{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:B4RTGF62WZQZB3DMXRIDZVQ7JU","short_pith_number":"pith:B4RTGF62","canonical_record":{"source":{"id":"1606.06438","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-21T06:50:55Z","cross_cats_sorted":[],"title_canon_sha256":"465dc84370af4910eb5f1286d6e086af97057dfa354ba1fdbac11a1f93d48ce3","abstract_canon_sha256":"aa8aa4e0b4beadf49b0312f8701dcc12879accc07472804a912ab0b347cb76fb"},"schema_version":"1.0"},"canonical_sha256":"0f233317dab66190ec6cbc503cd61f4d30edfa775e0fed657fe1840abbffcbc3","source":{"kind":"arxiv","id":"1606.06438","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06438","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06438v2","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06438","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"pith_short_12","alias_value":"B4RTGF62WZQZ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B4RTGF62WZQZB3DM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B4RTGF62","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:B4RTGF62WZQZB3DMXRIDZVQ7JU","target":"record","payload":{"canonical_record":{"source":{"id":"1606.06438","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-21T06:50:55Z","cross_cats_sorted":[],"title_canon_sha256":"465dc84370af4910eb5f1286d6e086af97057dfa354ba1fdbac11a1f93d48ce3","abstract_canon_sha256":"aa8aa4e0b4beadf49b0312f8701dcc12879accc07472804a912ab0b347cb76fb"},"schema_version":"1.0"},"canonical_sha256":"0f233317dab66190ec6cbc503cd61f4d30edfa775e0fed657fe1840abbffcbc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:25.491064Z","signature_b64":"kzMF+YOmjFb/RSY/7d6DvCarWiDXP3ftWCaQ1/woRLC1IrLF995Yy7iXH+Mwc1LKjhNSnz4B8jdkrxxUqoQdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f233317dab66190ec6cbc503cd61f4d30edfa775e0fed657fe1840abbffcbc3","last_reissued_at":"2026-05-18T00:52:25.490388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:25.490388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.06438","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":"2026-05-18T00:52:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhejDIiyBwANl51leCUu5uUG9FiWbcdaWwMiMO4QZ04w5Pdhdj7nlQkPNy/JJ7tpOXoh0BNnMBgfcMsBkUsEAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:01:25.233204Z"},"content_sha256":"10be2194ece35206fb328b7b62534b0827d7b6c039a298d66704393069d04092","schema_version":"1.0","event_id":"sha256:10be2194ece35206fb328b7b62534b0827d7b6c039a298d66704393069d04092"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:B4RTGF62WZQZB3DMXRIDZVQ7JU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivalence of finite dimensional input-output models of solute transport and diffusion in geosciences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alain Rapaport (MISTEA), Alejandro Rojas-Palma (MISTEA, CMM), DIM, Hector Ramirez (DIM, Jean-Raynald De Dreuzy (GR)","submitted_at":"2016-06-21T06:50:55Z","abstract_excerpt":"We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting continua representations, which are quite popular in geo-sciences. Moreover, we provide explicit methods to construct these equivalent representations. The proofs show that controllability property is playing a crucial role for obtaining equivalence. These results contribute to our fundamental understanding on the effect of fine-scale geological structures on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06438","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":"2026-05-18T00:52:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pj/15swiK70ky0TceJVXE5gIxXpsVga70a4PLqsy//syfjfch53eZkTmojEJaq808JnhhqUD6h2zkMlALJzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:01:25.233573Z"},"content_sha256":"c1a8068e1ad6b009ebbd7784920cb694b1d67759ce34272333d29dad5c14a607","schema_version":"1.0","event_id":"sha256:c1a8068e1ad6b009ebbd7784920cb694b1d67759ce34272333d29dad5c14a607"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4RTGF62WZQZB3DMXRIDZVQ7JU/bundle.json","state_url":"https://pith.science/pith/B4RTGF62WZQZB3DMXRIDZVQ7JU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4RTGF62WZQZB3DMXRIDZVQ7JU/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":"2026-06-21T02:01:25Z","links":{"resolver":"https://pith.science/pith/B4RTGF62WZQZB3DMXRIDZVQ7JU","bundle":"https://pith.science/pith/B4RTGF62WZQZB3DMXRIDZVQ7JU/bundle.json","state":"https://pith.science/pith/B4RTGF62WZQZB3DMXRIDZVQ7JU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4RTGF62WZQZB3DMXRIDZVQ7JU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:B4RTGF62WZQZB3DMXRIDZVQ7JU","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":"aa8aa4e0b4beadf49b0312f8701dcc12879accc07472804a912ab0b347cb76fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-21T06:50:55Z","title_canon_sha256":"465dc84370af4910eb5f1286d6e086af97057dfa354ba1fdbac11a1f93d48ce3"},"schema_version":"1.0","source":{"id":"1606.06438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06438","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06438v2","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06438","created_at":"2026-05-18T00:52:25Z"},{"alias_kind":"pith_short_12","alias_value":"B4RTGF62WZQZ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B4RTGF62WZQZB3DM","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B4RTGF62","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:c1a8068e1ad6b009ebbd7784920cb694b1d67759ce34272333d29dad5c14a607","target":"graph","created_at":"2026-05-18T00:52:25Z","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 show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting continua representations, which are quite popular in geo-sciences. Moreover, we provide explicit methods to construct these equivalent representations. The proofs show that controllability property is playing a crucial role for obtaining equivalence. These results contribute to our fundamental understanding on the effect of fine-scale geological structures on ","authors_text":"Alain Rapaport (MISTEA), Alejandro Rojas-Palma (MISTEA, CMM), DIM, Hector Ramirez (DIM, Jean-Raynald De Dreuzy (GR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-21T06:50:55Z","title":"Equivalence of finite dimensional input-output models of solute transport and diffusion in geosciences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06438","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":"sha256:10be2194ece35206fb328b7b62534b0827d7b6c039a298d66704393069d04092","target":"record","created_at":"2026-05-18T00:52:25Z","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":"aa8aa4e0b4beadf49b0312f8701dcc12879accc07472804a912ab0b347cb76fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-21T06:50:55Z","title_canon_sha256":"465dc84370af4910eb5f1286d6e086af97057dfa354ba1fdbac11a1f93d48ce3"},"schema_version":"1.0","source":{"id":"1606.06438","kind":"arxiv","version":2}},"canonical_sha256":"0f233317dab66190ec6cbc503cd61f4d30edfa775e0fed657fe1840abbffcbc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f233317dab66190ec6cbc503cd61f4d30edfa775e0fed657fe1840abbffcbc3","first_computed_at":"2026-05-18T00:52:25.490388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:25.490388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kzMF+YOmjFb/RSY/7d6DvCarWiDXP3ftWCaQ1/woRLC1IrLF995Yy7iXH+Mwc1LKjhNSnz4B8jdkrxxUqoQdDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:25.491064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10be2194ece35206fb328b7b62534b0827d7b6c039a298d66704393069d04092","sha256:c1a8068e1ad6b009ebbd7784920cb694b1d67759ce34272333d29dad5c14a607"],"state_sha256":"6d51b9f7fe8ba8eef507ccb37dfc6e503d2cd6ebd72f447b872c59566bf7e180"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TeQjfEwWAh04icQMIXSg3bBq5BQqlbP86PpLqIRt8XSOqVYCItLF+d1Q9/u21msqu8L5xiQ6iaQxV1g5EmiwDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T02:01:25.235476Z","bundle_sha256":"364d650c992c51180b9d8503653613537c2b097a770e5687dcaac406b41e462c"}}