08-12T08:40:02Z","title_canon_sha256":"0072ea772c2c257737fc57e28ae4569436d85170bcace21c86c591f911a33fb0"},"schema_version":"1.0","source":{"id":"1508.02847","kind":"arxiv","version":1}},"canonical_sha256":"b7393c836c03051cd06c53576d13a5b35284d888f17730b1d0f9a5c08238a122","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7393c836c03051cd06c53576d13a5b35284d888f17730b1d0f9a5c08238a122","first_computed_at":"2026-05-18T01:35:23.670184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:23.670184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZJCUJisE99pRQRKqNP6R8ObdDAWHU9CQubawJUBjSQYnzL9CZougFUqyFhoUaloavRQzV3paTGnWunH1GLZDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:23.670815Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a9259902f25acdc7c63cba445b54e557bfe7fc3eb352385fa1e2ad1936ab9da","sha256:fad4c66ef6ab33c008b8b5fdb49f1a44062bf2931e38189c0407b7d53a9b979c"],"state_sha256":"4c85fe97896bbccbaae4d12bb46be6d2b99371d06ea1237591bcf9aba6a156d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fFtghSDEj5lhf0OSgbfjCKCIro570vBI31f7jQCGl4v2rSlMtrXeSBcChNfb/ccpgaZTsFaqKw9la6V4rzxUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:01:34.726650Z","bundle_sha256":"0a3f257e86258333a5808e20402254b107910d69889fd6bf1e89716f98f341f6"}}