{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OBC6X64RNTFIDHZVJRGV65E4SZ","short_pith_number":"pith:OBC6X64R","canonical_record":{"source":{"id":"1911.02183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-11-06T03:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"92b40d2508a006cff1e33dff50be6edcf122ec8c8ec13e890646ba9ebe00422a","abstract_canon_sha256":"d628048bcb0c7ca4a8d38b14273691e28c2c896e45fd0b18e1e1ea00c160de60"},"schema_version":"1.0"},"canonical_sha256":"7045ebfb916cca819f354c4d5f749c96611c2358af5412e412456262e792e38d","source":{"kind":"arxiv","id":"1911.02183","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.02183","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1911.02183v1","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.02183","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"OBC6X64RNTFI","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"pith_short_16","alias_value":"OBC6X64RNTFIDHZV","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"pith_short_8","alias_value":"OBC6X64R","created_at":"2026-07-05T00:17:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OBC6X64RNTFIDHZVJRGV65E4SZ","target":"record","payload":{"canonical_record":{"source":{"id":"1911.02183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-11-06T03:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"92b40d2508a006cff1e33dff50be6edcf122ec8c8ec13e890646ba9ebe00422a","abstract_canon_sha256":"d628048bcb0c7ca4a8d38b14273691e28c2c896e45fd0b18e1e1ea00c160de60"},"schema_version":"1.0"},"canonical_sha256":"7045ebfb916cca819f354c4d5f749c96611c2358af5412e412456262e792e38d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:17:31.439282Z","signature_b64":"yxlLDhp0MOr2AknwMzKHBtTOUI9OYZXY+Pt+vN7/7HvX1420m7DnJMrsGzhFfHOamL6QA6K1s04ifOlNgjzVAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7045ebfb916cca819f354c4d5f749c96611c2358af5412e412456262e792e38d","last_reissued_at":"2026-07-05T00:17:31.438875Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:17:31.438875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.02183","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":"2026-07-05T00:17:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Km7svOHa67Gy4Eyz923Ix5IFl2TSeWPU3SNNzet0/jU3BFvn1vev9cUEubLvWWJhPcwo2htC62W3afcTWwusAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:29:27.281524Z"},"content_sha256":"3781e45899276fa1b57ce6c1fe8733f8cc0bdebc8e05f62dbd3ec9e82de7b372","schema_version":"1.0","event_id":"sha256:3781e45899276fa1b57ce6c1fe8733f8cc0bdebc8e05f62dbd3ec9e82de7b372"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OBC6X64RNTFIDHZVJRGV65E4SZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random walk in random environment and their time-reversed counterpart","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"R\\'emy Poudevigne","submitted_at":"2019-11-06T03:37:21Z","abstract_excerpt":"The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal which leads to several results. More precisely, a time-reversed random walk in Dirichlet environment (with null divergence) is also a random walk in random environment where the transition probabilities are independent Dirichlet random variables with different parameters. We show that on all graphs that satisfy a few weak assumptions, a random walk in random "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.02183","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.02183/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:17:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1h/UUDyY7qnAT5qt+azmURrTP/Ii+Eh+p6v7O3guHst+CKu91MhlU73KYpR/5enkoZZUSm8gehpPG5iVVVzpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:29:27.281922Z"},"content_sha256":"d185e6a17aa8f9c6c1e09bfe7a9ed5c57aef10b50ef542080614eb23635a13ff","schema_version":"1.0","event_id":"sha256:d185e6a17aa8f9c6c1e09bfe7a9ed5c57aef10b50ef542080614eb23635a13ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBC6X64RNTFIDHZVJRGV65E4SZ/bundle.json","state_url":"https://pith.science/pith/OBC6X64RNTFIDHZVJRGV65E4SZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBC6X64RNTFIDHZVJRGV65E4SZ/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":"2026-07-07T05:29:27Z","links":{"resolver":"https://pith.science/pith/OBC6X64RNTFIDHZVJRGV65E4SZ","bundle":"https://pith.science/pith/OBC6X64RNTFIDHZVJRGV65E4SZ/bundle.json","state":"https://pith.science/pith/OBC6X64RNTFIDHZVJRGV65E4SZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBC6X64RNTFIDHZVJRGV65E4SZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OBC6X64RNTFIDHZVJRGV65E4SZ","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":"d628048bcb0c7ca4a8d38b14273691e28c2c896e45fd0b18e1e1ea00c160de60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-11-06T03:37:21Z","title_canon_sha256":"92b40d2508a006cff1e33dff50be6edcf122ec8c8ec13e890646ba9ebe00422a"},"schema_version":"1.0","source":{"id":"1911.02183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.02183","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1911.02183v1","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.02183","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"OBC6X64RNTFI","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"pith_short_16","alias_value":"OBC6X64RNTFIDHZV","created_at":"2026-07-05T00:17:31Z"},{"alias_kind":"pith_short_8","alias_value":"OBC6X64R","created_at":"2026-07-05T00:17:31Z"}],"graph_snapshots":[{"event_id":"sha256:d185e6a17aa8f9c6c1e09bfe7a9ed5c57aef10b50ef542080614eb23635a13ff","target":"graph","created_at":"2026-07-05T00:17:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1911.02183/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal which leads to several results. More precisely, a time-reversed random walk in Dirichlet environment (with null divergence) is also a random walk in random environment where the transition probabilities are independent Dirichlet random variables with different parameters. We show that on all graphs that satisfy a few weak assumptions, a random walk in random ","authors_text":"R\\'emy Poudevigne","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-11-06T03:37:21Z","title":"Random walk in random environment and their time-reversed counterpart"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.02183","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":"sha256:3781e45899276fa1b57ce6c1fe8733f8cc0bdebc8e05f62dbd3ec9e82de7b372","target":"record","created_at":"2026-07-05T00:17:31Z","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":"d628048bcb0c7ca4a8d38b14273691e28c2c896e45fd0b18e1e1ea00c160de60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-11-06T03:37:21Z","title_canon_sha256":"92b40d2508a006cff1e33dff50be6edcf122ec8c8ec13e890646ba9ebe00422a"},"schema_version":"1.0","source":{"id":"1911.02183","kind":"arxiv","version":1}},"canonical_sha256":"7045ebfb916cca819f354c4d5f749c96611c2358af5412e412456262e792e38d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7045ebfb916cca819f354c4d5f749c96611c2358af5412e412456262e792e38d","first_computed_at":"2026-07-05T00:17:31.438875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:17:31.438875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxlLDhp0MOr2AknwMzKHBtTOUI9OYZXY+Pt+vN7/7HvX1420m7DnJMrsGzhFfHOamL6QA6K1s04ifOlNgjzVAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:17:31.439282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.02183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3781e45899276fa1b57ce6c1fe8733f8cc0bdebc8e05f62dbd3ec9e82de7b372","sha256:d185e6a17aa8f9c6c1e09bfe7a9ed5c57aef10b50ef542080614eb23635a13ff"],"state_sha256":"c2da487204b7e8704f7c535aaecad4a6addd4a9003e04f881ff20b1c99bc53e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kt6SvQnINm6hYtJuum2/ew5eCIqtAiqbycvBjre1CmBJRBdDF93OaaPt9k4fqRbqANAN67yip4KoKxx9FLiHDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T05:29:27.284141Z","bundle_sha256":"4d36ef540500530f8ad00e6e6c23c63512b9961345d1a280dcfa30bfa2204d7c"}}