{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:JOPZBZUTXG3JYQKU5C6VIVMCK5","short_pith_number":"pith:JOPZBZUT","canonical_record":{"source":{"id":"1801.02748","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-09T01:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"f699d587e72112dd0a7db3425b28a730c9a23a47a5ffc884d182d8eb22e70907","abstract_canon_sha256":"50c75e045584cc756bc3f13381a5e223278539f10fa4b120332487cf24c9282d"},"schema_version":"1.0"},"canonical_sha256":"4b9f90e693b9b69c4154e8bd54558257437a86c0f0597c898bc7893e3518d109","source":{"kind":"arxiv","id":"1801.02748","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02748","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02748v3","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02748","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"JOPZBZUTXG3J","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JOPZBZUTXG3JYQKU","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JOPZBZUT","created_at":"2026-05-18T12:32:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:JOPZBZUTXG3JYQKU5C6VIVMCK5","target":"record","payload":{"canonical_record":{"source":{"id":"1801.02748","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-09T01:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"f699d587e72112dd0a7db3425b28a730c9a23a47a5ffc884d182d8eb22e70907","abstract_canon_sha256":"50c75e045584cc756bc3f13381a5e223278539f10fa4b120332487cf24c9282d"},"schema_version":"1.0"},"canonical_sha256":"4b9f90e693b9b69c4154e8bd54558257437a86c0f0597c898bc7893e3518d109","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:50.662048Z","signature_b64":"+zGkMYXwIaStngEllv4sfodUbwdyGr0F1rMdB4BO3yH8XbIwLhBVbT+aPxdP8Nl6MzkVyVfvIBd3pOBSAWt9Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b9f90e693b9b69c4154e8bd54558257437a86c0f0597c898bc7893e3518d109","last_reissued_at":"2026-05-18T00:21:50.661595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:50.661595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.02748","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":"2026-05-18T00:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eY7jsMwuVOkFQJqPoe8Ila99w9MlY5UbuTU0uBs1QxeFIXpwdaUOC1UNxwR1/jT4PQqog5aDgEMJAgYsN9BKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:44:22.872743Z"},"content_sha256":"a2510875f054c34be5f9f4464cda4cd00f1c3a2730e16ee9c7c2b500220f16cd","schema_version":"1.0","event_id":"sha256:a2510875f054c34be5f9f4464cda4cd00f1c3a2730e16ee9c7c2b500220f16cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:JOPZBZUTXG3JYQKU5C6VIVMCK5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semiconservative random walks in weak sense","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Vyacheslav M. Abramov","submitted_at":"2018-01-09T01:54:16Z","abstract_excerpt":"Conservative and semiconservative random walks in $\\mathbb{Z}^d$ were introduced and studied in [V.M. Abramov, J. Theor. Probab. (2017). https://doi.org/10.1007/s10959-017-0747-3]. In the present paper, we extend these concepts for random walks in $\\mathbb{R}^d$ introducing semiconservative random walks in weak sense and construct such a family of random walks in $\\mathbb{R}^d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02748","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":"2026-05-18T00:21:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ObYgqzsa0CiOmjhVvnt1L7hu7TLWjSyQirA2gDo2yInWXd4SESspePRvyW5MCpRf49J4/R3s6TQO4bjCHrgtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:44:22.873082Z"},"content_sha256":"4f34f3b48f784291d140c590f6fdf9a62d7c4496765c555fc7ae221e10a6a67d","schema_version":"1.0","event_id":"sha256:4f34f3b48f784291d140c590f6fdf9a62d7c4496765c555fc7ae221e10a6a67d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JOPZBZUTXG3JYQKU5C6VIVMCK5/bundle.json","state_url":"https://pith.science/pith/JOPZBZUTXG3JYQKU5C6VIVMCK5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JOPZBZUTXG3JYQKU5C6VIVMCK5/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":"2026-06-11T09:44:22Z","links":{"resolver":"https://pith.science/pith/JOPZBZUTXG3JYQKU5C6VIVMCK5","bundle":"https://pith.science/pith/JOPZBZUTXG3JYQKU5C6VIVMCK5/bundle.json","state":"https://pith.science/pith/JOPZBZUTXG3JYQKU5C6VIVMCK5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JOPZBZUTXG3JYQKU5C6VIVMCK5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:JOPZBZUTXG3JYQKU5C6VIVMCK5","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":"50c75e045584cc756bc3f13381a5e223278539f10fa4b120332487cf24c9282d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-09T01:54:16Z","title_canon_sha256":"f699d587e72112dd0a7db3425b28a730c9a23a47a5ffc884d182d8eb22e70907"},"schema_version":"1.0","source":{"id":"1801.02748","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02748","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02748v3","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02748","created_at":"2026-05-18T00:21:50Z"},{"alias_kind":"pith_short_12","alias_value":"JOPZBZUTXG3J","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"JOPZBZUTXG3JYQKU","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"JOPZBZUT","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:4f34f3b48f784291d140c590f6fdf9a62d7c4496765c555fc7ae221e10a6a67d","target":"graph","created_at":"2026-05-18T00:21:50Z","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":"Conservative and semiconservative random walks in $\\mathbb{Z}^d$ were introduced and studied in [V.M. Abramov, J. Theor. Probab. (2017). https://doi.org/10.1007/s10959-017-0747-3]. In the present paper, we extend these concepts for random walks in $\\mathbb{R}^d$ introducing semiconservative random walks in weak sense and construct such a family of random walks in $\\mathbb{R}^d$.","authors_text":"Vyacheslav M. Abramov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-09T01:54:16Z","title":"Semiconservative random walks in weak sense"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02748","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:a2510875f054c34be5f9f4464cda4cd00f1c3a2730e16ee9c7c2b500220f16cd","target":"record","created_at":"2026-05-18T00:21:50Z","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":"50c75e045584cc756bc3f13381a5e223278539f10fa4b120332487cf24c9282d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-09T01:54:16Z","title_canon_sha256":"f699d587e72112dd0a7db3425b28a730c9a23a47a5ffc884d182d8eb22e70907"},"schema_version":"1.0","source":{"id":"1801.02748","kind":"arxiv","version":3}},"canonical_sha256":"4b9f90e693b9b69c4154e8bd54558257437a86c0f0597c898bc7893e3518d109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b9f90e693b9b69c4154e8bd54558257437a86c0f0597c898bc7893e3518d109","first_computed_at":"2026-05-18T00:21:50.661595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:50.661595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+zGkMYXwIaStngEllv4sfodUbwdyGr0F1rMdB4BO3yH8XbIwLhBVbT+aPxdP8Nl6MzkVyVfvIBd3pOBSAWt9Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:50.662048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02748","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2510875f054c34be5f9f4464cda4cd00f1c3a2730e16ee9c7c2b500220f16cd","sha256:4f34f3b48f784291d140c590f6fdf9a62d7c4496765c555fc7ae221e10a6a67d"],"state_sha256":"9cfa0ae6866274adbd707a672ea7c06625f1c6f07bc31b8bc2bf14f5efe1b2bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZIfLAGwJ7z/Bh6Pjb3eNf4A1rRBnr3DT0GZJCOXfne/YcTLIfK1RkT5toINWB8Dg8h970NH9o2rqc7yqYeJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:44:22.875259Z","bundle_sha256":"a6ecce62a98b5eac9fec7eefab6ceef6688a35cef68aee911f5579215213e406"}}