{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FRTBKQNJHTNI2LQQBUDSWMBBCE","short_pith_number":"pith:FRTBKQNJ","canonical_record":{"source":{"id":"1108.1258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-05T06:02:07Z","cross_cats_sorted":[],"title_canon_sha256":"68304ac45ba31c2369e8dc00340bc0b938fd9198b655cfef7f9d227616c6d469","abstract_canon_sha256":"04411f25c1d37130bd288d8803e11ee25524ef5343bb37f5f0d55cb68cfa56bf"},"schema_version":"1.0"},"canonical_sha256":"2c661541a93cda8d2e100d072b302111123f6b270f5f0567726e3b19030356be","source":{"kind":"arxiv","id":"1108.1258","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1258","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1258v2","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1258","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"FRTBKQNJHTNI","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FRTBKQNJHTNI2LQQ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FRTBKQNJ","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FRTBKQNJHTNI2LQQBUDSWMBBCE","target":"record","payload":{"canonical_record":{"source":{"id":"1108.1258","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-05T06:02:07Z","cross_cats_sorted":[],"title_canon_sha256":"68304ac45ba31c2369e8dc00340bc0b938fd9198b655cfef7f9d227616c6d469","abstract_canon_sha256":"04411f25c1d37130bd288d8803e11ee25524ef5343bb37f5f0d55cb68cfa56bf"},"schema_version":"1.0"},"canonical_sha256":"2c661541a93cda8d2e100d072b302111123f6b270f5f0567726e3b19030356be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:35.885013Z","signature_b64":"dBKtdcGOSynQzQc27XTyV4la+sZxw0g0WCX2wv3bjoGKTL4LhqxVNFbd5jvJsZcGIWNdA/GOzh3qElRQnGa6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c661541a93cda8d2e100d072b302111123f6b270f5f0567726e3b19030356be","last_reissued_at":"2026-05-18T03:34:35.884273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:35.884273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.1258","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":"2026-05-18T03:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ts31etp+AAjOSnoEI0JixKSqGHFljADTqDSAj+SQd5k9lslIUmJCQ0cJbueizW7fUfdI5IrqQJfMSrEHWgJiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:36.566356Z"},"content_sha256":"95b3de4e48b7ec67f2ea81e3601580e53c3b009659d78008d0882d04e42d5057","schema_version":"1.0","event_id":"sha256:95b3de4e48b7ec67f2ea81e3601580e53c3b009659d78008d0882d04e42d5057"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FRTBKQNJHTNI2LQQBUDSWMBBCE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Brownian Web in the Scaling Limit of Supercritical Oriented Percolation in Dimension 1+1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anish Sarkar, Rongfeng Sun","submitted_at":"2011-08-05T06:02:07Z","abstract_excerpt":"We prove that, after centering and diffusively rescaling space and time, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2_{even}:={(x,i) in Z^2: x+i is even} converges in distribution to the Brownian web. This proves a conjecture of Wu and Zhang. Our key observation is that each rightmost infinite open path can be approximated by a percolation exploration cluster, and different exploration clusters evolve independently before they intersect."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1258","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":""},"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":"2026-05-18T03:34:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O1HvKBljVrRkQ51kbHOZciw4mYIansOecdaQhCMwL14l4DBaeV8WPamObtUm5CBGwAoRPfw8bIV0FvJOAF0KCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:36.567031Z"},"content_sha256":"2018a921bb38cfb757ec69d9c54f6e449834274932ed5175e926de60f245cc36","schema_version":"1.0","event_id":"sha256:2018a921bb38cfb757ec69d9c54f6e449834274932ed5175e926de60f245cc36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FRTBKQNJHTNI2LQQBUDSWMBBCE/bundle.json","state_url":"https://pith.science/pith/FRTBKQNJHTNI2LQQBUDSWMBBCE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FRTBKQNJHTNI2LQQBUDSWMBBCE/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":"2026-05-31T08:38:36Z","links":{"resolver":"https://pith.science/pith/FRTBKQNJHTNI2LQQBUDSWMBBCE","bundle":"https://pith.science/pith/FRTBKQNJHTNI2LQQBUDSWMBBCE/bundle.json","state":"https://pith.science/pith/FRTBKQNJHTNI2LQQBUDSWMBBCE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FRTBKQNJHTNI2LQQBUDSWMBBCE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FRTBKQNJHTNI2LQQBUDSWMBBCE","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":"04411f25c1d37130bd288d8803e11ee25524ef5343bb37f5f0d55cb68cfa56bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-05T06:02:07Z","title_canon_sha256":"68304ac45ba31c2369e8dc00340bc0b938fd9198b655cfef7f9d227616c6d469"},"schema_version":"1.0","source":{"id":"1108.1258","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.1258","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"arxiv_version","alias_value":"1108.1258v2","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1258","created_at":"2026-05-18T03:34:35Z"},{"alias_kind":"pith_short_12","alias_value":"FRTBKQNJHTNI","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FRTBKQNJHTNI2LQQ","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FRTBKQNJ","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:2018a921bb38cfb757ec69d9c54f6e449834274932ed5175e926de60f245cc36","target":"graph","created_at":"2026-05-18T03:34:35Z","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, after centering and diffusively rescaling space and time, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2_{even}:={(x,i) in Z^2: x+i is even} converges in distribution to the Brownian web. This proves a conjecture of Wu and Zhang. Our key observation is that each rightmost infinite open path can be approximated by a percolation exploration cluster, and different exploration clusters evolve independently before they intersect.","authors_text":"Anish Sarkar, Rongfeng Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-05T06:02:07Z","title":"Brownian Web in the Scaling Limit of Supercritical Oriented Percolation in Dimension 1+1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1258","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":"sha256:95b3de4e48b7ec67f2ea81e3601580e53c3b009659d78008d0882d04e42d5057","target":"record","created_at":"2026-05-18T03:34:35Z","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":"04411f25c1d37130bd288d8803e11ee25524ef5343bb37f5f0d55cb68cfa56bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-05T06:02:07Z","title_canon_sha256":"68304ac45ba31c2369e8dc00340bc0b938fd9198b655cfef7f9d227616c6d469"},"schema_version":"1.0","source":{"id":"1108.1258","kind":"arxiv","version":2}},"canonical_sha256":"2c661541a93cda8d2e100d072b302111123f6b270f5f0567726e3b19030356be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c661541a93cda8d2e100d072b302111123f6b270f5f0567726e3b19030356be","first_computed_at":"2026-05-18T03:34:35.884273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:35.884273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dBKtdcGOSynQzQc27XTyV4la+sZxw0g0WCX2wv3bjoGKTL4LhqxVNFbd5jvJsZcGIWNdA/GOzh3qElRQnGa6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:35.885013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.1258","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95b3de4e48b7ec67f2ea81e3601580e53c3b009659d78008d0882d04e42d5057","sha256:2018a921bb38cfb757ec69d9c54f6e449834274932ed5175e926de60f245cc36"],"state_sha256":"e024c9e5a1ea8302bd031644fd084b42b0b9329b1d5fd2ad7ed4921f3ef36441"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZpkziLR4Rx9zLQkD4G0YO7PzgJusjGz8oLrndpd3+JA6txuQoRCi12rrItMto005zITc/0MncEJnDhgDoJ8DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:38:36.571595Z","bundle_sha256":"d165b7737802497314da61faf3ec736b6be871b29ebe7e143ccea13e64804b05"}}