{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DOEXDUYPS52CJEB7LDTK26KGSR","short_pith_number":"pith:DOEXDUYP","canonical_record":{"source":{"id":"2407.15162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-21T13:33:53Z","cross_cats_sorted":[],"title_canon_sha256":"d81cbc7cf7fcfcece6423ec9efc24ca15d34a59e0fc356345e5871d0489b98fa","abstract_canon_sha256":"7c44068b187112129a23717ef23cab7eeae97fe898975d4ec725e27b75bb8241"},"schema_version":"1.0"},"canonical_sha256":"1b8971d30f977424903f58e6ad7946944eaa345910417add2766e6657f2ec943","source":{"kind":"arxiv","id":"2407.15162","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.15162","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"2407.15162v3","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.15162","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"DOEXDUYPS52C","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"pith_short_16","alias_value":"DOEXDUYPS52CJEB7","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"pith_short_8","alias_value":"DOEXDUYP","created_at":"2026-07-05T09:28:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DOEXDUYPS52CJEB7LDTK26KGSR","target":"record","payload":{"canonical_record":{"source":{"id":"2407.15162","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-21T13:33:53Z","cross_cats_sorted":[],"title_canon_sha256":"d81cbc7cf7fcfcece6423ec9efc24ca15d34a59e0fc356345e5871d0489b98fa","abstract_canon_sha256":"7c44068b187112129a23717ef23cab7eeae97fe898975d4ec725e27b75bb8241"},"schema_version":"1.0"},"canonical_sha256":"1b8971d30f977424903f58e6ad7946944eaa345910417add2766e6657f2ec943","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:28:53.469464Z","signature_b64":"7MLrse587G+4ZmVuNfoIR9l0dtHLnGa64i3zbU10BzQRSUlLhd3iQegxhy8WtosU99BKyBdkeyYTgUgfUnmnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b8971d30f977424903f58e6ad7946944eaa345910417add2766e6657f2ec943","last_reissued_at":"2026-07-05T09:28:53.468985Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:28:53.468985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.15162","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":"2026-07-05T09:28:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JCXyqAFxz/wrxyVwGu/9Wtc1OZqSZ4cm3kAHXb6ZDj6y5MyZeMC5k5SjyXGgIJuAMclmjRVM3f4VbrBUFNdcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:41:44.837018Z"},"content_sha256":"e6c80145de805da813c12bad83bbc7709bbd82ca34e3a5754d056ec39c65554a","schema_version":"1.0","event_id":"sha256:e6c80145de805da813c12bad83bbc7709bbd82ca34e3a5754d056ec39c65554a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DOEXDUYPS52CJEB7LDTK26KGSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random walk on dynamical percolation in Euclidean lattices: separating critical and supercritical regimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chenlin Gu, Fan Yang, Hao Wu, Jianping Jiang, Yuval Peres, Zhan Shi","submitted_at":"2024-07-21T13:33:53Z","abstract_excerpt":"We study the random walk on dynamical percolation of $\\mathbb{Z}^d$ (resp., the two-dimensional triangular lattice $\\mathcal{T}$), where each edge (resp., each site) can be either open or closed, refreshing its status at rate $\\mu\\in (0,1/e]$. The random walk moves along open edges in $\\mathbb{Z}^d$ (resp., open sites in $\\mathcal{T}$) at rate $1$. For the critical regime $p=p_c$, we prove the following two results: on $\\mathcal{T}$, the mean squared displacement of the random walk from $0$ to $t$ is at most $O(t\\mu^{5/132-\\epsilon})$ for any $\\epsilon>0$; on $\\mathbb{Z}^d$ with $d\\geq 11$, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.15162","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.15162/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":"2026-07-05T09:28:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VS+fiFdVEnENyTGpx420z9UyDbJ/rSCjhQiAto/kh8z6ujfOGdyBEAQgtugnONkKFATp+dvxZUy8mZkMk57TBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:41:44.837542Z"},"content_sha256":"120694f12f714f663114d5a6419079641de0fa8cc1562a5f205e3945c7b07498","schema_version":"1.0","event_id":"sha256:120694f12f714f663114d5a6419079641de0fa8cc1562a5f205e3945c7b07498"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOEXDUYPS52CJEB7LDTK26KGSR/bundle.json","state_url":"https://pith.science/pith/DOEXDUYPS52CJEB7LDTK26KGSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOEXDUYPS52CJEB7LDTK26KGSR/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":"2026-08-05T21:41:44Z","links":{"resolver":"https://pith.science/pith/DOEXDUYPS52CJEB7LDTK26KGSR","bundle":"https://pith.science/pith/DOEXDUYPS52CJEB7LDTK26KGSR/bundle.json","state":"https://pith.science/pith/DOEXDUYPS52CJEB7LDTK26KGSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOEXDUYPS52CJEB7LDTK26KGSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DOEXDUYPS52CJEB7LDTK26KGSR","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":"7c44068b187112129a23717ef23cab7eeae97fe898975d4ec725e27b75bb8241","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-21T13:33:53Z","title_canon_sha256":"d81cbc7cf7fcfcece6423ec9efc24ca15d34a59e0fc356345e5871d0489b98fa"},"schema_version":"1.0","source":{"id":"2407.15162","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.15162","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"2407.15162v3","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.15162","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"DOEXDUYPS52C","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"pith_short_16","alias_value":"DOEXDUYPS52CJEB7","created_at":"2026-07-05T09:28:53Z"},{"alias_kind":"pith_short_8","alias_value":"DOEXDUYP","created_at":"2026-07-05T09:28:53Z"}],"graph_snapshots":[{"event_id":"sha256:120694f12f714f663114d5a6419079641de0fa8cc1562a5f205e3945c7b07498","target":"graph","created_at":"2026-07-05T09:28:53Z","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/2407.15162/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the random walk on dynamical percolation of $\\mathbb{Z}^d$ (resp., the two-dimensional triangular lattice $\\mathcal{T}$), where each edge (resp., each site) can be either open or closed, refreshing its status at rate $\\mu\\in (0,1/e]$. The random walk moves along open edges in $\\mathbb{Z}^d$ (resp., open sites in $\\mathcal{T}$) at rate $1$. For the critical regime $p=p_c$, we prove the following two results: on $\\mathcal{T}$, the mean squared displacement of the random walk from $0$ to $t$ is at most $O(t\\mu^{5/132-\\epsilon})$ for any $\\epsilon>0$; on $\\mathbb{Z}^d$ with $d\\geq 11$, th","authors_text":"Chenlin Gu, Fan Yang, Hao Wu, Jianping Jiang, Yuval Peres, Zhan Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-21T13:33:53Z","title":"Random walk on dynamical percolation in Euclidean lattices: separating critical and supercritical regimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.15162","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:e6c80145de805da813c12bad83bbc7709bbd82ca34e3a5754d056ec39c65554a","target":"record","created_at":"2026-07-05T09:28:53Z","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":"7c44068b187112129a23717ef23cab7eeae97fe898975d4ec725e27b75bb8241","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-07-21T13:33:53Z","title_canon_sha256":"d81cbc7cf7fcfcece6423ec9efc24ca15d34a59e0fc356345e5871d0489b98fa"},"schema_version":"1.0","source":{"id":"2407.15162","kind":"arxiv","version":3}},"canonical_sha256":"1b8971d30f977424903f58e6ad7946944eaa345910417add2766e6657f2ec943","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b8971d30f977424903f58e6ad7946944eaa345910417add2766e6657f2ec943","first_computed_at":"2026-07-05T09:28:53.468985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:28:53.468985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7MLrse587G+4ZmVuNfoIR9l0dtHLnGa64i3zbU10BzQRSUlLhd3iQegxhy8WtosU99BKyBdkeyYTgUgfUnmnDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:28:53.469464Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.15162","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6c80145de805da813c12bad83bbc7709bbd82ca34e3a5754d056ec39c65554a","sha256:120694f12f714f663114d5a6419079641de0fa8cc1562a5f205e3945c7b07498"],"state_sha256":"a0fbeabccbdd0bf72b91399ba4f3587d79c5a55e531a2a53f3c7236679f68b08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+6MwXTRJkiqBPKsoS6tBVXq8xSi1MHYFoL/3NC1y3J5qpuGAu4bL4ZrUXZZRfhDSC+66LmzoIBR20UoNqukBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T21:41:44.842622Z","bundle_sha256":"7006015e5d44616a228a60faa91e9cfd1a892faf3e4bf082e8a5d320f2f59033"}}