{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3TVT5LDNR5DQ4YPB2UJU2KPK3K","short_pith_number":"pith:3TVT5LDN","canonical_record":{"source":{"id":"1707.08544","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-26T17:10:48Z","cross_cats_sorted":[],"title_canon_sha256":"e9065ce06165b1e8ca43774cd924a84734f6549f1a23a353bf5ee396d766dfa1","abstract_canon_sha256":"692dc155ef8637bd58f69ee0961ecebc3689a2633926287cd07dbd8b61a1fedb"},"schema_version":"1.0"},"canonical_sha256":"dceb3eac6d8f470e61e1d5134d29eadabad943f9d490cb30aff569c670cbd767","source":{"kind":"arxiv","id":"1707.08544","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08544","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08544v3","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08544","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"pith_short_12","alias_value":"3TVT5LDNR5DQ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3TVT5LDNR5DQ4YPB","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3TVT5LDN","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3TVT5LDNR5DQ4YPB2UJU2KPK3K","target":"record","payload":{"canonical_record":{"source":{"id":"1707.08544","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-26T17:10:48Z","cross_cats_sorted":[],"title_canon_sha256":"e9065ce06165b1e8ca43774cd924a84734f6549f1a23a353bf5ee396d766dfa1","abstract_canon_sha256":"692dc155ef8637bd58f69ee0961ecebc3689a2633926287cd07dbd8b61a1fedb"},"schema_version":"1.0"},"canonical_sha256":"dceb3eac6d8f470e61e1d5134d29eadabad943f9d490cb30aff569c670cbd767","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:19.296242Z","signature_b64":"AJaGLK4wNT0g2+++WMSs+3dw40pLT6msSGcX6Zz+7VUcoyZyLtMtRn29rHCvSGa8EFXY0hx/AVS6pGqXatE3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dceb3eac6d8f470e61e1d5134d29eadabad943f9d490cb30aff569c670cbd767","last_reissued_at":"2026-05-18T00:27:19.295770Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:19.295770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.08544","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":"2026-05-18T00:27:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qyPoE2pylglVjDS3sQzo3MOTzsE3msxkPnE6Zl+QhEGp9Zlhqk5RokY1XAWgAeWgwIzauNIQ9+BU0r2659Z7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:58:39.335905Z"},"content_sha256":"29238ad309953f3a623bf95b7922bf8941613fba14aa2ed6bdf49bdaa5f7b763","schema_version":"1.0","event_id":"sha256:29238ad309953f3a623bf95b7922bf8941613fba14aa2ed6bdf49bdaa5f7b763"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3TVT5LDNR5DQ4YPB2UJU2KPK3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$p_c$, $p_u$ and graph limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Itai Benjamini","submitted_at":"2017-07-26T17:10:48Z","abstract_excerpt":"A question relating the critical probability for percolation, the critical probability for a unique infinite cluster and graph limits is presented, together with some partial results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08544","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":""},"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":"2026-05-18T00:27:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pnno5h95u1hJX3BDNGP7XtlbQdtd89BvYqYbRgCmx2eBQEyc8RNqO2s0fZgeEVMbRmbQpxG7c+b8nc+iOZkuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:58:39.336254Z"},"content_sha256":"faca330e7153b6e58ff20d90bc3e51366a670c501e6a46f325557f8093b2e29d","schema_version":"1.0","event_id":"sha256:faca330e7153b6e58ff20d90bc3e51366a670c501e6a46f325557f8093b2e29d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TVT5LDNR5DQ4YPB2UJU2KPK3K/bundle.json","state_url":"https://pith.science/pith/3TVT5LDNR5DQ4YPB2UJU2KPK3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TVT5LDNR5DQ4YPB2UJU2KPK3K/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":"2026-05-31T05:58:39Z","links":{"resolver":"https://pith.science/pith/3TVT5LDNR5DQ4YPB2UJU2KPK3K","bundle":"https://pith.science/pith/3TVT5LDNR5DQ4YPB2UJU2KPK3K/bundle.json","state":"https://pith.science/pith/3TVT5LDNR5DQ4YPB2UJU2KPK3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TVT5LDNR5DQ4YPB2UJU2KPK3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3TVT5LDNR5DQ4YPB2UJU2KPK3K","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":"692dc155ef8637bd58f69ee0961ecebc3689a2633926287cd07dbd8b61a1fedb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-26T17:10:48Z","title_canon_sha256":"e9065ce06165b1e8ca43774cd924a84734f6549f1a23a353bf5ee396d766dfa1"},"schema_version":"1.0","source":{"id":"1707.08544","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08544","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08544v3","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08544","created_at":"2026-05-18T00:27:19Z"},{"alias_kind":"pith_short_12","alias_value":"3TVT5LDNR5DQ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3TVT5LDNR5DQ4YPB","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3TVT5LDN","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:faca330e7153b6e58ff20d90bc3e51366a670c501e6a46f325557f8093b2e29d","target":"graph","created_at":"2026-05-18T00:27:19Z","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":"A question relating the critical probability for percolation, the critical probability for a unique infinite cluster and graph limits is presented, together with some partial results.","authors_text":"Itai Benjamini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-26T17:10:48Z","title":"$p_c$, $p_u$ and graph limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08544","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":"sha256:29238ad309953f3a623bf95b7922bf8941613fba14aa2ed6bdf49bdaa5f7b763","target":"record","created_at":"2026-05-18T00:27:19Z","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":"692dc155ef8637bd58f69ee0961ecebc3689a2633926287cd07dbd8b61a1fedb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-26T17:10:48Z","title_canon_sha256":"e9065ce06165b1e8ca43774cd924a84734f6549f1a23a353bf5ee396d766dfa1"},"schema_version":"1.0","source":{"id":"1707.08544","kind":"arxiv","version":3}},"canonical_sha256":"dceb3eac6d8f470e61e1d5134d29eadabad943f9d490cb30aff569c670cbd767","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dceb3eac6d8f470e61e1d5134d29eadabad943f9d490cb30aff569c670cbd767","first_computed_at":"2026-05-18T00:27:19.295770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:19.295770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AJaGLK4wNT0g2+++WMSs+3dw40pLT6msSGcX6Zz+7VUcoyZyLtMtRn29rHCvSGa8EFXY0hx/AVS6pGqXatE3Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:19.296242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.08544","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29238ad309953f3a623bf95b7922bf8941613fba14aa2ed6bdf49bdaa5f7b763","sha256:faca330e7153b6e58ff20d90bc3e51366a670c501e6a46f325557f8093b2e29d"],"state_sha256":"4313575d514e00a97fad4a00189c998c545e9257e8da24bc1066af86bc7f7650"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"02xLGp7rYMVKIj9t4wKW9EyTDVo8Mqf6+dM5FX5kWzmXYKhO3Q7R2DD2NA3iR+eM6WQJFYkL2RMNoU8J1606BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:58:39.338773Z","bundle_sha256":"effb262edd047cc55a3ebb7393cf2d555c02fa515ac36458d26b03f5b7d69edd"}}