{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4PMCJ4NHCXZYJDTNG2V5HQ4S37","short_pith_number":"pith:4PMCJ4NH","canonical_record":{"source":{"id":"1007.3199","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-19T16:21:26Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"5700f72e11550e91f02a1f15e7cbb1ac4208eec939efaee2bb153290acd9552e","abstract_canon_sha256":"ec4c9b0d3c1ad748f757689200198f0bb0e8b9955a90013cc8e200a745c36e9c"},"schema_version":"1.0"},"canonical_sha256":"e3d824f1a715f3848e6d36abd3c392dfcc3a2aa28eb836083fde8e3d98aaeb94","source":{"kind":"arxiv","id":"1007.3199","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3199","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3199v4","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3199","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"pith_short_12","alias_value":"4PMCJ4NHCXZY","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4PMCJ4NHCXZYJDTN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4PMCJ4NH","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4PMCJ4NHCXZYJDTNG2V5HQ4S37","target":"record","payload":{"canonical_record":{"source":{"id":"1007.3199","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-19T16:21:26Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"5700f72e11550e91f02a1f15e7cbb1ac4208eec939efaee2bb153290acd9552e","abstract_canon_sha256":"ec4c9b0d3c1ad748f757689200198f0bb0e8b9955a90013cc8e200a745c36e9c"},"schema_version":"1.0"},"canonical_sha256":"e3d824f1a715f3848e6d36abd3c392dfcc3a2aa28eb836083fde8e3d98aaeb94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:54.085355Z","signature_b64":"FX5xTHWoajfSGxdYQeMpveq5bHvo32R+OZDBt0PYWvB12uRK1HZJpK0yJq4rVrF7nogJrcd4cj5s21ynNE76CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3d824f1a715f3848e6d36abd3c392dfcc3a2aa28eb836083fde8e3d98aaeb94","last_reissued_at":"2026-05-18T03:30:54.084575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:54.084575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.3199","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XK7jQ6i1WvnZ2ga2Twv2bLZzlSLvJ0gjW9vIqycW0BeU7QR4wdyuWQua8gj2n1Noz4OFL8VLt16yYVzVAbF2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:56:34.094697Z"},"content_sha256":"87bc26faee1fddc1d259c9c66ee2ac33bb0270d19a6cf614384e6fff080d55ed","schema_version":"1.0","event_id":"sha256:87bc26faee1fddc1d259c9c66ee2ac33bb0270d19a6cf614384e6fff080d55ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4PMCJ4NHCXZYJDTNG2V5HQ4S37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shy couplings, CAT(0) spaces, and the lion and man","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Krzysztof Burdzy, Maury Bramson, Wilfrid Kendall","submitted_at":"2010-07-19T16:21:26Z","abstract_excerpt":"Two random processes X and Y on a metric space are said to be $\\varepsilon$-shy coupled if there is positive probability of them staying at least a positive distance $\\varepsilon$ apart from each other forever. Interest in the literature centres on nonexistence results subject to topological and geometric conditions; motivation arises from the desire to gain a better understanding of probabilistic coupling. Previous nonexistence results for co-adapted shy coupling of reflected Brownian motion required convexity conditions; we remove these conditions by showing the nonexistence of shy co-adapte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3199","kind":"arxiv","version":4},"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":"2026-05-18T03:30:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OqU9a1M/0/1nXChX8yEV1Yz7P4fW+Jbqpxq6HHkab4Kvsk/7XlYo1zCFYnAVA79WFd1D9sxGU4WOiT4FpJfqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:56:34.095037Z"},"content_sha256":"b1cf4e8b4e23708d17d54a1ed4ce36ee8ccc0af66139182d759676b0cfa9d068","schema_version":"1.0","event_id":"sha256:b1cf4e8b4e23708d17d54a1ed4ce36ee8ccc0af66139182d759676b0cfa9d068"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4PMCJ4NHCXZYJDTNG2V5HQ4S37/bundle.json","state_url":"https://pith.science/pith/4PMCJ4NHCXZYJDTNG2V5HQ4S37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4PMCJ4NHCXZYJDTNG2V5HQ4S37/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":"2026-06-09T10:56:34Z","links":{"resolver":"https://pith.science/pith/4PMCJ4NHCXZYJDTNG2V5HQ4S37","bundle":"https://pith.science/pith/4PMCJ4NHCXZYJDTNG2V5HQ4S37/bundle.json","state":"https://pith.science/pith/4PMCJ4NHCXZYJDTNG2V5HQ4S37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4PMCJ4NHCXZYJDTNG2V5HQ4S37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4PMCJ4NHCXZYJDTNG2V5HQ4S37","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":"ec4c9b0d3c1ad748f757689200198f0bb0e8b9955a90013cc8e200a745c36e9c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-19T16:21:26Z","title_canon_sha256":"5700f72e11550e91f02a1f15e7cbb1ac4208eec939efaee2bb153290acd9552e"},"schema_version":"1.0","source":{"id":"1007.3199","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3199","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3199v4","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3199","created_at":"2026-05-18T03:30:54Z"},{"alias_kind":"pith_short_12","alias_value":"4PMCJ4NHCXZY","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4PMCJ4NHCXZYJDTN","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4PMCJ4NH","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:b1cf4e8b4e23708d17d54a1ed4ce36ee8ccc0af66139182d759676b0cfa9d068","target":"graph","created_at":"2026-05-18T03:30:54Z","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":"Two random processes X and Y on a metric space are said to be $\\varepsilon$-shy coupled if there is positive probability of them staying at least a positive distance $\\varepsilon$ apart from each other forever. Interest in the literature centres on nonexistence results subject to topological and geometric conditions; motivation arises from the desire to gain a better understanding of probabilistic coupling. Previous nonexistence results for co-adapted shy coupling of reflected Brownian motion required convexity conditions; we remove these conditions by showing the nonexistence of shy co-adapte","authors_text":"Krzysztof Burdzy, Maury Bramson, Wilfrid Kendall","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-19T16:21:26Z","title":"Shy couplings, CAT(0) spaces, and the lion and man"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3199","kind":"arxiv","version":4},"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":"sha256:87bc26faee1fddc1d259c9c66ee2ac33bb0270d19a6cf614384e6fff080d55ed","target":"record","created_at":"2026-05-18T03:30:54Z","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":"ec4c9b0d3c1ad748f757689200198f0bb0e8b9955a90013cc8e200a745c36e9c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-19T16:21:26Z","title_canon_sha256":"5700f72e11550e91f02a1f15e7cbb1ac4208eec939efaee2bb153290acd9552e"},"schema_version":"1.0","source":{"id":"1007.3199","kind":"arxiv","version":4}},"canonical_sha256":"e3d824f1a715f3848e6d36abd3c392dfcc3a2aa28eb836083fde8e3d98aaeb94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3d824f1a715f3848e6d36abd3c392dfcc3a2aa28eb836083fde8e3d98aaeb94","first_computed_at":"2026-05-18T03:30:54.084575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:54.084575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FX5xTHWoajfSGxdYQeMpveq5bHvo32R+OZDBt0PYWvB12uRK1HZJpK0yJq4rVrF7nogJrcd4cj5s21ynNE76CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:54.085355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3199","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87bc26faee1fddc1d259c9c66ee2ac33bb0270d19a6cf614384e6fff080d55ed","sha256:b1cf4e8b4e23708d17d54a1ed4ce36ee8ccc0af66139182d759676b0cfa9d068"],"state_sha256":"1067e6a78b8c26441992ed140605ee935eb2d795f988158000059014c4da8027"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kINe20vQvegljWnDQR8El7qwoalT+XvoKnRbou1ueAbrLvxiC5WpCTCi13OFF61zP6uDi5Lpsk/TSIyObaugDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:56:34.097091Z","bundle_sha256":"3c8057b8bdd3cd2a288fdebd8a1135ec360e969a1626ea6e922e76598ef5cbdb"}}