{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PD4J6AWNW3ROFHWLD6PSKDEY24","short_pith_number":"pith:PD4J6AWN","canonical_record":{"source":{"id":"1401.7130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-28T10:36:11Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b003aabd747c37bf367f2d922108f2f01c112dc1c0f92f0345961e672bd69c25","abstract_canon_sha256":"6620db6a765433c71cbfff84c8729b5379475039e0862f1e05cc96cdab7f0ea7"},"schema_version":"1.0"},"canonical_sha256":"78f89f02cdb6e2e29ecb1f9f250c98d7387dd4ef533eaa2fc7fcdb3de8b07688","source":{"kind":"arxiv","id":"1401.7130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7130","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7130v1","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7130","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"pith_short_12","alias_value":"PD4J6AWNW3RO","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PD4J6AWNW3ROFHWL","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PD4J6AWN","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PD4J6AWNW3ROFHWLD6PSKDEY24","target":"record","payload":{"canonical_record":{"source":{"id":"1401.7130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-28T10:36:11Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b003aabd747c37bf367f2d922108f2f01c112dc1c0f92f0345961e672bd69c25","abstract_canon_sha256":"6620db6a765433c71cbfff84c8729b5379475039e0862f1e05cc96cdab7f0ea7"},"schema_version":"1.0"},"canonical_sha256":"78f89f02cdb6e2e29ecb1f9f250c98d7387dd4ef533eaa2fc7fcdb3de8b07688","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:50.775660Z","signature_b64":"tjqhZE8PRIjOF1ftx8wnajaNielu/0cHyKvHNEGRGkzJ8OOSo7baQGph1O6/WYfOoU1Cg8wkzP1r1ZkmMKoRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78f89f02cdb6e2e29ecb1f9f250c98d7387dd4ef533eaa2fc7fcdb3de8b07688","last_reissued_at":"2026-05-18T03:00:50.775012Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:50.775012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.7130","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":"2026-05-18T03:00:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ap5zdzNAXyMZFfC5ixhBPN46BqyQDaQ+CAH/G/WpPleZMbKKhqH7sg3j8umeeX9bvxOn2R3Grvl+eB2evcBLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:19:33.111471Z"},"content_sha256":"777599e4e63fa8082254e38239307628cf5d0e3191a2bb2bc6f74d72040b09c5","schema_version":"1.0","event_id":"sha256:777599e4e63fa8082254e38239307628cf5d0e3191a2bb2bc6f74d72040b09c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PD4J6AWNW3ROFHWLD6PSKDEY24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absence of infinite cluster for critical Bernoulli percolation on slabs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hugo Duminil-Copin, Vincent Tassion, Vladas Sidoravicius","submitted_at":"2014-01-28T10:36:11Z","abstract_excerpt":"We prove that for Bernoulli percolation on a graph $\\mathbb{Z}^2\\times\\{0,\\dots,k\\}$ ($k\\ge 0$), there is no infinite cluster at criticality, almost surely. The proof extends to finite range Bernoulli percolation models on $\\mathbb{Z}^2$ which are invariant under $\\pi/2$-rotation and reflection."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7130","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":"2026-05-18T03:00:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QauZ2SVdKYgiF7xrJ3cRVfnSO30edKb8qRdXSLom9s6xGR4JRpbEk//d2f2VAbC3XON4gxax/N+mVmn+iwRdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:19:33.112107Z"},"content_sha256":"ed99a472c7f1e0deaf8ec0fe1cde1c24fddb948b7c114ad0c38c42e61237a6d5","schema_version":"1.0","event_id":"sha256:ed99a472c7f1e0deaf8ec0fe1cde1c24fddb948b7c114ad0c38c42e61237a6d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PD4J6AWNW3ROFHWLD6PSKDEY24/bundle.json","state_url":"https://pith.science/pith/PD4J6AWNW3ROFHWLD6PSKDEY24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PD4J6AWNW3ROFHWLD6PSKDEY24/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":"2026-05-28T00:19:33Z","links":{"resolver":"https://pith.science/pith/PD4J6AWNW3ROFHWLD6PSKDEY24","bundle":"https://pith.science/pith/PD4J6AWNW3ROFHWLD6PSKDEY24/bundle.json","state":"https://pith.science/pith/PD4J6AWNW3ROFHWLD6PSKDEY24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PD4J6AWNW3ROFHWLD6PSKDEY24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PD4J6AWNW3ROFHWLD6PSKDEY24","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":"6620db6a765433c71cbfff84c8729b5379475039e0862f1e05cc96cdab7f0ea7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-28T10:36:11Z","title_canon_sha256":"b003aabd747c37bf367f2d922108f2f01c112dc1c0f92f0345961e672bd69c25"},"schema_version":"1.0","source":{"id":"1401.7130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7130","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7130v1","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7130","created_at":"2026-05-18T03:00:50Z"},{"alias_kind":"pith_short_12","alias_value":"PD4J6AWNW3RO","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PD4J6AWNW3ROFHWL","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PD4J6AWN","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:ed99a472c7f1e0deaf8ec0fe1cde1c24fddb948b7c114ad0c38c42e61237a6d5","target":"graph","created_at":"2026-05-18T03:00:50Z","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":"We prove that for Bernoulli percolation on a graph $\\mathbb{Z}^2\\times\\{0,\\dots,k\\}$ ($k\\ge 0$), there is no infinite cluster at criticality, almost surely. The proof extends to finite range Bernoulli percolation models on $\\mathbb{Z}^2$ which are invariant under $\\pi/2$-rotation and reflection.","authors_text":"Hugo Duminil-Copin, Vincent Tassion, Vladas Sidoravicius","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-28T10:36:11Z","title":"Absence of infinite cluster for critical Bernoulli percolation on slabs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7130","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":"sha256:777599e4e63fa8082254e38239307628cf5d0e3191a2bb2bc6f74d72040b09c5","target":"record","created_at":"2026-05-18T03:00:50Z","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":"6620db6a765433c71cbfff84c8729b5379475039e0862f1e05cc96cdab7f0ea7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-28T10:36:11Z","title_canon_sha256":"b003aabd747c37bf367f2d922108f2f01c112dc1c0f92f0345961e672bd69c25"},"schema_version":"1.0","source":{"id":"1401.7130","kind":"arxiv","version":1}},"canonical_sha256":"78f89f02cdb6e2e29ecb1f9f250c98d7387dd4ef533eaa2fc7fcdb3de8b07688","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78f89f02cdb6e2e29ecb1f9f250c98d7387dd4ef533eaa2fc7fcdb3de8b07688","first_computed_at":"2026-05-18T03:00:50.775012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:50.775012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tjqhZE8PRIjOF1ftx8wnajaNielu/0cHyKvHNEGRGkzJ8OOSo7baQGph1O6/WYfOoU1Cg8wkzP1r1ZkmMKoRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:50.775660Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:777599e4e63fa8082254e38239307628cf5d0e3191a2bb2bc6f74d72040b09c5","sha256:ed99a472c7f1e0deaf8ec0fe1cde1c24fddb948b7c114ad0c38c42e61237a6d5"],"state_sha256":"33946352d4caad907be8aecdcb8f22f95869a72f837ecdf943c0a67774a9928d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uWduLvj1GEd8+e+diEIEZBzj3xEF0RqC3V+vg+VEtgmlHZmeH0m627DApm7mbuqMFvk+UJQVhycbHnssgwh3Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:19:33.115276Z","bundle_sha256":"870d9d04b89e1cd723ac8d6a1595b06d44451f9da5bc7f47e67db48196418292"}}