{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2ZSJQLJLPTSVT5IR3A2GHZ276O","short_pith_number":"pith:2ZSJQLJL","canonical_record":{"source":{"id":"1501.02580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-12T09:39:24Z","cross_cats_sorted":["cond-mat.stat-mech","math.CO","math.MP","math.PR"],"title_canon_sha256":"535959879a7a23a47ee811aa294554ce9038e95aacc4cb1f4d967dfabc2f5939","abstract_canon_sha256":"cd634bb99f158c03478f07ac90538022082b959fac63ab139dc60a8370b351e2"},"schema_version":"1.0"},"canonical_sha256":"d664982d2b7ce559f511d83463e75ff38018114e0767a1a66e19e59f277f95b7","source":{"kind":"arxiv","id":"1501.02580","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02580","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02580v2","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02580","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"2ZSJQLJLPTSV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZSJQLJLPTSVT5IR","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZSJQLJL","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2ZSJQLJLPTSVT5IR3A2GHZ276O","target":"record","payload":{"canonical_record":{"source":{"id":"1501.02580","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-12T09:39:24Z","cross_cats_sorted":["cond-mat.stat-mech","math.CO","math.MP","math.PR"],"title_canon_sha256":"535959879a7a23a47ee811aa294554ce9038e95aacc4cb1f4d967dfabc2f5939","abstract_canon_sha256":"cd634bb99f158c03478f07ac90538022082b959fac63ab139dc60a8370b351e2"},"schema_version":"1.0"},"canonical_sha256":"d664982d2b7ce559f511d83463e75ff38018114e0767a1a66e19e59f277f95b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:06.578031Z","signature_b64":"QQDbohqAWKQ4SExGE03I5wAf/SBA1lxJTNHtxyTPVvPn1f4X7yd0lQI0Uyl5wD9hSFhd3OR7MIY9BE/wnLlLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d664982d2b7ce559f511d83463e75ff38018114e0767a1a66e19e59f277f95b7","last_reissued_at":"2026-05-18T01:20:06.577359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:06.577359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.02580","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":"2026-05-18T01:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKAIualmaaPKmrwR9lWXUEsMJqtVw1qcBNvWxIiyjjS+YpuAkUfKpaVfthJ0+3yZbxgJIdDlX0B72CzG+8mKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:36:54.601243Z"},"content_sha256":"71b49e8e12612ab7987fc405a2b050e18ae482d84ffb0e67fb31810187bf345a","schema_version":"1.0","event_id":"sha256:71b49e8e12612ab7987fc405a2b050e18ae482d84ffb0e67fb31810187bf345a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2ZSJQLJLPTSVT5IR3A2GHZ276O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Loop Reversibility and Subdiffusion of the Rotor-Router Walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CO","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"V.B. Priezzhev, Vl.V. Papoyan, V.S. Poghosyan","submitted_at":"2015-01-12T09:39:24Z","abstract_excerpt":"The rotor-router model on a graph describes a discrete-time walk accompanied by the deterministic evolution of configurations of rotors randomly placed on vertices of the graph. We prove the following property: if at some moment of time, the rotors form a closed clockwise contour on the planar graph, then the clockwise rotations of rotors generate a walk which enters into the contour at some vertex $v$, performs a number of steps inside the contour so that the contour formed by rotors becomes anti-clockwise, and then leaves the contour at the same vertex $v$. This property generalizes the prev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02580","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":"2026-05-18T01:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVw3KQYA0bZbNZUCD9AMJ/luJurWW3AVrhMPd+j5OzJcOSTYw3zOFHiwHT/zLuTXZQfwCW7KNHNlgdOBIeuVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:36:54.601927Z"},"content_sha256":"d1a9fbd0e4a4325f38f90e8754c9809337b9421313e09821871ebdd4ff038676","schema_version":"1.0","event_id":"sha256:d1a9fbd0e4a4325f38f90e8754c9809337b9421313e09821871ebdd4ff038676"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZSJQLJLPTSVT5IR3A2GHZ276O/bundle.json","state_url":"https://pith.science/pith/2ZSJQLJLPTSVT5IR3A2GHZ276O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZSJQLJLPTSVT5IR3A2GHZ276O/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":"2026-06-08T20:36:54Z","links":{"resolver":"https://pith.science/pith/2ZSJQLJLPTSVT5IR3A2GHZ276O","bundle":"https://pith.science/pith/2ZSJQLJLPTSVT5IR3A2GHZ276O/bundle.json","state":"https://pith.science/pith/2ZSJQLJLPTSVT5IR3A2GHZ276O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZSJQLJLPTSVT5IR3A2GHZ276O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2ZSJQLJLPTSVT5IR3A2GHZ276O","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":"cd634bb99f158c03478f07ac90538022082b959fac63ab139dc60a8370b351e2","cross_cats_sorted":["cond-mat.stat-mech","math.CO","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-12T09:39:24Z","title_canon_sha256":"535959879a7a23a47ee811aa294554ce9038e95aacc4cb1f4d967dfabc2f5939"},"schema_version":"1.0","source":{"id":"1501.02580","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.02580","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"1501.02580v2","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02580","created_at":"2026-05-18T01:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"2ZSJQLJLPTSV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZSJQLJLPTSVT5IR","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZSJQLJL","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:d1a9fbd0e4a4325f38f90e8754c9809337b9421313e09821871ebdd4ff038676","target":"graph","created_at":"2026-05-18T01:20:06Z","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":"The rotor-router model on a graph describes a discrete-time walk accompanied by the deterministic evolution of configurations of rotors randomly placed on vertices of the graph. We prove the following property: if at some moment of time, the rotors form a closed clockwise contour on the planar graph, then the clockwise rotations of rotors generate a walk which enters into the contour at some vertex $v$, performs a number of steps inside the contour so that the contour formed by rotors becomes anti-clockwise, and then leaves the contour at the same vertex $v$. This property generalizes the prev","authors_text":"V.B. Priezzhev, Vl.V. Papoyan, V.S. Poghosyan","cross_cats":["cond-mat.stat-mech","math.CO","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-12T09:39:24Z","title":"A Loop Reversibility and Subdiffusion of the Rotor-Router Walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02580","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":"sha256:71b49e8e12612ab7987fc405a2b050e18ae482d84ffb0e67fb31810187bf345a","target":"record","created_at":"2026-05-18T01:20:06Z","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":"cd634bb99f158c03478f07ac90538022082b959fac63ab139dc60a8370b351e2","cross_cats_sorted":["cond-mat.stat-mech","math.CO","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-01-12T09:39:24Z","title_canon_sha256":"535959879a7a23a47ee811aa294554ce9038e95aacc4cb1f4d967dfabc2f5939"},"schema_version":"1.0","source":{"id":"1501.02580","kind":"arxiv","version":2}},"canonical_sha256":"d664982d2b7ce559f511d83463e75ff38018114e0767a1a66e19e59f277f95b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d664982d2b7ce559f511d83463e75ff38018114e0767a1a66e19e59f277f95b7","first_computed_at":"2026-05-18T01:20:06.577359Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:06.577359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QQDbohqAWKQ4SExGE03I5wAf/SBA1lxJTNHtxyTPVvPn1f4X7yd0lQI0Uyl5wD9hSFhd3OR7MIY9BE/wnLlLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:06.578031Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.02580","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71b49e8e12612ab7987fc405a2b050e18ae482d84ffb0e67fb31810187bf345a","sha256:d1a9fbd0e4a4325f38f90e8754c9809337b9421313e09821871ebdd4ff038676"],"state_sha256":"e26bc798cf4c7398e34fc2cee8322c7f5b97988bddba8d1d577c760da839cb28"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOYB//vIbEIteOe1t/J6HEfdjXCbPVL4fup1GCSLfmIoTelCXyKFJDBBe9jN4eksbuw8VRtyvpTFoAeyr9vwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:36:54.606008Z","bundle_sha256":"6a271b15eeaf0726ac906f9d46895dcdd5a069c875538c07ab401a45592e2dd9"}}