{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FC5F3HEJTWXQGQFUZXP2YVNL32","short_pith_number":"pith:FC5F3HEJ","canonical_record":{"source":{"id":"1506.04804","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-16T00:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"5d32029add103fa944ec95c0e9645dc4664a90c18af251c7ffca588c597fa196","abstract_canon_sha256":"c6b795b7cfd73f56e02d21b78f71891590323866b9805296893f1a589da5a057"},"schema_version":"1.0"},"canonical_sha256":"28ba5d9c899daf0340b4cddfac55abdeb5656a595f4ae2f36015b12b35e3b871","source":{"kind":"arxiv","id":"1506.04804","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04804","created_at":"2026-05-18T01:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04804v3","created_at":"2026-05-18T01:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04804","created_at":"2026-05-18T01:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"FC5F3HEJTWXQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FC5F3HEJTWXQGQFU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FC5F3HEJ","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FC5F3HEJTWXQGQFUZXP2YVNL32","target":"record","payload":{"canonical_record":{"source":{"id":"1506.04804","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-16T00:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"5d32029add103fa944ec95c0e9645dc4664a90c18af251c7ffca588c597fa196","abstract_canon_sha256":"c6b795b7cfd73f56e02d21b78f71891590323866b9805296893f1a589da5a057"},"schema_version":"1.0"},"canonical_sha256":"28ba5d9c899daf0340b4cddfac55abdeb5656a595f4ae2f36015b12b35e3b871","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:01.053002Z","signature_b64":"Lg+5Bocpi/btDz4oerlZqgdTRp5ZP9tKkSV+KslKSHL24DusJhFK/279MMGSfupeBhpi/j7aSGd5RbJxdHMACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28ba5d9c899daf0340b4cddfac55abdeb5656a595f4ae2f36015b12b35e3b871","last_reissued_at":"2026-05-18T01:21:01.052610Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:01.052610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.04804","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBG92M6fplzaxFbMIXkEk1JOfqMQl5xYYi0c3dscP4un/tHn4oBsmZaddPAfD9NXcNPwyD+lcSHPm38UkFeLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:03:36.230383Z"},"content_sha256":"fd36f7231ae44ec12a5a767904e0383662882d5883978041cf99774566936d2e","schema_version":"1.0","event_id":"sha256:fd36f7231ae44ec12a5a767904e0383662882d5883978041cf99774566936d2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FC5F3HEJTWXQGQFUZXP2YVNL32","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coupling the Kolmogorov Diffusion: maximality and efficiency considerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sayan Banerjee, Wilfrid S. Kendall","submitted_at":"2015-06-16T00:39:37Z","abstract_excerpt":"This is a case study concerning the rate at which probabilistic coupling occurs for nilpotent diffusions. We focus on the simplest case of Kolmogorov diffusion (Brownian motion together with its time integral, or, slightly more generally, together with a finite number of iterated time integrals). In this case there can be no Markovian maximal coupling. Indeed, Markovian couplings cannot even be efficient (extending the terminology of Burdzy and Kendall, Efficient Markovian couplings: examples and counterexamples; Annals of Applied Probability, 2000). Finally, at least in the classical case of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04804","kind":"arxiv","version":3},"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":"2026-05-18T01:21:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4jUrXJaF1OFIDFQcjkezh0cUT5Iw+D1K42ND+rDFCFhJytS6x78+ayrz40+1VxpxvjTxg4PWc8dgD6NpYQ3iDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:03:36.230731Z"},"content_sha256":"b38219779b4c88f97e4d858e003b0803e3bf8e439c3ef8b99f824b8c7a5810da","schema_version":"1.0","event_id":"sha256:b38219779b4c88f97e4d858e003b0803e3bf8e439c3ef8b99f824b8c7a5810da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FC5F3HEJTWXQGQFUZXP2YVNL32/bundle.json","state_url":"https://pith.science/pith/FC5F3HEJTWXQGQFUZXP2YVNL32/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FC5F3HEJTWXQGQFUZXP2YVNL32/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":"2026-06-23T19:03:36Z","links":{"resolver":"https://pith.science/pith/FC5F3HEJTWXQGQFUZXP2YVNL32","bundle":"https://pith.science/pith/FC5F3HEJTWXQGQFUZXP2YVNL32/bundle.json","state":"https://pith.science/pith/FC5F3HEJTWXQGQFUZXP2YVNL32/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FC5F3HEJTWXQGQFUZXP2YVNL32/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FC5F3HEJTWXQGQFUZXP2YVNL32","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":"c6b795b7cfd73f56e02d21b78f71891590323866b9805296893f1a589da5a057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-16T00:39:37Z","title_canon_sha256":"5d32029add103fa944ec95c0e9645dc4664a90c18af251c7ffca588c597fa196"},"schema_version":"1.0","source":{"id":"1506.04804","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04804","created_at":"2026-05-18T01:21:01Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04804v3","created_at":"2026-05-18T01:21:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04804","created_at":"2026-05-18T01:21:01Z"},{"alias_kind":"pith_short_12","alias_value":"FC5F3HEJTWXQ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FC5F3HEJTWXQGQFU","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FC5F3HEJ","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:b38219779b4c88f97e4d858e003b0803e3bf8e439c3ef8b99f824b8c7a5810da","target":"graph","created_at":"2026-05-18T01:21:01Z","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":"This is a case study concerning the rate at which probabilistic coupling occurs for nilpotent diffusions. We focus on the simplest case of Kolmogorov diffusion (Brownian motion together with its time integral, or, slightly more generally, together with a finite number of iterated time integrals). In this case there can be no Markovian maximal coupling. Indeed, Markovian couplings cannot even be efficient (extending the terminology of Burdzy and Kendall, Efficient Markovian couplings: examples and counterexamples; Annals of Applied Probability, 2000). Finally, at least in the classical case of ","authors_text":"Sayan Banerjee, Wilfrid S. Kendall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-16T00:39:37Z","title":"Coupling the Kolmogorov Diffusion: maximality and efficiency considerations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04804","kind":"arxiv","version":3},"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:fd36f7231ae44ec12a5a767904e0383662882d5883978041cf99774566936d2e","target":"record","created_at":"2026-05-18T01:21:01Z","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":"c6b795b7cfd73f56e02d21b78f71891590323866b9805296893f1a589da5a057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-16T00:39:37Z","title_canon_sha256":"5d32029add103fa944ec95c0e9645dc4664a90c18af251c7ffca588c597fa196"},"schema_version":"1.0","source":{"id":"1506.04804","kind":"arxiv","version":3}},"canonical_sha256":"28ba5d9c899daf0340b4cddfac55abdeb5656a595f4ae2f36015b12b35e3b871","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28ba5d9c899daf0340b4cddfac55abdeb5656a595f4ae2f36015b12b35e3b871","first_computed_at":"2026-05-18T01:21:01.052610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:01.052610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lg+5Bocpi/btDz4oerlZqgdTRp5ZP9tKkSV+KslKSHL24DusJhFK/279MMGSfupeBhpi/j7aSGd5RbJxdHMACA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:01.053002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04804","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd36f7231ae44ec12a5a767904e0383662882d5883978041cf99774566936d2e","sha256:b38219779b4c88f97e4d858e003b0803e3bf8e439c3ef8b99f824b8c7a5810da"],"state_sha256":"4d71eb2cc99bfec6d3af99455f9ee636e9501d5692be7bda604fa69ceb539984"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"09Zez20sxvLvoVuSb55aqF8ZkaWQP7dSMDElZz3f1LP7lcXNq1U0ptHrngORNqgDK8pkXb+WE2NQynzcMQLwAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:03:36.232698Z","bundle_sha256":"b307703bb2ec8be30d67abe99d5fe33ef4690a963c92af9fbd994ca20c710e57"}}