{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NQJZQVILWZKINQA3KV6EXCQXP6","short_pith_number":"pith:NQJZQVIL","canonical_record":{"source":{"id":"1808.01277","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-03T17:57:27Z","cross_cats_sorted":[],"title_canon_sha256":"d47c5656525c50e0f5f94bb5064a4128257cbac98b26225b9cdd6f25534cc3eb","abstract_canon_sha256":"c056adeb1a5954c8f6dbde108d0f29d90bb1e7725f209cfed4e6f7cdccaed25f"},"schema_version":"1.0"},"canonical_sha256":"6c1398550bb65486c01b557c4b8a177fb6ce3d6db02d60dcb67cbc2e167f379d","source":{"kind":"arxiv","id":"1808.01277","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01277","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01277v2","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01277","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"NQJZQVILWZKI","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"pith_short_16","alias_value":"NQJZQVILWZKINQA3","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"pith_short_8","alias_value":"NQJZQVIL","created_at":"2026-07-05T00:06:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NQJZQVILWZKINQA3KV6EXCQXP6","target":"record","payload":{"canonical_record":{"source":{"id":"1808.01277","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-03T17:57:27Z","cross_cats_sorted":[],"title_canon_sha256":"d47c5656525c50e0f5f94bb5064a4128257cbac98b26225b9cdd6f25534cc3eb","abstract_canon_sha256":"c056adeb1a5954c8f6dbde108d0f29d90bb1e7725f209cfed4e6f7cdccaed25f"},"schema_version":"1.0"},"canonical_sha256":"6c1398550bb65486c01b557c4b8a177fb6ce3d6db02d60dcb67cbc2e167f379d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:06:29.822863Z","signature_b64":"3WsQIrqcRhXOMpNnF1ZN0o+YzQqam2/E+u1uBUlx4SDl5F4zcQFMr4MKe0gK7h1z/8XrQMq3JP+KjD25bRJyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c1398550bb65486c01b557c4b8a177fb6ce3d6db02d60dcb67cbc2e167f379d","last_reissued_at":"2026-07-05T00:06:29.822395Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:06:29.822395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.01277","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":"2026-07-05T00:06:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJc4xfJjWDLvrqgjXhsUOiLADZcf1LlxU75NZdcWiNDPxo01byngXIaQiOaMtWgiL5utd61PDe1HROppXc/yCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T20:14:06.545722Z"},"content_sha256":"60935eafbacc3c2a77698b8e99d7eb1d3de735f7cad6a3748909b030162c5620","schema_version":"1.0","event_id":"sha256:60935eafbacc3c2a77698b8e99d7eb1d3de735f7cad6a3748909b030162c5620"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NQJZQVILWZKINQA3KV6EXCQXP6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Artem Sapozhnikov, Caio Alves","submitted_at":"2018-08-03T17:57:27Z","abstract_excerpt":"It has been recently understood (arXiv:1212.2885, arXiv:1310.4764, arXiv:1410.0605) that for a general class of percolation models on $\\mathbb{Z}^d$ satisfying suitable decoupling inequalities, which includes i.a.\\ Bernoulli percolation, random interlacements and level sets of the Gaussian free field, large scale geometry of the unique infinite cluster in strongly percolative regime is qualitatively the same; in particular, the random walk on the infinite cluster satisfies the quenched invariance principle, Gaussian heat-kernel bounds and local CLT.\n  In this paper we consider the random walk "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01277","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1808.01277/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":"2026-07-05T00:06:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKvKOQE1ttFAyibtLf9Y7FlvF+gTUQjDg4T60GEV6Fjjim5xEPeQntvUC+PkbTD6H2LVbszkxpM/r6ljEFdwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T20:14:06.546045Z"},"content_sha256":"6f1ce9c6ad4847802cc8f910ad2679f80abc3095898092f6e196d4f1c92bf6ff","schema_version":"1.0","event_id":"sha256:6f1ce9c6ad4847802cc8f910ad2679f80abc3095898092f6e196d4f1c92bf6ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQJZQVILWZKINQA3KV6EXCQXP6/bundle.json","state_url":"https://pith.science/pith/NQJZQVILWZKINQA3KV6EXCQXP6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQJZQVILWZKINQA3KV6EXCQXP6/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":"2026-08-19T20:14:06Z","links":{"resolver":"https://pith.science/pith/NQJZQVILWZKINQA3KV6EXCQXP6","bundle":"https://pith.science/pith/NQJZQVILWZKINQA3KV6EXCQXP6/bundle.json","state":"https://pith.science/pith/NQJZQVILWZKINQA3KV6EXCQXP6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQJZQVILWZKINQA3KV6EXCQXP6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NQJZQVILWZKINQA3KV6EXCQXP6","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":"c056adeb1a5954c8f6dbde108d0f29d90bb1e7725f209cfed4e6f7cdccaed25f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-03T17:57:27Z","title_canon_sha256":"d47c5656525c50e0f5f94bb5064a4128257cbac98b26225b9cdd6f25534cc3eb"},"schema_version":"1.0","source":{"id":"1808.01277","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01277","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01277v2","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01277","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"pith_short_12","alias_value":"NQJZQVILWZKI","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"pith_short_16","alias_value":"NQJZQVILWZKINQA3","created_at":"2026-07-05T00:06:29Z"},{"alias_kind":"pith_short_8","alias_value":"NQJZQVIL","created_at":"2026-07-05T00:06:29Z"}],"graph_snapshots":[{"event_id":"sha256:6f1ce9c6ad4847802cc8f910ad2679f80abc3095898092f6e196d4f1c92bf6ff","target":"graph","created_at":"2026-07-05T00:06:29Z","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/1808.01277/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It has been recently understood (arXiv:1212.2885, arXiv:1310.4764, arXiv:1410.0605) that for a general class of percolation models on $\\mathbb{Z}^d$ satisfying suitable decoupling inequalities, which includes i.a.\\ Bernoulli percolation, random interlacements and level sets of the Gaussian free field, large scale geometry of the unique infinite cluster in strongly percolative regime is qualitatively the same; in particular, the random walk on the infinite cluster satisfies the quenched invariance principle, Gaussian heat-kernel bounds and local CLT.\n  In this paper we consider the random walk ","authors_text":"Artem Sapozhnikov, Caio Alves","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-03T17:57:27Z","title":"Decoupling inequalities and supercritical percolation for the vacant set of random walk loop soup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01277","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":"sha256:60935eafbacc3c2a77698b8e99d7eb1d3de735f7cad6a3748909b030162c5620","target":"record","created_at":"2026-07-05T00:06:29Z","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":"c056adeb1a5954c8f6dbde108d0f29d90bb1e7725f209cfed4e6f7cdccaed25f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-03T17:57:27Z","title_canon_sha256":"d47c5656525c50e0f5f94bb5064a4128257cbac98b26225b9cdd6f25534cc3eb"},"schema_version":"1.0","source":{"id":"1808.01277","kind":"arxiv","version":2}},"canonical_sha256":"6c1398550bb65486c01b557c4b8a177fb6ce3d6db02d60dcb67cbc2e167f379d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c1398550bb65486c01b557c4b8a177fb6ce3d6db02d60dcb67cbc2e167f379d","first_computed_at":"2026-07-05T00:06:29.822395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:06:29.822395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3WsQIrqcRhXOMpNnF1ZN0o+YzQqam2/E+u1uBUlx4SDl5F4zcQFMr4MKe0gK7h1z/8XrQMq3JP+KjD25bRJyCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:06:29.822863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01277","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60935eafbacc3c2a77698b8e99d7eb1d3de735f7cad6a3748909b030162c5620","sha256:6f1ce9c6ad4847802cc8f910ad2679f80abc3095898092f6e196d4f1c92bf6ff"],"state_sha256":"fb831143ac8aeaa9e5b5a99a7b5e173424ec32962fb04c8b62f8aae9c7da07a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9oNtq0WjGh+chLxgtlniLtd9oCW743gCuYyRBJDdYljcW2P1SX2gcKZS4kxgdOrJfzO+3NZ3/zxErHtuyr9vDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T20:14:06.549037Z","bundle_sha256":"b4a339ad5d8f8b425f8c465087a784042acda17130416500128766e87292aaf6"}}