{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KHZIT7YSTC3VCDVZ7WOE6DFUXH","short_pith_number":"pith:KHZIT7YS","canonical_record":{"source":{"id":"1705.08300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-23T14:18:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a386869d8c6cc39d6c13647d68eb521fac29b0e294635653e075d26909ce2792","abstract_canon_sha256":"74465384eb016b6af508bd0a440ac847dd904672a0e11f8237f4e42c56695d17"},"schema_version":"1.0"},"canonical_sha256":"51f289ff1298b7510eb9fd9c4f0cb4b9e6f40cb5f6557accf2ed728f6cdc4382","source":{"kind":"arxiv","id":"1705.08300","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08300","created_at":"2026-05-18T00:43:48Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08300v1","created_at":"2026-05-18T00:43:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08300","created_at":"2026-05-18T00:43:48Z"},{"alias_kind":"pith_short_12","alias_value":"KHZIT7YSTC3V","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KHZIT7YSTC3VCDVZ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KHZIT7YS","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KHZIT7YSTC3VCDVZ7WOE6DFUXH","target":"record","payload":{"canonical_record":{"source":{"id":"1705.08300","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-23T14:18:38Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a386869d8c6cc39d6c13647d68eb521fac29b0e294635653e075d26909ce2792","abstract_canon_sha256":"74465384eb016b6af508bd0a440ac847dd904672a0e11f8237f4e42c56695d17"},"schema_version":"1.0"},"canonical_sha256":"51f289ff1298b7510eb9fd9c4f0cb4b9e6f40cb5f6557accf2ed728f6cdc4382","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:48.704161Z","signature_b64":"JBCVL33jvHEW9uIF4urTLBqvwJBN/1f37thFaw72YpkxwPALqiPxTmlYDX8+xXj/eML+IqgRI8YCBZPVTPo7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51f289ff1298b7510eb9fd9c4f0cb4b9e6f40cb5f6557accf2ed728f6cdc4382","last_reissued_at":"2026-05-18T00:43:48.703554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:48.703554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.08300","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":"2026-05-18T00:43:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0cTd4Hu1eYjwGFNgmH3o4VKVs5wtwSmMviEdeyPzRIFxhKQYKbimT2H9r9w+46hc9aAUEp65TfVHbQc7b9ArBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:23:05.615543Z"},"content_sha256":"6e4634d31090ac7bfb311494ac22c0724af6986ed2262af6eae65a7969b464a7","schema_version":"1.0","event_id":"sha256:6e4634d31090ac7bfb311494ac22c0724af6986ed2262af6eae65a7969b464a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KHZIT7YSTC3VCDVZ7WOE6DFUXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coupling of Brownian motions in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Elisabetta Candellero, Wilfrid S. Kendall","submitted_at":"2017-05-23T14:18:38Z","abstract_excerpt":"Consider a separable Banach space $ \\mathcal{W}$ supporting a non-trivial Gaussian measure $\\mu$. The following is an immediate consequence of the theory of Gaussian measure on Banach spaces: there exist (almost surely) successful couplings of two $\\mathcal{W}$-valued Brownian motions $ \\mathbf{B}$ and $\\widetilde{\\mathbf{B}}$ begun at starting points $\\mathbf{B}(0)$ and $\\widetilde{\\mathbf{B}}(0)$ if and only if the difference $\\mathbf{B}(0)-\\widetilde{\\mathbf{B}}(0)$ of their initial positions belongs to the Cameron-Martin space $\\mathcal{H}_{\\mu} $ of $\\mathcal{W}$ corresponding to $\\mu$. F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08300","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":"2026-05-18T00:43:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ArVnyhvauCwVG4QFRh7jmrUIIhzD71gKoNNPNBAU8sMIk7yKSdvKgSYvxLWB6haQsUi9Pw8sMveQcNfI4qyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:23:05.615889Z"},"content_sha256":"97c56e90c6a1499267e346cbe3adcaeec43c1eaf74494b4ecb3768bfe670ecab","schema_version":"1.0","event_id":"sha256:97c56e90c6a1499267e346cbe3adcaeec43c1eaf74494b4ecb3768bfe670ecab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KHZIT7YSTC3VCDVZ7WOE6DFUXH/bundle.json","state_url":"https://pith.science/pith/KHZIT7YSTC3VCDVZ7WOE6DFUXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KHZIT7YSTC3VCDVZ7WOE6DFUXH/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":"2026-06-23T15:23:05Z","links":{"resolver":"https://pith.science/pith/KHZIT7YSTC3VCDVZ7WOE6DFUXH","bundle":"https://pith.science/pith/KHZIT7YSTC3VCDVZ7WOE6DFUXH/bundle.json","state":"https://pith.science/pith/KHZIT7YSTC3VCDVZ7WOE6DFUXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KHZIT7YSTC3VCDVZ7WOE6DFUXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KHZIT7YSTC3VCDVZ7WOE6DFUXH","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":"74465384eb016b6af508bd0a440ac847dd904672a0e11f8237f4e42c56695d17","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-23T14:18:38Z","title_canon_sha256":"a386869d8c6cc39d6c13647d68eb521fac29b0e294635653e075d26909ce2792"},"schema_version":"1.0","source":{"id":"1705.08300","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08300","created_at":"2026-05-18T00:43:48Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08300v1","created_at":"2026-05-18T00:43:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08300","created_at":"2026-05-18T00:43:48Z"},{"alias_kind":"pith_short_12","alias_value":"KHZIT7YSTC3V","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KHZIT7YSTC3VCDVZ","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KHZIT7YS","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:97c56e90c6a1499267e346cbe3adcaeec43c1eaf74494b4ecb3768bfe670ecab","target":"graph","created_at":"2026-05-18T00:43:48Z","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":"Consider a separable Banach space $ \\mathcal{W}$ supporting a non-trivial Gaussian measure $\\mu$. The following is an immediate consequence of the theory of Gaussian measure on Banach spaces: there exist (almost surely) successful couplings of two $\\mathcal{W}$-valued Brownian motions $ \\mathbf{B}$ and $\\widetilde{\\mathbf{B}}$ begun at starting points $\\mathbf{B}(0)$ and $\\widetilde{\\mathbf{B}}(0)$ if and only if the difference $\\mathbf{B}(0)-\\widetilde{\\mathbf{B}}(0)$ of their initial positions belongs to the Cameron-Martin space $\\mathcal{H}_{\\mu} $ of $\\mathcal{W}$ corresponding to $\\mu$. F","authors_text":"Elisabetta Candellero, Wilfrid S. Kendall","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-23T14:18:38Z","title":"Coupling of Brownian motions in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08300","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":"sha256:6e4634d31090ac7bfb311494ac22c0724af6986ed2262af6eae65a7969b464a7","target":"record","created_at":"2026-05-18T00:43:48Z","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":"74465384eb016b6af508bd0a440ac847dd904672a0e11f8237f4e42c56695d17","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-23T14:18:38Z","title_canon_sha256":"a386869d8c6cc39d6c13647d68eb521fac29b0e294635653e075d26909ce2792"},"schema_version":"1.0","source":{"id":"1705.08300","kind":"arxiv","version":1}},"canonical_sha256":"51f289ff1298b7510eb9fd9c4f0cb4b9e6f40cb5f6557accf2ed728f6cdc4382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51f289ff1298b7510eb9fd9c4f0cb4b9e6f40cb5f6557accf2ed728f6cdc4382","first_computed_at":"2026-05-18T00:43:48.703554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:48.703554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JBCVL33jvHEW9uIF4urTLBqvwJBN/1f37thFaw72YpkxwPALqiPxTmlYDX8+xXj/eML+IqgRI8YCBZPVTPo7Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:48.704161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08300","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e4634d31090ac7bfb311494ac22c0724af6986ed2262af6eae65a7969b464a7","sha256:97c56e90c6a1499267e346cbe3adcaeec43c1eaf74494b4ecb3768bfe670ecab"],"state_sha256":"63cf9d267926d257ce973cc4a3986cdc33fac27a6298373ab9ca646e833c51e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"chd3pc6WpED6TC8vsyFbYJMPJvAygFXpCkVo6MeYSmgtkVtj3KbprI4c5oWfwYsJUlUGwRiljMjyVgCjnAmFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:23:05.617871Z","bundle_sha256":"a81492d18ff9339580a3ae2defdcede24414a6923d5a1e4a268a4d075d483577"}}