{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QKGWWQCISDHDADOQMKOSQ65ZBD","short_pith_number":"pith:QKGWWQCI","canonical_record":{"source":{"id":"1201.4921","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-24T08:01:17Z","cross_cats_sorted":[],"title_canon_sha256":"607aa2e6a6c4ee2c6247fccfa31d3ea4d0e3eae8f77cf857c782d5f5c9c2d6ac","abstract_canon_sha256":"2459c3de06422eecbc59d6c35ef772d91a21d7a0b597aa5e20090c963d8ae2ee"},"schema_version":"1.0"},"canonical_sha256":"828d6b404890ce300dd0629d287bb908e4a2a799271589b0d1b2399738117672","source":{"kind":"arxiv","id":"1201.4921","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4921","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4921v2","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4921","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"QKGWWQCISDHD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QKGWWQCISDHDADOQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QKGWWQCI","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QKGWWQCISDHDADOQMKOSQ65ZBD","target":"record","payload":{"canonical_record":{"source":{"id":"1201.4921","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-24T08:01:17Z","cross_cats_sorted":[],"title_canon_sha256":"607aa2e6a6c4ee2c6247fccfa31d3ea4d0e3eae8f77cf857c782d5f5c9c2d6ac","abstract_canon_sha256":"2459c3de06422eecbc59d6c35ef772d91a21d7a0b597aa5e20090c963d8ae2ee"},"schema_version":"1.0"},"canonical_sha256":"828d6b404890ce300dd0629d287bb908e4a2a799271589b0d1b2399738117672","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:27.892130Z","signature_b64":"Qqy9OEVpr778BAAXyq2t5eYIcOxrAYsRvglOOoWj6ldp+UcVg3OYKTEE18AqTjbcixIQmSCg1apUgiX2HxwABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"828d6b404890ce300dd0629d287bb908e4a2a799271589b0d1b2399738117672","last_reissued_at":"2026-05-18T02:55:27.891457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:27.891457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.4921","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":"2026-05-18T02:55:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hdW+Z8Z9A5MsyTEkNBkaA+0pTdyo5dzq4Okeir30mTLaL0/UDTLya1+n9eYd70VAiaoN8PthW4Ab6PXBD9kCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:06:56.388571Z"},"content_sha256":"61b7546fa77bd5d49bad4f132b87b740017a872ea4a02d965f063b87fd42becd","schema_version":"1.0","event_id":"sha256:61b7546fa77bd5d49bad4f132b87b740017a872ea4a02d965f063b87fd42becd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QKGWWQCISDHDADOQMKOSQ65ZBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal stream and minimal cutset for first passage percolation through a domain of $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marie Th\\'eret, Rapha\\\"el Cerf","submitted_at":"2012-01-24T08:01:17Z","abstract_excerpt":"We consider the standard first passage percolation model in the rescaled graph $\\mathbb{Z}^d/n$ for $d\\geq2$ and a domain $\\Omega$ of boundary $\\Gamma$ in $\\mathbb{R}^d$. Let $\\Gamma ^1$ and $\\Gamma ^2$ be two disjoint open subsets of $\\Gamma$, representing the parts of $\\Gamma$ through which some water can enter and escape from $\\Omega$. A law of large numbers for the maximal flow from $\\Gamma ^1$ to $\\Gamma ^2$ in $\\Omega$ is already known. In this paper we investigate the asymptotic behavior of a maximal stream and a minimal cutset. A maximal stream is a vector measure $\\vec{\\mu}_n^{\\max}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4921","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":"2026-05-18T02:55:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"po3fIgN812Ho3ywmQLXfZCadndqvJ6GpdtFNpGeyCFHfr4UEE+1Kse3t8XrgLL8nCfQXoE51kfa9TFFaxjT0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:06:56.389214Z"},"content_sha256":"b7204b4f79ec981e88f4884dee36bf084e250f53e8370be70f2375b1505e134f","schema_version":"1.0","event_id":"sha256:b7204b4f79ec981e88f4884dee36bf084e250f53e8370be70f2375b1505e134f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QKGWWQCISDHDADOQMKOSQ65ZBD/bundle.json","state_url":"https://pith.science/pith/QKGWWQCISDHDADOQMKOSQ65ZBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QKGWWQCISDHDADOQMKOSQ65ZBD/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":"2026-05-28T20:06:56Z","links":{"resolver":"https://pith.science/pith/QKGWWQCISDHDADOQMKOSQ65ZBD","bundle":"https://pith.science/pith/QKGWWQCISDHDADOQMKOSQ65ZBD/bundle.json","state":"https://pith.science/pith/QKGWWQCISDHDADOQMKOSQ65ZBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QKGWWQCISDHDADOQMKOSQ65ZBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QKGWWQCISDHDADOQMKOSQ65ZBD","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":"2459c3de06422eecbc59d6c35ef772d91a21d7a0b597aa5e20090c963d8ae2ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-24T08:01:17Z","title_canon_sha256":"607aa2e6a6c4ee2c6247fccfa31d3ea4d0e3eae8f77cf857c782d5f5c9c2d6ac"},"schema_version":"1.0","source":{"id":"1201.4921","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4921","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4921v2","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4921","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"QKGWWQCISDHD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QKGWWQCISDHDADOQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QKGWWQCI","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:b7204b4f79ec981e88f4884dee36bf084e250f53e8370be70f2375b1505e134f","target":"graph","created_at":"2026-05-18T02:55:27Z","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 consider the standard first passage percolation model in the rescaled graph $\\mathbb{Z}^d/n$ for $d\\geq2$ and a domain $\\Omega$ of boundary $\\Gamma$ in $\\mathbb{R}^d$. Let $\\Gamma ^1$ and $\\Gamma ^2$ be two disjoint open subsets of $\\Gamma$, representing the parts of $\\Gamma$ through which some water can enter and escape from $\\Omega$. A law of large numbers for the maximal flow from $\\Gamma ^1$ to $\\Gamma ^2$ in $\\Omega$ is already known. In this paper we investigate the asymptotic behavior of a maximal stream and a minimal cutset. A maximal stream is a vector measure $\\vec{\\mu}_n^{\\max}$ ","authors_text":"Marie Th\\'eret, Rapha\\\"el Cerf","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-24T08:01:17Z","title":"Maximal stream and minimal cutset for first passage percolation through a domain of $\\mathbb{R}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4921","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":"sha256:61b7546fa77bd5d49bad4f132b87b740017a872ea4a02d965f063b87fd42becd","target":"record","created_at":"2026-05-18T02:55:27Z","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":"2459c3de06422eecbc59d6c35ef772d91a21d7a0b597aa5e20090c963d8ae2ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-24T08:01:17Z","title_canon_sha256":"607aa2e6a6c4ee2c6247fccfa31d3ea4d0e3eae8f77cf857c782d5f5c9c2d6ac"},"schema_version":"1.0","source":{"id":"1201.4921","kind":"arxiv","version":2}},"canonical_sha256":"828d6b404890ce300dd0629d287bb908e4a2a799271589b0d1b2399738117672","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"828d6b404890ce300dd0629d287bb908e4a2a799271589b0d1b2399738117672","first_computed_at":"2026-05-18T02:55:27.891457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:27.891457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qqy9OEVpr778BAAXyq2t5eYIcOxrAYsRvglOOoWj6ldp+UcVg3OYKTEE18AqTjbcixIQmSCg1apUgiX2HxwABA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:27.892130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4921","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61b7546fa77bd5d49bad4f132b87b740017a872ea4a02d965f063b87fd42becd","sha256:b7204b4f79ec981e88f4884dee36bf084e250f53e8370be70f2375b1505e134f"],"state_sha256":"f09da2a2bb07032c2ef0206f46f0ea96743e5d941b6987125148a064e9f3aa2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTdMymqKbHykveiPiABmt82JubxJWMFC9kktzCH4fgnH69uXt5UICWp08jkHeVlrlTWgs/niwYzgpGvOCA4jDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:06:56.392448Z","bundle_sha256":"ceed59476d487a47ea8fa43433bde004c56d27027849c12d1c643a3ce912ae2c"}}