{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7RO3Y6TFWTW7UIP7CFHZCWSQI6","short_pith_number":"pith:7RO3Y6TF","canonical_record":{"source":{"id":"1708.08492","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-28T19:20:18Z","cross_cats_sorted":[],"title_canon_sha256":"b368acff268c080a008ac6d0a7718a89ede06b2e9f02c80386e6db21e401791c","abstract_canon_sha256":"af35d0b56281f1fbde129f9304a838d64b77235ea702bd221b91d5bf3a80bf01"},"schema_version":"1.0"},"canonical_sha256":"fc5dbc7a65b4edfa21ff114f915a50478eae46e63c6c8062690210b20f55bc53","source":{"kind":"arxiv","id":"1708.08492","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08492","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08492v1","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08492","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"7RO3Y6TFWTW7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7RO3Y6TFWTW7UIP7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7RO3Y6TF","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7RO3Y6TFWTW7UIP7CFHZCWSQI6","target":"record","payload":{"canonical_record":{"source":{"id":"1708.08492","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-28T19:20:18Z","cross_cats_sorted":[],"title_canon_sha256":"b368acff268c080a008ac6d0a7718a89ede06b2e9f02c80386e6db21e401791c","abstract_canon_sha256":"af35d0b56281f1fbde129f9304a838d64b77235ea702bd221b91d5bf3a80bf01"},"schema_version":"1.0"},"canonical_sha256":"fc5dbc7a65b4edfa21ff114f915a50478eae46e63c6c8062690210b20f55bc53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:27.590564Z","signature_b64":"76+H6/LCc4ZAcn2t7d3FBBufd3KM/S6hBOc5PV3rYTJOT04zYGkEI/9i/mpvKiLq7OA21zWkjolsz+dEyxKzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc5dbc7a65b4edfa21ff114f915a50478eae46e63c6c8062690210b20f55bc53","last_reissued_at":"2026-05-18T00:36:27.589832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:27.589832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.08492","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":"2026-05-18T00:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f1qRamadUazi3Xtfw0zVokdwzgHxsur4ZA3vO8zshqEQkNaSbKIpAU43FGLdOhQHjg9ki8cdbAoecE8qZ89tCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:17:58.578581Z"},"content_sha256":"1949a50e035098f297f41bcc271640a4c06e02d83bce2d2e5069e574364ca4a6","schema_version":"1.0","event_id":"sha256:1949a50e035098f297f41bcc271640a4c06e02d83bce2d2e5069e574364ca4a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7RO3Y6TFWTW7UIP7CFHZCWSQI6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Martingale approximations for random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Magda Peligrad, Na Zhang","submitted_at":"2017-08-28T19:20:18Z","abstract_excerpt":"In this paper we provide necessary and sufficient conditions for the mean square approximation of a random field with an ortho-martingale. The conditions are formulated in terms of projective criteria. Applications are given to linear and nonlinear random fields with independent innovations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08492","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":"2026-05-18T00:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g8k4IeIZ4MvuDwmqP5ADgKrbnFZEh+EIuQftxeCZXI2j83lJ1DagHw/CHwqecFMHFVxEK2Uuw1Fedw55EBvWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:17:58.578929Z"},"content_sha256":"d32a7419b8473f62bf33a9ec1137215b5190e1eb3dae2ee9c482f96272564ee0","schema_version":"1.0","event_id":"sha256:d32a7419b8473f62bf33a9ec1137215b5190e1eb3dae2ee9c482f96272564ee0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RO3Y6TFWTW7UIP7CFHZCWSQI6/bundle.json","state_url":"https://pith.science/pith/7RO3Y6TFWTW7UIP7CFHZCWSQI6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RO3Y6TFWTW7UIP7CFHZCWSQI6/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":"2026-05-25T22:17:58Z","links":{"resolver":"https://pith.science/pith/7RO3Y6TFWTW7UIP7CFHZCWSQI6","bundle":"https://pith.science/pith/7RO3Y6TFWTW7UIP7CFHZCWSQI6/bundle.json","state":"https://pith.science/pith/7RO3Y6TFWTW7UIP7CFHZCWSQI6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RO3Y6TFWTW7UIP7CFHZCWSQI6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7RO3Y6TFWTW7UIP7CFHZCWSQI6","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":"af35d0b56281f1fbde129f9304a838d64b77235ea702bd221b91d5bf3a80bf01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-28T19:20:18Z","title_canon_sha256":"b368acff268c080a008ac6d0a7718a89ede06b2e9f02c80386e6db21e401791c"},"schema_version":"1.0","source":{"id":"1708.08492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08492","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08492v1","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08492","created_at":"2026-05-18T00:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"7RO3Y6TFWTW7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7RO3Y6TFWTW7UIP7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7RO3Y6TF","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:d32a7419b8473f62bf33a9ec1137215b5190e1eb3dae2ee9c482f96272564ee0","target":"graph","created_at":"2026-05-18T00:36:27Z","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 necessary and sufficient conditions for the mean square approximation of a random field with an ortho-martingale. The conditions are formulated in terms of projective criteria. Applications are given to linear and nonlinear random fields with independent innovations.","authors_text":"Magda Peligrad, Na Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-28T19:20:18Z","title":"Martingale approximations for random fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08492","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":"sha256:1949a50e035098f297f41bcc271640a4c06e02d83bce2d2e5069e574364ca4a6","target":"record","created_at":"2026-05-18T00:36:27Z","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":"af35d0b56281f1fbde129f9304a838d64b77235ea702bd221b91d5bf3a80bf01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-28T19:20:18Z","title_canon_sha256":"b368acff268c080a008ac6d0a7718a89ede06b2e9f02c80386e6db21e401791c"},"schema_version":"1.0","source":{"id":"1708.08492","kind":"arxiv","version":1}},"canonical_sha256":"fc5dbc7a65b4edfa21ff114f915a50478eae46e63c6c8062690210b20f55bc53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc5dbc7a65b4edfa21ff114f915a50478eae46e63c6c8062690210b20f55bc53","first_computed_at":"2026-05-18T00:36:27.589832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:27.589832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"76+H6/LCc4ZAcn2t7d3FBBufd3KM/S6hBOc5PV3rYTJOT04zYGkEI/9i/mpvKiLq7OA21zWkjolsz+dEyxKzAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:27.590564Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1949a50e035098f297f41bcc271640a4c06e02d83bce2d2e5069e574364ca4a6","sha256:d32a7419b8473f62bf33a9ec1137215b5190e1eb3dae2ee9c482f96272564ee0"],"state_sha256":"15146f3b86945f778a5617e01c5cc27e210d6e5c99dd37c103eb32ee0cb42442"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ALI3e6WqCv7IShv1gCszMJpmlkcsJ9LtJLDrxnc17kostYFj0DxxIMM8NgglARS0JFCVu0+1VjknpWibiGk0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:17:58.582399Z","bundle_sha256":"f40f230ebbc00c45a939e42d3eadacbf271f8b40f46cf058e3e7106466e8392a"}}