{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QEFCWCCAOLSKJRETUUSLP24MCY","short_pith_number":"pith:QEFCWCCA","canonical_record":{"source":{"id":"1610.08046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-24T21:31:52Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fa199969bf16beccd06b483c1f0c5d51b9312da9f5ee2afb37d64da79e073817","abstract_canon_sha256":"65ab7e5276244d5ba93450206343b41296048d10e7c95aaffa6589c0bc1e8340"},"schema_version":"1.0"},"canonical_sha256":"810a2b084072e4a4c493a524b7eb8c1601b6f6bf4a336aefe1c681c0ae20518d","source":{"kind":"arxiv","id":"1610.08046","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08046","created_at":"2026-05-18T00:47:33Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08046v2","created_at":"2026-05-18T00:47:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08046","created_at":"2026-05-18T00:47:33Z"},{"alias_kind":"pith_short_12","alias_value":"QEFCWCCAOLSK","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QEFCWCCAOLSKJRET","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QEFCWCCA","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QEFCWCCAOLSKJRETUUSLP24MCY","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08046","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-24T21:31:52Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fa199969bf16beccd06b483c1f0c5d51b9312da9f5ee2afb37d64da79e073817","abstract_canon_sha256":"65ab7e5276244d5ba93450206343b41296048d10e7c95aaffa6589c0bc1e8340"},"schema_version":"1.0"},"canonical_sha256":"810a2b084072e4a4c493a524b7eb8c1601b6f6bf4a336aefe1c681c0ae20518d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:33.511202Z","signature_b64":"TFVCJ0vf12UJ99+k1qrfuns15dXRhfLV00+VFq0Q+I+lUNluOme7QH9Q+mkUUnhQiFRkcgiR5Xs8u3hwxpReCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"810a2b084072e4a4c493a524b7eb8c1601b6f6bf4a336aefe1c681c0ae20518d","last_reissued_at":"2026-05-18T00:47:33.510604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:33.510604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08046","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":"2026-05-18T00:47:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ksoBDKYTFT81xRFpAO9fjJYXrpw/jOFA+bpXaWwSuJ1ajqkqP6QAAHRoXfY5FZ3EEJvE8z3tnHTGbcR+QBY9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:06:53.839204Z"},"content_sha256":"7e4516c9d9f4ca33e56f71081a8a315482c239b7c277e0c719dfa32e8ea42878","schema_version":"1.0","event_id":"sha256:7e4516c9d9f4ca33e56f71081a8a315482c239b7c277e0c719dfa32e8ea42878"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QEFCWCCAOLSKJRETUUSLP24MCY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-Dimensional Random Walk in Multi-Zone Environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"A.V. Nazarenko, V. Blavatska","submitted_at":"2016-10-24T21:31:52Z","abstract_excerpt":"We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are considered to be differently fixed. We derive analytically the probability to find a walker at the given position and time. The probability distribution function is found and has no Gaussian form because of properties of adsorption in the bulk of zones and partial reflection at the separation points. Time dependence of the mean squared displacement of a walker is stu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08046","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":"2026-05-18T00:47:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMrBxtKs5j6K3ZionGBsTi/NZrLwm546IjGG7wxpdEMH9GsmTPiIjNtKtAZG+F76opmcfHF6RKW5ZX5F1k+aDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:06:53.839573Z"},"content_sha256":"dacef1bbbb6477b6438f688bb9e2b1fbc303f2158740294c072e054f78119161","schema_version":"1.0","event_id":"sha256:dacef1bbbb6477b6438f688bb9e2b1fbc303f2158740294c072e054f78119161"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QEFCWCCAOLSKJRETUUSLP24MCY/bundle.json","state_url":"https://pith.science/pith/QEFCWCCAOLSKJRETUUSLP24MCY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QEFCWCCAOLSKJRETUUSLP24MCY/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":"2026-06-21T13:06:53Z","links":{"resolver":"https://pith.science/pith/QEFCWCCAOLSKJRETUUSLP24MCY","bundle":"https://pith.science/pith/QEFCWCCAOLSKJRETUUSLP24MCY/bundle.json","state":"https://pith.science/pith/QEFCWCCAOLSKJRETUUSLP24MCY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QEFCWCCAOLSKJRETUUSLP24MCY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QEFCWCCAOLSKJRETUUSLP24MCY","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":"65ab7e5276244d5ba93450206343b41296048d10e7c95aaffa6589c0bc1e8340","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-24T21:31:52Z","title_canon_sha256":"fa199969bf16beccd06b483c1f0c5d51b9312da9f5ee2afb37d64da79e073817"},"schema_version":"1.0","source":{"id":"1610.08046","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08046","created_at":"2026-05-18T00:47:33Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08046v2","created_at":"2026-05-18T00:47:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08046","created_at":"2026-05-18T00:47:33Z"},{"alias_kind":"pith_short_12","alias_value":"QEFCWCCAOLSK","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QEFCWCCAOLSKJRET","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QEFCWCCA","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:dacef1bbbb6477b6438f688bb9e2b1fbc303f2158740294c072e054f78119161","target":"graph","created_at":"2026-05-18T00:47:33Z","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 study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are considered to be differently fixed. We derive analytically the probability to find a walker at the given position and time. The probability distribution function is found and has no Gaussian form because of properties of adsorption in the bulk of zones and partial reflection at the separation points. Time dependence of the mean squared displacement of a walker is stu","authors_text":"A.V. Nazarenko, V. Blavatska","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-24T21:31:52Z","title":"One-Dimensional Random Walk in Multi-Zone Environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08046","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":"sha256:7e4516c9d9f4ca33e56f71081a8a315482c239b7c277e0c719dfa32e8ea42878","target":"record","created_at":"2026-05-18T00:47:33Z","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":"65ab7e5276244d5ba93450206343b41296048d10e7c95aaffa6589c0bc1e8340","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-24T21:31:52Z","title_canon_sha256":"fa199969bf16beccd06b483c1f0c5d51b9312da9f5ee2afb37d64da79e073817"},"schema_version":"1.0","source":{"id":"1610.08046","kind":"arxiv","version":2}},"canonical_sha256":"810a2b084072e4a4c493a524b7eb8c1601b6f6bf4a336aefe1c681c0ae20518d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"810a2b084072e4a4c493a524b7eb8c1601b6f6bf4a336aefe1c681c0ae20518d","first_computed_at":"2026-05-18T00:47:33.510604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:33.510604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TFVCJ0vf12UJ99+k1qrfuns15dXRhfLV00+VFq0Q+I+lUNluOme7QH9Q+mkUUnhQiFRkcgiR5Xs8u3hwxpReCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:33.511202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08046","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e4516c9d9f4ca33e56f71081a8a315482c239b7c277e0c719dfa32e8ea42878","sha256:dacef1bbbb6477b6438f688bb9e2b1fbc303f2158740294c072e054f78119161"],"state_sha256":"d159389a038794e3ef536f81cbc196f6e82749f24aaf87a45abed1966cca8a9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dGESD2DgsjSGR9RYNYAvA0kH3PC5TdnBg2/gSTZAebr6Z+DzvTntbnV0gdDGcA+Wk8rGJ2XgOwQ1M6H9a1oXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T13:06:53.842510Z","bundle_sha256":"73a3cf76209584f2798a5acf646c78cc6c19dd9d95ee4865e83342cf4006c755"}}