{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XBRMSH6IERFKDBAMARRJ5P5GIJ","short_pith_number":"pith:XBRMSH6I","canonical_record":{"source":{"id":"1204.3737","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-17T09:09:28Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"6322bfa57510e0eb5d0666ba10ee16f890d77af4fc90ec5bd744cb35b2dac821","abstract_canon_sha256":"21be9c436eaafa487270bcf56159668b06f8cea97495ea852b8c1a0f3b5b33ef"},"schema_version":"1.0"},"canonical_sha256":"b862c91fc8244aa1840c04629ebfa6424da8c3f204895dcc6012bc62a0aa110e","source":{"kind":"arxiv","id":"1204.3737","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3737","created_at":"2026-05-18T03:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3737v3","created_at":"2026-05-18T03:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3737","created_at":"2026-05-18T03:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"XBRMSH6IERFK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XBRMSH6IERFKDBAM","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XBRMSH6I","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XBRMSH6IERFKDBAMARRJ5P5GIJ","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3737","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-17T09:09:28Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"6322bfa57510e0eb5d0666ba10ee16f890d77af4fc90ec5bd744cb35b2dac821","abstract_canon_sha256":"21be9c436eaafa487270bcf56159668b06f8cea97495ea852b8c1a0f3b5b33ef"},"schema_version":"1.0"},"canonical_sha256":"b862c91fc8244aa1840c04629ebfa6424da8c3f204895dcc6012bc62a0aa110e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:46.084654Z","signature_b64":"V6FnIi2LSujOEKU6raoN/3wlBQBkbpC7Yxg58PVmlUjGwYbMW6nmH0w0/a4+8plCNdz47qu5E3nwlo/ZUkr4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b862c91fc8244aa1840c04629ebfa6424da8c3f204895dcc6012bc62a0aa110e","last_reissued_at":"2026-05-18T03:42:46.084207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:46.084207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3737","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":"2026-05-18T03:42:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3vcTaloyGEAoWUUuuuEKWsSrS4LTZwHcPFVp0qG2Jjm6N2wtam/K1Idl36BvgkxZzx1kmYCXWlXTv5tOyADUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:02:52.420709Z"},"content_sha256":"cf520b096798aa4d2f5280b72f24da17cdd8e2a02fe5cabcb7b8c03f34070141","schema_version":"1.0","event_id":"sha256:cf520b096798aa4d2f5280b72f24da17cdd8e2a02fe5cabcb7b8c03f34070141"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XBRMSH6IERFKDBAMARRJ5P5GIJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to share underground reservoirs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"H. J. Herrmann, K. J. Schrenk, N. A. M. Ara\\'ujo","submitted_at":"2012-04-17T09:09:28Z","abstract_excerpt":"Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective shares can be obtained by invading the porous medium simultaneously with various fluids. Partitioning a volume in two parts requires one division surface while the simultaneous boundary between three parts consists of lines. We identify and characterize these lines, showing that they form a fractal set consisting of a single thread spanning the medium and a surrounding cloud of loops. While the spanning thread has fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3737","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":"2026-05-18T03:42:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3hrgmpWazAhTDi6HRxII1rcepcTYe75kHXPu42T8EGK9+bwsWdDOfsyuooIlDViixevkEyHwjGZIKkpVyIytDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:02:52.421054Z"},"content_sha256":"431dd045ef2170ad3c5b75f0f46ef375d651f16a827a7e76f5a251c9658e9547","schema_version":"1.0","event_id":"sha256:431dd045ef2170ad3c5b75f0f46ef375d651f16a827a7e76f5a251c9658e9547"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBRMSH6IERFKDBAMARRJ5P5GIJ/bundle.json","state_url":"https://pith.science/pith/XBRMSH6IERFKDBAMARRJ5P5GIJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBRMSH6IERFKDBAMARRJ5P5GIJ/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":"2026-06-24T20:02:52Z","links":{"resolver":"https://pith.science/pith/XBRMSH6IERFKDBAMARRJ5P5GIJ","bundle":"https://pith.science/pith/XBRMSH6IERFKDBAMARRJ5P5GIJ/bundle.json","state":"https://pith.science/pith/XBRMSH6IERFKDBAMARRJ5P5GIJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBRMSH6IERFKDBAMARRJ5P5GIJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XBRMSH6IERFKDBAMARRJ5P5GIJ","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":"21be9c436eaafa487270bcf56159668b06f8cea97495ea852b8c1a0f3b5b33ef","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-17T09:09:28Z","title_canon_sha256":"6322bfa57510e0eb5d0666ba10ee16f890d77af4fc90ec5bd744cb35b2dac821"},"schema_version":"1.0","source":{"id":"1204.3737","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3737","created_at":"2026-05-18T03:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3737v3","created_at":"2026-05-18T03:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3737","created_at":"2026-05-18T03:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"XBRMSH6IERFK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XBRMSH6IERFKDBAM","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XBRMSH6I","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:431dd045ef2170ad3c5b75f0f46ef375d651f16a827a7e76f5a251c9658e9547","target":"graph","created_at":"2026-05-18T03:42:46Z","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":"Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective shares can be obtained by invading the porous medium simultaneously with various fluids. Partitioning a volume in two parts requires one division surface while the simultaneous boundary between three parts consists of lines. We identify and characterize these lines, showing that they form a fractal set consisting of a single thread spanning the medium and a surrounding cloud of loops. While the spanning thread has fra","authors_text":"H. J. Herrmann, K. J. Schrenk, N. A. M. Ara\\'ujo","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-17T09:09:28Z","title":"How to share underground reservoirs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3737","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:cf520b096798aa4d2f5280b72f24da17cdd8e2a02fe5cabcb7b8c03f34070141","target":"record","created_at":"2026-05-18T03:42:46Z","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":"21be9c436eaafa487270bcf56159668b06f8cea97495ea852b8c1a0f3b5b33ef","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-04-17T09:09:28Z","title_canon_sha256":"6322bfa57510e0eb5d0666ba10ee16f890d77af4fc90ec5bd744cb35b2dac821"},"schema_version":"1.0","source":{"id":"1204.3737","kind":"arxiv","version":3}},"canonical_sha256":"b862c91fc8244aa1840c04629ebfa6424da8c3f204895dcc6012bc62a0aa110e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b862c91fc8244aa1840c04629ebfa6424da8c3f204895dcc6012bc62a0aa110e","first_computed_at":"2026-05-18T03:42:46.084207Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:46.084207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V6FnIi2LSujOEKU6raoN/3wlBQBkbpC7Yxg58PVmlUjGwYbMW6nmH0w0/a4+8plCNdz47qu5E3nwlo/ZUkr4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:46.084654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3737","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf520b096798aa4d2f5280b72f24da17cdd8e2a02fe5cabcb7b8c03f34070141","sha256:431dd045ef2170ad3c5b75f0f46ef375d651f16a827a7e76f5a251c9658e9547"],"state_sha256":"7222f8aa0e025f3d89f5021692299c2d46ebbd4b82a2d6ff49ae203ce6b5acea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csG9NahMjMh/whnGgMjBvAp1jFzSdGx3T8EqTC2Dt+1BuSj8/C9QnzLrUFbrjjRyyyyJ7Upulnmq2pgJHkNhCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:02:52.423211Z","bundle_sha256":"654a01d236ab6a45e5678e405d4d4e48452f933d9bf7fc19d16a20babc6a1eee"}}