{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PVNQFFYZID33DB2BG4BX6VZCQZ","short_pith_number":"pith:PVNQFFYZ","canonical_record":{"source":{"id":"1809.03240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-10T11:31:08Z","cross_cats_sorted":[],"title_canon_sha256":"3cd2ec532c3916ddbf5fa010814aefebe4dd4b537808b3f5bed0f896e1a27e34","abstract_canon_sha256":"b572c4f85429583283f6533e2879dbae370e6038b03d5be8102ba9994bbb9345"},"schema_version":"1.0"},"canonical_sha256":"7d5b02971940f7b1874137037f57228672b69c9de74584f5894a3a81b29f3d94","source":{"kind":"arxiv","id":"1809.03240","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03240","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03240v1","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03240","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"PVNQFFYZID33","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PVNQFFYZID33DB2B","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PVNQFFYZ","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PVNQFFYZID33DB2BG4BX6VZCQZ","target":"record","payload":{"canonical_record":{"source":{"id":"1809.03240","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-10T11:31:08Z","cross_cats_sorted":[],"title_canon_sha256":"3cd2ec532c3916ddbf5fa010814aefebe4dd4b537808b3f5bed0f896e1a27e34","abstract_canon_sha256":"b572c4f85429583283f6533e2879dbae370e6038b03d5be8102ba9994bbb9345"},"schema_version":"1.0"},"canonical_sha256":"7d5b02971940f7b1874137037f57228672b69c9de74584f5894a3a81b29f3d94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:09.536864Z","signature_b64":"2ZI+sDt9Uxa3bWyjH1G1yxgDh0TYO4N/eIotmvks9op8S0f1GEljLLWhZWiUYHa+HDzQsKyMMXVU0iEyolUXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d5b02971940f7b1874137037f57228672b69c9de74584f5894a3a81b29f3d94","last_reissued_at":"2026-05-18T00:06:09.536140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:09.536140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.03240","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":"2026-05-18T00:06:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iV5h1vncD40IGPR+6OzKbq1CNfSFMCyiNtFHnjIkGbXV8GNjb3xgomZGahUlfS4TvkLzlaMjogOy3dJgxX4dBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:37:50.810050Z"},"content_sha256":"53594ef0af6abb89c2f787dd974c1c0c8db8f06fb4eb7b965bc91c7dc8c60bca","schema_version":"1.0","event_id":"sha256:53594ef0af6abb89c2f787dd974c1c0c8db8f06fb4eb7b965bc91c7dc8c60bca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PVNQFFYZID33DB2BG4BX6VZCQZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of fully discrete FEM for miscible displacement in porous media with Bear--Scheidegger diffusion tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Buyang Li, Weiwei Sun, Wentao Cai, Yanping Lin","submitted_at":"2018-09-10T11:31:08Z","abstract_excerpt":"Fully discrete Galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly-used Bear--Scheidegger diffusion-dispersion tensor: $$ D({\\bf u}) = \\gamma d_m I + |{\\bf u}|\\bigg( \\alpha_T I + (\\alpha_L - \\alpha_T) \\frac{{\\bf u} \\otimes {\\bf u}}{|{\\bf u}|^2}\\bigg) \\, . $$ Previous works on optimal-order $L^\\infty(0,T;L^2)$-norm error estimate required the regularity assumption $\\nabla_x\\partial_tD({\\bf u}(x,t)) \\in L^\\infty(0,T;L^\\infty(\\Omega))$, while the Bear--Scheidegger diffusion-dispersion tensor is only Lipschitz continuous even for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03240","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":"2026-05-18T00:06:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ohz6tQwOOtNaX1gEUzXVq2wa5JCyPFznrI1KUwX96jAaN9A6+KIUKlZRoypbkhC73VQ/a8jRRlXT+cpApzwzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:37:50.810774Z"},"content_sha256":"7931be8b98bc97e7fe47374cbb0333e7fc8385dfb2b93d930294163d3ec6b0fc","schema_version":"1.0","event_id":"sha256:7931be8b98bc97e7fe47374cbb0333e7fc8385dfb2b93d930294163d3ec6b0fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVNQFFYZID33DB2BG4BX6VZCQZ/bundle.json","state_url":"https://pith.science/pith/PVNQFFYZID33DB2BG4BX6VZCQZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVNQFFYZID33DB2BG4BX6VZCQZ/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":"2026-05-31T18:37:50Z","links":{"resolver":"https://pith.science/pith/PVNQFFYZID33DB2BG4BX6VZCQZ","bundle":"https://pith.science/pith/PVNQFFYZID33DB2BG4BX6VZCQZ/bundle.json","state":"https://pith.science/pith/PVNQFFYZID33DB2BG4BX6VZCQZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVNQFFYZID33DB2BG4BX6VZCQZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PVNQFFYZID33DB2BG4BX6VZCQZ","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":"b572c4f85429583283f6533e2879dbae370e6038b03d5be8102ba9994bbb9345","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-10T11:31:08Z","title_canon_sha256":"3cd2ec532c3916ddbf5fa010814aefebe4dd4b537808b3f5bed0f896e1a27e34"},"schema_version":"1.0","source":{"id":"1809.03240","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03240","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03240v1","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03240","created_at":"2026-05-18T00:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"PVNQFFYZID33","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PVNQFFYZID33DB2B","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PVNQFFYZ","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:7931be8b98bc97e7fe47374cbb0333e7fc8385dfb2b93d930294163d3ec6b0fc","target":"graph","created_at":"2026-05-18T00:06:09Z","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":"Fully discrete Galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly-used Bear--Scheidegger diffusion-dispersion tensor: $$ D({\\bf u}) = \\gamma d_m I + |{\\bf u}|\\bigg( \\alpha_T I + (\\alpha_L - \\alpha_T) \\frac{{\\bf u} \\otimes {\\bf u}}{|{\\bf u}|^2}\\bigg) \\, . $$ Previous works on optimal-order $L^\\infty(0,T;L^2)$-norm error estimate required the regularity assumption $\\nabla_x\\partial_tD({\\bf u}(x,t)) \\in L^\\infty(0,T;L^\\infty(\\Omega))$, while the Bear--Scheidegger diffusion-dispersion tensor is only Lipschitz continuous even for","authors_text":"Buyang Li, Weiwei Sun, Wentao Cai, Yanping Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-10T11:31:08Z","title":"Analysis of fully discrete FEM for miscible displacement in porous media with Bear--Scheidegger diffusion tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03240","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":"sha256:53594ef0af6abb89c2f787dd974c1c0c8db8f06fb4eb7b965bc91c7dc8c60bca","target":"record","created_at":"2026-05-18T00:06:09Z","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":"b572c4f85429583283f6533e2879dbae370e6038b03d5be8102ba9994bbb9345","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-10T11:31:08Z","title_canon_sha256":"3cd2ec532c3916ddbf5fa010814aefebe4dd4b537808b3f5bed0f896e1a27e34"},"schema_version":"1.0","source":{"id":"1809.03240","kind":"arxiv","version":1}},"canonical_sha256":"7d5b02971940f7b1874137037f57228672b69c9de74584f5894a3a81b29f3d94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d5b02971940f7b1874137037f57228672b69c9de74584f5894a3a81b29f3d94","first_computed_at":"2026-05-18T00:06:09.536140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:09.536140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2ZI+sDt9Uxa3bWyjH1G1yxgDh0TYO4N/eIotmvks9op8S0f1GEljLLWhZWiUYHa+HDzQsKyMMXVU0iEyolUXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:09.536864Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03240","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53594ef0af6abb89c2f787dd974c1c0c8db8f06fb4eb7b965bc91c7dc8c60bca","sha256:7931be8b98bc97e7fe47374cbb0333e7fc8385dfb2b93d930294163d3ec6b0fc"],"state_sha256":"a86b6c1ce2ee0ae52f3a84152ca14b53dc3598a15958979c4ea67007691bab5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7TI6/UfmZITeNt5NE8eRXuQrfAwiM1UDYn2Ot/GwZaUeExY+G9tcjzjUG+YbkOCu1wa24LfkinMcjkcKEdNCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:37:50.815099Z","bundle_sha256":"72ac15791f141a926da7a2ae4071301caf9df383a4571dd430ab2d3b90e374a2"}}