{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:7EHC5GVN5GXEY3HOWGDIHT5L2A","short_pith_number":"pith:7EHC5GVN","canonical_record":{"source":{"id":"1902.08481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-22T13:12:07Z","cross_cats_sorted":[],"title_canon_sha256":"e6519f4329030e00fdd3a669246f0494b3de9c0340398e1d67dc5c6ddb9e7d56","abstract_canon_sha256":"ec5d20c77ff675e08e94bfe0c4005a52b85096610a56dad2607d3d306ac8553c"},"schema_version":"1.0"},"canonical_sha256":"f90e2e9aade9ae4c6ceeb18683cfabd020464948cfefd5dcf14bb4329f057cef","source":{"kind":"arxiv","id":"1902.08481","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08481","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08481v1","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08481","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"7EHC5GVN5GXE","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7EHC5GVN5GXEY3HO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7EHC5GVN","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:7EHC5GVN5GXEY3HOWGDIHT5L2A","target":"record","payload":{"canonical_record":{"source":{"id":"1902.08481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-22T13:12:07Z","cross_cats_sorted":[],"title_canon_sha256":"e6519f4329030e00fdd3a669246f0494b3de9c0340398e1d67dc5c6ddb9e7d56","abstract_canon_sha256":"ec5d20c77ff675e08e94bfe0c4005a52b85096610a56dad2607d3d306ac8553c"},"schema_version":"1.0"},"canonical_sha256":"f90e2e9aade9ae4c6ceeb18683cfabd020464948cfefd5dcf14bb4329f057cef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:57.108573Z","signature_b64":"DHziN7u1I1l+dB2vZaQxrJaSdZKSsFyqwS3o7S1SFt62ZDs2nbIXAD2JQ3sc9S+QY/zOyCbdik2QZPhhWvxDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f90e2e9aade9ae4c6ceeb18683cfabd020464948cfefd5dcf14bb4329f057cef","last_reissued_at":"2026-05-17T23:52:57.107956Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:57.107956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.08481","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":"2026-05-17T23:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uVDmhg6FRnovg3aDM1Bpgy0N3CmSrlrZc04WI68vbqAXoLHHolzQvpZ4G/UIKhCPn/wiH8xypMQzpd2hzsBNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:25:38.435252Z"},"content_sha256":"a476da0fdb8355ed25dbeb94644abdcec5b5ff3e25300779c695625b4152a5b7","schema_version":"1.0","event_id":"sha256:a476da0fdb8355ed25dbeb94644abdcec5b5ff3e25300779c695625b4152a5b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:7EHC5GVN5GXEY3HOWGDIHT5L2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random walks are determined by their trace on the positive half-line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mateusz Kwa\\'snicki","submitted_at":"2019-02-22T13:12:07Z","abstract_excerpt":"We prove that the law of a random walk $X_n$ is determined by the one-dimensional distributions of $\\max(X_n, 0)$ for $n = 1, 2, \\ldots$, as conjectured recently by Lo\\\"ic Chaumont and Ron Doney. Equivalently, the law of $X_n$ is determined by its upward space-time Wiener-Hopf factor. Our methods are complex-analytic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08481","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":"2026-05-17T23:52:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kk1MJLA5wGOdJKSMbDJnSKvaweG4z/UGi7qBGl7CKyGUWXDcJNiBXADET7E4UA8nPHkQ4zek3DIHwzUxDdXxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:25:38.435859Z"},"content_sha256":"4e1ca47a8d7f1ff55087e3f6cd75aad06fe36591987c5e460660f1553deb91d0","schema_version":"1.0","event_id":"sha256:4e1ca47a8d7f1ff55087e3f6cd75aad06fe36591987c5e460660f1553deb91d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EHC5GVN5GXEY3HOWGDIHT5L2A/bundle.json","state_url":"https://pith.science/pith/7EHC5GVN5GXEY3HOWGDIHT5L2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EHC5GVN5GXEY3HOWGDIHT5L2A/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":"2026-05-27T10:25:38Z","links":{"resolver":"https://pith.science/pith/7EHC5GVN5GXEY3HOWGDIHT5L2A","bundle":"https://pith.science/pith/7EHC5GVN5GXEY3HOWGDIHT5L2A/bundle.json","state":"https://pith.science/pith/7EHC5GVN5GXEY3HOWGDIHT5L2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EHC5GVN5GXEY3HOWGDIHT5L2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7EHC5GVN5GXEY3HOWGDIHT5L2A","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":"ec5d20c77ff675e08e94bfe0c4005a52b85096610a56dad2607d3d306ac8553c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-22T13:12:07Z","title_canon_sha256":"e6519f4329030e00fdd3a669246f0494b3de9c0340398e1d67dc5c6ddb9e7d56"},"schema_version":"1.0","source":{"id":"1902.08481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08481","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08481v1","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08481","created_at":"2026-05-17T23:52:57Z"},{"alias_kind":"pith_short_12","alias_value":"7EHC5GVN5GXE","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7EHC5GVN5GXEY3HO","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7EHC5GVN","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:4e1ca47a8d7f1ff55087e3f6cd75aad06fe36591987c5e460660f1553deb91d0","target":"graph","created_at":"2026-05-17T23:52:57Z","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 prove that the law of a random walk $X_n$ is determined by the one-dimensional distributions of $\\max(X_n, 0)$ for $n = 1, 2, \\ldots$, as conjectured recently by Lo\\\"ic Chaumont and Ron Doney. Equivalently, the law of $X_n$ is determined by its upward space-time Wiener-Hopf factor. Our methods are complex-analytic.","authors_text":"Mateusz Kwa\\'snicki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-22T13:12:07Z","title":"Random walks are determined by their trace on the positive half-line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08481","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:a476da0fdb8355ed25dbeb94644abdcec5b5ff3e25300779c695625b4152a5b7","target":"record","created_at":"2026-05-17T23:52:57Z","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":"ec5d20c77ff675e08e94bfe0c4005a52b85096610a56dad2607d3d306ac8553c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-22T13:12:07Z","title_canon_sha256":"e6519f4329030e00fdd3a669246f0494b3de9c0340398e1d67dc5c6ddb9e7d56"},"schema_version":"1.0","source":{"id":"1902.08481","kind":"arxiv","version":1}},"canonical_sha256":"f90e2e9aade9ae4c6ceeb18683cfabd020464948cfefd5dcf14bb4329f057cef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f90e2e9aade9ae4c6ceeb18683cfabd020464948cfefd5dcf14bb4329f057cef","first_computed_at":"2026-05-17T23:52:57.107956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:57.107956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DHziN7u1I1l+dB2vZaQxrJaSdZKSsFyqwS3o7S1SFt62ZDs2nbIXAD2JQ3sc9S+QY/zOyCbdik2QZPhhWvxDBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:57.108573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a476da0fdb8355ed25dbeb94644abdcec5b5ff3e25300779c695625b4152a5b7","sha256:4e1ca47a8d7f1ff55087e3f6cd75aad06fe36591987c5e460660f1553deb91d0"],"state_sha256":"7c9233989751a457a16b72956e817ec6b5cc92baf08a933ff09ae116a283d1f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ubqqXlrzJi29A9aEnWZtKdaVG9/NdDyZhfmCN85a00FgCpoAW0E+T9YcOxUM9T8/sy5vWQGA1lSNNWGjiPooBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:25:38.438941Z","bundle_sha256":"ea6a27fdd16ff007712fd5e0108dd5a530a0caf1d88fc953c0185921699fdb74"}}