{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VZ7O5D6LUQXGTSYADLYH44Z2PQ","short_pith_number":"pith:VZ7O5D6L","canonical_record":{"source":{"id":"1206.4350","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-19T22:20:56Z","cross_cats_sorted":[],"title_canon_sha256":"59754b9b608019bc88e46677bdf65bc237191a831e7966dd154eb357a7dc939b","abstract_canon_sha256":"106afcaa9efce92beea44990aa373dda2fc57d09eaa1be94bbf1f0a961685d7f"},"schema_version":"1.0"},"canonical_sha256":"ae7eee8fcba42e69cb001af07e733a7c1654112d46ad1d43c198cf06acc9fe35","source":{"kind":"arxiv","id":"1206.4350","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4350","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4350v2","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4350","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"VZ7O5D6LUQXG","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VZ7O5D6LUQXGTSYA","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VZ7O5D6L","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VZ7O5D6LUQXGTSYADLYH44Z2PQ","target":"record","payload":{"canonical_record":{"source":{"id":"1206.4350","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-19T22:20:56Z","cross_cats_sorted":[],"title_canon_sha256":"59754b9b608019bc88e46677bdf65bc237191a831e7966dd154eb357a7dc939b","abstract_canon_sha256":"106afcaa9efce92beea44990aa373dda2fc57d09eaa1be94bbf1f0a961685d7f"},"schema_version":"1.0"},"canonical_sha256":"ae7eee8fcba42e69cb001af07e733a7c1654112d46ad1d43c198cf06acc9fe35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:13.221433Z","signature_b64":"9Z6grsywErT3zza0oxuST0WX2dkpbAKbZxTglYli08vltBOaQY/ZV/HO2Yue8yjZ11VY0aApFkI3XLN8c5CGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae7eee8fcba42e69cb001af07e733a7c1654112d46ad1d43c198cf06acc9fe35","last_reissued_at":"2026-05-18T03:48:13.220578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:13.220578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.4350","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:48:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"98566SfO32D/Yuo1X0LGzPfahMDj+pSUzc/CKGiKJ51XMDejPNgDHFuACpsNHSPgSdQPhDyzjASshIbk8e9bAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:38:32.958598Z"},"content_sha256":"a5b9905f488072587984f829ab0636c12b3396e0774d33fb4dbd864d7e5943fe","schema_version":"1.0","event_id":"sha256:a5b9905f488072587984f829ab0636c12b3396e0774d33fb4dbd864d7e5943fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VZ7O5D6LUQXGTSYADLYH44Z2PQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two Brownian Particles with Rank-Based Characteristics and Skew-Elastic Collisions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Robert Fernholz, Ioannis Karatzas, Tomoyuki Ichiba","submitted_at":"2012-06-19T22:20:56Z","abstract_excerpt":"We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic collision, to perfect reflection of one particle on the other. These interactions are governed by the left- and right-local times at the origin for the distance between the two particles. We realize this diffusion in terms of appropriate, apparently novel systems of stochastic differential equations involving local times, which we show are well posed. Questions of p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4350","kind":"arxiv","version":2},"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":"2026-05-18T03:48:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ptdlST/OxcFc4L5mrOqWqX8pLuX7GVJiR2zQU/dHXyzqd2dBFidN7/ECiEKEmKocsMBhekd95ZsrV4Vjhx6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:38:32.959385Z"},"content_sha256":"619192ad220c99ef3c14e1f627cf86b0eb770040d93a1e630b7cbfd8245e4c3d","schema_version":"1.0","event_id":"sha256:619192ad220c99ef3c14e1f627cf86b0eb770040d93a1e630b7cbfd8245e4c3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZ7O5D6LUQXGTSYADLYH44Z2PQ/bundle.json","state_url":"https://pith.science/pith/VZ7O5D6LUQXGTSYADLYH44Z2PQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZ7O5D6LUQXGTSYADLYH44Z2PQ/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":"2026-05-26T20:38:32Z","links":{"resolver":"https://pith.science/pith/VZ7O5D6LUQXGTSYADLYH44Z2PQ","bundle":"https://pith.science/pith/VZ7O5D6LUQXGTSYADLYH44Z2PQ/bundle.json","state":"https://pith.science/pith/VZ7O5D6LUQXGTSYADLYH44Z2PQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZ7O5D6LUQXGTSYADLYH44Z2PQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VZ7O5D6LUQXGTSYADLYH44Z2PQ","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":"106afcaa9efce92beea44990aa373dda2fc57d09eaa1be94bbf1f0a961685d7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-19T22:20:56Z","title_canon_sha256":"59754b9b608019bc88e46677bdf65bc237191a831e7966dd154eb357a7dc939b"},"schema_version":"1.0","source":{"id":"1206.4350","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4350","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4350v2","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4350","created_at":"2026-05-18T03:48:13Z"},{"alias_kind":"pith_short_12","alias_value":"VZ7O5D6LUQXG","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VZ7O5D6LUQXGTSYA","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VZ7O5D6L","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:619192ad220c99ef3c14e1f627cf86b0eb770040d93a1e630b7cbfd8245e4c3d","target":"graph","created_at":"2026-05-18T03:48:13Z","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":"We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic collision, to perfect reflection of one particle on the other. These interactions are governed by the left- and right-local times at the origin for the distance between the two particles. We realize this diffusion in terms of appropriate, apparently novel systems of stochastic differential equations involving local times, which we show are well posed. Questions of p","authors_text":"E. Robert Fernholz, Ioannis Karatzas, Tomoyuki Ichiba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-19T22:20:56Z","title":"Two Brownian Particles with Rank-Based Characteristics and Skew-Elastic Collisions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4350","kind":"arxiv","version":2},"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:a5b9905f488072587984f829ab0636c12b3396e0774d33fb4dbd864d7e5943fe","target":"record","created_at":"2026-05-18T03:48:13Z","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":"106afcaa9efce92beea44990aa373dda2fc57d09eaa1be94bbf1f0a961685d7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-19T22:20:56Z","title_canon_sha256":"59754b9b608019bc88e46677bdf65bc237191a831e7966dd154eb357a7dc939b"},"schema_version":"1.0","source":{"id":"1206.4350","kind":"arxiv","version":2}},"canonical_sha256":"ae7eee8fcba42e69cb001af07e733a7c1654112d46ad1d43c198cf06acc9fe35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae7eee8fcba42e69cb001af07e733a7c1654112d46ad1d43c198cf06acc9fe35","first_computed_at":"2026-05-18T03:48:13.220578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:13.220578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Z6grsywErT3zza0oxuST0WX2dkpbAKbZxTglYli08vltBOaQY/ZV/HO2Yue8yjZ11VY0aApFkI3XLN8c5CGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:13.221433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4350","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5b9905f488072587984f829ab0636c12b3396e0774d33fb4dbd864d7e5943fe","sha256:619192ad220c99ef3c14e1f627cf86b0eb770040d93a1e630b7cbfd8245e4c3d"],"state_sha256":"65fc2f524b8a15829b394f93dab32b54ca1ff791db4c11539674f234bcaf965e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NX0KtM/bPelo3MNtj3f5xfNNL2VCsbWHUaWpivSr6leNe+msNooICPXvfXSBLzocuSObF6X+wZ7iGX3SgusGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:38:32.962902Z","bundle_sha256":"75a5e9447865f0ecadccf50b949edecd8a8843aae12051f5d0855f7e80118ca4"}}