{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WZVF7F4VTXGEXDVRVHEJDFCNEK","short_pith_number":"pith:WZVF7F4V","canonical_record":{"source":{"id":"1701.01349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-19T11:08:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1f6d856b536cf56ff18b237f54545562fd361034d57df0713ffff39e9e8fd4e2","abstract_canon_sha256":"7b266b394c3e27003c8465eb7b3d0a1fa585ba9ab608e6fa83d5b0ee686dc086"},"schema_version":"1.0"},"canonical_sha256":"b66a5f97959dcc4b8eb1a9c891944d22afef4c98c33a4076a1890482ec7c4af5","source":{"kind":"arxiv","id":"1701.01349","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01349","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01349v1","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01349","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"WZVF7F4VTXGE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WZVF7F4VTXGEXDVR","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WZVF7F4V","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WZVF7F4VTXGEXDVRVHEJDFCNEK","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-19T11:08:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1f6d856b536cf56ff18b237f54545562fd361034d57df0713ffff39e9e8fd4e2","abstract_canon_sha256":"7b266b394c3e27003c8465eb7b3d0a1fa585ba9ab608e6fa83d5b0ee686dc086"},"schema_version":"1.0"},"canonical_sha256":"b66a5f97959dcc4b8eb1a9c891944d22afef4c98c33a4076a1890482ec7c4af5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:14.092206Z","signature_b64":"Ms4Tci3C62PpYwfmF/biwRaKEzyOzWleB0DFXoIANKOXHW9LTbDHHhD6QAgKj6fbOzMUePXzxMjLc77iLm/pAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b66a5f97959dcc4b8eb1a9c891944d22afef4c98c33a4076a1890482ec7c4af5","last_reissued_at":"2026-05-18T00:32:14.091629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:14.091629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01349","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":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBnfnkPNuoPIsIUb64Nk8fIVn1lgArSyGfEBYOLHq+VgTdQlSaccHwCaBiDyQ+q16aOes8+QO3MlkrEuVhpjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:25:04.825957Z"},"content_sha256":"8cb903f0feb2754c6f641f5eee0c4073367782c5cb44510ef061ca27f47eab27","schema_version":"1.0","event_id":"sha256:8cb903f0feb2754c6f641f5eee0c4073367782c5cb44510ef061ca27f47eab27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WZVF7F4VTXGEXDVRVHEJDFCNEK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large time behaviour of symmetric random walk in high-contrast periodic environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Andrey Piatnitski, Elena Zhizhina","submitted_at":"2016-12-19T11:08:42Z","abstract_excerpt":"The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in $\\mathbb Z^d$, $d\\geq 1$. We show that under proper diffusive scaling the random walk exhibits a non-standard limit behaviour. In addition to the coordinate of the random walk in $\\mathbb Z^d$ we introduce an extra variable that characterizes the position of the random walk in the period and show that this two-component process converges in law to a limit Markov process. The components of the limit process are mutually coupled, thus we cannot expect that the limit behaviour of the co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01349","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":"2026-05-18T00:32:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DJJw/8pcLP1dF9h5VkTMpNdje3EZ55u/PzkRw9q9bTKdfi2PI5swKV8EPv4PBEZu+/1uMesALfL68WVusBhJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:25:04.826306Z"},"content_sha256":"bb2390c7d86a87e79925221adb40b24f4cc148f35972ab1cbd063673806b53c1","schema_version":"1.0","event_id":"sha256:bb2390c7d86a87e79925221adb40b24f4cc148f35972ab1cbd063673806b53c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WZVF7F4VTXGEXDVRVHEJDFCNEK/bundle.json","state_url":"https://pith.science/pith/WZVF7F4VTXGEXDVRVHEJDFCNEK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WZVF7F4VTXGEXDVRVHEJDFCNEK/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":"2026-06-03T03:25:04Z","links":{"resolver":"https://pith.science/pith/WZVF7F4VTXGEXDVRVHEJDFCNEK","bundle":"https://pith.science/pith/WZVF7F4VTXGEXDVRVHEJDFCNEK/bundle.json","state":"https://pith.science/pith/WZVF7F4VTXGEXDVRVHEJDFCNEK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WZVF7F4VTXGEXDVRVHEJDFCNEK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WZVF7F4VTXGEXDVRVHEJDFCNEK","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":"7b266b394c3e27003c8465eb7b3d0a1fa585ba9ab608e6fa83d5b0ee686dc086","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-19T11:08:42Z","title_canon_sha256":"1f6d856b536cf56ff18b237f54545562fd361034d57df0713ffff39e9e8fd4e2"},"schema_version":"1.0","source":{"id":"1701.01349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01349","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01349v1","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01349","created_at":"2026-05-18T00:32:14Z"},{"alias_kind":"pith_short_12","alias_value":"WZVF7F4VTXGE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WZVF7F4VTXGEXDVR","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WZVF7F4V","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:bb2390c7d86a87e79925221adb40b24f4cc148f35972ab1cbd063673806b53c1","target":"graph","created_at":"2026-05-18T00:32:14Z","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 paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in $\\mathbb Z^d$, $d\\geq 1$. We show that under proper diffusive scaling the random walk exhibits a non-standard limit behaviour. In addition to the coordinate of the random walk in $\\mathbb Z^d$ we introduce an extra variable that characterizes the position of the random walk in the period and show that this two-component process converges in law to a limit Markov process. The components of the limit process are mutually coupled, thus we cannot expect that the limit behaviour of the co","authors_text":"Andrey Piatnitski, Elena Zhizhina","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-19T11:08:42Z","title":"Large time behaviour of symmetric random walk in high-contrast periodic environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01349","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":"sha256:8cb903f0feb2754c6f641f5eee0c4073367782c5cb44510ef061ca27f47eab27","target":"record","created_at":"2026-05-18T00:32:14Z","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":"7b266b394c3e27003c8465eb7b3d0a1fa585ba9ab608e6fa83d5b0ee686dc086","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-19T11:08:42Z","title_canon_sha256":"1f6d856b536cf56ff18b237f54545562fd361034d57df0713ffff39e9e8fd4e2"},"schema_version":"1.0","source":{"id":"1701.01349","kind":"arxiv","version":1}},"canonical_sha256":"b66a5f97959dcc4b8eb1a9c891944d22afef4c98c33a4076a1890482ec7c4af5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b66a5f97959dcc4b8eb1a9c891944d22afef4c98c33a4076a1890482ec7c4af5","first_computed_at":"2026-05-18T00:32:14.091629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:14.091629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ms4Tci3C62PpYwfmF/biwRaKEzyOzWleB0DFXoIANKOXHW9LTbDHHhD6QAgKj6fbOzMUePXzxMjLc77iLm/pAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:14.092206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cb903f0feb2754c6f641f5eee0c4073367782c5cb44510ef061ca27f47eab27","sha256:bb2390c7d86a87e79925221adb40b24f4cc148f35972ab1cbd063673806b53c1"],"state_sha256":"fda5ef6271a0657952a43e9505ba89788b1d6425f43b6a2b0e0318b1199d0b2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhuWtatnACS6PWUjcriFxPRIhE3WftYRF9r8wmCyst/P5gvEPiMAww8ewEDD3JmzZLZcs450IYs3CT/NSHpvBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:25:04.828152Z","bundle_sha256":"a1d2f93b9d8f94c77a8370bdd7ed81a6926c72cf4fd89d5fbff104ba28c65bf9"}}