{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:563HL7IRZ62RHG4ZLXF336BUZO","short_pith_number":"pith:563HL7IR","canonical_record":{"source":{"id":"1803.07382","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-20T11:43:41Z","cross_cats_sorted":["cond-mat.mtrl-sci","physics.flu-dyn","physics.geo-ph"],"title_canon_sha256":"e5fa7ab2d531898fb423242b1f8274545bfed99f9bd2ab4b9b7a1d77ff2753f2","abstract_canon_sha256":"4b4b0ab1f983ba9a5809c61bda8dfb698ea00b85ef0231634a299515a4ba56a3"},"schema_version":"1.0"},"canonical_sha256":"efb675fd11cfb5139b995dcbbdf834cb820912e804f77e9c175589091d6d79c3","source":{"kind":"arxiv","id":"1803.07382","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07382","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07382v1","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07382","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"pith_short_12","alias_value":"563HL7IRZ62R","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"563HL7IRZ62RHG4Z","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"563HL7IR","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:563HL7IRZ62RHG4ZLXF336BUZO","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07382","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-20T11:43:41Z","cross_cats_sorted":["cond-mat.mtrl-sci","physics.flu-dyn","physics.geo-ph"],"title_canon_sha256":"e5fa7ab2d531898fb423242b1f8274545bfed99f9bd2ab4b9b7a1d77ff2753f2","abstract_canon_sha256":"4b4b0ab1f983ba9a5809c61bda8dfb698ea00b85ef0231634a299515a4ba56a3"},"schema_version":"1.0"},"canonical_sha256":"efb675fd11cfb5139b995dcbbdf834cb820912e804f77e9c175589091d6d79c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:10.559218Z","signature_b64":"kSUCxDyB+31HcUb8E9yxCMWCRcAWdkChS2Zvcz4ur7bzhn5KRcwGIAfNhUuglsT9dEQd7M+qzP+pst327U9UDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efb675fd11cfb5139b995dcbbdf834cb820912e804f77e9c175589091d6d79c3","last_reissued_at":"2026-05-18T00:18:10.558679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:10.558679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07382","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":"2026-05-18T00:18:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0KwW+bALLMMVlwnswUf4jwHaQY/9OdPeGOZid7jXNnZXpkgIbLiXILaWAr4JDjsHzbyXUWQmr/HzSkKlqjneAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T17:05:22.355343Z"},"content_sha256":"d2cff568a10fc073ba404a57a3fb5209d668f1480290bf5155135d0d86dd2d55","schema_version":"1.0","event_id":"sha256:d2cff568a10fc073ba404a57a3fb5209d668f1480290bf5155135d0d86dd2d55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:563HL7IRZ62RHG4ZLXF336BUZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluation of the path integral for flow through random porous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","physics.flu-dyn","physics.geo-ph"],"primary_cat":"physics.comp-ph","authors_text":"Dimitri D. Vvedensky, Gil-Arnaud Coche, Marise J. E. Westbroek, Peter R. King","submitted_at":"2018-03-20T11:43:41Z","abstract_excerpt":"We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multi-variate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07382","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":"2026-05-18T00:18:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkPcDTg8O0qg4X2VX4V9lDvogVerzC+P7ncVNpt0bQ6PpkzGBMSvHaKT8tTiy86luhdG3cjK8HNrBkSDNohiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T17:05:22.355709Z"},"content_sha256":"f153b4b362825d79f99e2be45a0338c855264644c71b65c4d8cca60b4159a49a","schema_version":"1.0","event_id":"sha256:f153b4b362825d79f99e2be45a0338c855264644c71b65c4d8cca60b4159a49a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/563HL7IRZ62RHG4ZLXF336BUZO/bundle.json","state_url":"https://pith.science/pith/563HL7IRZ62RHG4ZLXF336BUZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/563HL7IRZ62RHG4ZLXF336BUZO/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":"2026-06-20T17:05:22Z","links":{"resolver":"https://pith.science/pith/563HL7IRZ62RHG4ZLXF336BUZO","bundle":"https://pith.science/pith/563HL7IRZ62RHG4ZLXF336BUZO/bundle.json","state":"https://pith.science/pith/563HL7IRZ62RHG4ZLXF336BUZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/563HL7IRZ62RHG4ZLXF336BUZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:563HL7IRZ62RHG4ZLXF336BUZO","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":"4b4b0ab1f983ba9a5809c61bda8dfb698ea00b85ef0231634a299515a4ba56a3","cross_cats_sorted":["cond-mat.mtrl-sci","physics.flu-dyn","physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-20T11:43:41Z","title_canon_sha256":"e5fa7ab2d531898fb423242b1f8274545bfed99f9bd2ab4b9b7a1d77ff2753f2"},"schema_version":"1.0","source":{"id":"1803.07382","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07382","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07382v1","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07382","created_at":"2026-05-18T00:18:10Z"},{"alias_kind":"pith_short_12","alias_value":"563HL7IRZ62R","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"563HL7IRZ62RHG4Z","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"563HL7IR","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:f153b4b362825d79f99e2be45a0338c855264644c71b65c4d8cca60b4159a49a","target":"graph","created_at":"2026-05-18T00:18:10Z","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 present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multi-variate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed.","authors_text":"Dimitri D. Vvedensky, Gil-Arnaud Coche, Marise J. E. Westbroek, Peter R. King","cross_cats":["cond-mat.mtrl-sci","physics.flu-dyn","physics.geo-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-20T11:43:41Z","title":"Evaluation of the path integral for flow through random porous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07382","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:d2cff568a10fc073ba404a57a3fb5209d668f1480290bf5155135d0d86dd2d55","target":"record","created_at":"2026-05-18T00:18:10Z","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":"4b4b0ab1f983ba9a5809c61bda8dfb698ea00b85ef0231634a299515a4ba56a3","cross_cats_sorted":["cond-mat.mtrl-sci","physics.flu-dyn","physics.geo-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2018-03-20T11:43:41Z","title_canon_sha256":"e5fa7ab2d531898fb423242b1f8274545bfed99f9bd2ab4b9b7a1d77ff2753f2"},"schema_version":"1.0","source":{"id":"1803.07382","kind":"arxiv","version":1}},"canonical_sha256":"efb675fd11cfb5139b995dcbbdf834cb820912e804f77e9c175589091d6d79c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efb675fd11cfb5139b995dcbbdf834cb820912e804f77e9c175589091d6d79c3","first_computed_at":"2026-05-18T00:18:10.558679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:10.558679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kSUCxDyB+31HcUb8E9yxCMWCRcAWdkChS2Zvcz4ur7bzhn5KRcwGIAfNhUuglsT9dEQd7M+qzP+pst327U9UDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:10.559218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07382","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2cff568a10fc073ba404a57a3fb5209d668f1480290bf5155135d0d86dd2d55","sha256:f153b4b362825d79f99e2be45a0338c855264644c71b65c4d8cca60b4159a49a"],"state_sha256":"94e343fb3e366aa280bb3cace9219597f5d6ae8b06d764dde58ae3a7bf7d6e56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oJI/CNIuFv9hx1mUtUtOT5r9B9P0dfj3+w4l5FbRkRQpRoNUMi3Lx7QZIZZUFQHj76FFPO7HXvCpqaaI+ryjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T17:05:22.357615Z","bundle_sha256":"33f60cc9a80a230a9999c755b2665a2ed971182773faaa0efd83917a19281690"}}