{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WIRLFCWYROT67OEELPAENQDDP7","short_pith_number":"pith:WIRLFCWY","canonical_record":{"source":{"id":"1502.00380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-02-02T07:07:21Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"80dbb4abb283335eee55ce0edcd73cb4242be18c93257a985f5c84d385272417","abstract_canon_sha256":"924aa30270a4c5f057515e6fe423452272c95e0cfa8d3fcf38749220d4bc631d"},"schema_version":"1.0"},"canonical_sha256":"b222b28ad88ba7efb8845bc046c0637fdff0c111f7eb57a6f6630c6e3376254b","source":{"kind":"arxiv","id":"1502.00380","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00380","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00380v1","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00380","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"WIRLFCWYROT6","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WIRLFCWYROT67OEE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WIRLFCWY","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WIRLFCWYROT67OEELPAENQDDP7","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-02-02T07:07:21Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"80dbb4abb283335eee55ce0edcd73cb4242be18c93257a985f5c84d385272417","abstract_canon_sha256":"924aa30270a4c5f057515e6fe423452272c95e0cfa8d3fcf38749220d4bc631d"},"schema_version":"1.0"},"canonical_sha256":"b222b28ad88ba7efb8845bc046c0637fdff0c111f7eb57a6f6630c6e3376254b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:06.092911Z","signature_b64":"Z6gMTgrnwziPMkAW1PftQzLygQQ9AAl714sHzsErr3WeSVdO1bbOqMbGRaa1j/y0KSeO3/wiEELuf3S01hmNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b222b28ad88ba7efb8845bc046c0637fdff0c111f7eb57a6f6630c6e3376254b","last_reissued_at":"2026-05-18T02:28:06.092495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:06.092495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00380","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":"2026-05-18T02:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z6wOfHyHK1bCc6u1Hu2shkMH+lzf0p7iB+dqPFXycz3RQX40s654uD6wAGLmFb1KpkzggnMZXREtVO9HpFvnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:58:01.016842Z"},"content_sha256":"be79e0fdfd4cb0c129d3a9ceadac098eea67585cf27baf600ccb32bba4a1cac5","schema_version":"1.0","event_id":"sha256:be79e0fdfd4cb0c129d3a9ceadac098eea67585cf27baf600ccb32bba4a1cac5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WIRLFCWYROT67OEELPAENQDDP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a three-layer Hele-Shaw model of enhanced oil recovery with a linear viscous profile","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"physics.flu-dyn","authors_text":"Oscar Orellana, Prabir Daripa, Rodrigo Meneses","submitted_at":"2015-02-02T07:07:21Z","abstract_excerpt":"We present a non-standard eigenvalue problem that arises in the linear stability of a three-layer Hele-Shaw model of enhanced oil recovery. A nonlinear transformation is introduced which allows reformulation of the non-standard eigenvalue problem as a boundary value problem for Kummer's equation when the viscous profile of the middle layer is linear. Using the existing body of works on Kummer's equation, we construct an exact solution of the eigenvalue problem and provide the dispersion relation implicitly through the existence criterion for the non-trivial solution. We also discuss the conver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00380","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":"2026-05-18T02:28:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OopiUYfH/0dOhI+tFjwGW5WSFgryrHt59AT6hwNYCUgDh7cYxKDlgI7Id2Q2XuSIhE53FeZc6kyARV5N2jZZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:58:01.017189Z"},"content_sha256":"28de216f1924c358d2fb9e6610388a25dd6eaf67e0a7f7df0af8a4b65d2adad9","schema_version":"1.0","event_id":"sha256:28de216f1924c358d2fb9e6610388a25dd6eaf67e0a7f7df0af8a4b65d2adad9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WIRLFCWYROT67OEELPAENQDDP7/bundle.json","state_url":"https://pith.science/pith/WIRLFCWYROT67OEELPAENQDDP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WIRLFCWYROT67OEELPAENQDDP7/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":"2026-06-01T12:58:01Z","links":{"resolver":"https://pith.science/pith/WIRLFCWYROT67OEELPAENQDDP7","bundle":"https://pith.science/pith/WIRLFCWYROT67OEELPAENQDDP7/bundle.json","state":"https://pith.science/pith/WIRLFCWYROT67OEELPAENQDDP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WIRLFCWYROT67OEELPAENQDDP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WIRLFCWYROT67OEELPAENQDDP7","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":"924aa30270a4c5f057515e6fe423452272c95e0cfa8d3fcf38749220d4bc631d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-02-02T07:07:21Z","title_canon_sha256":"80dbb4abb283335eee55ce0edcd73cb4242be18c93257a985f5c84d385272417"},"schema_version":"1.0","source":{"id":"1502.00380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00380","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00380v1","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00380","created_at":"2026-05-18T02:28:06Z"},{"alias_kind":"pith_short_12","alias_value":"WIRLFCWYROT6","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WIRLFCWYROT67OEE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WIRLFCWY","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:28de216f1924c358d2fb9e6610388a25dd6eaf67e0a7f7df0af8a4b65d2adad9","target":"graph","created_at":"2026-05-18T02:28:06Z","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 non-standard eigenvalue problem that arises in the linear stability of a three-layer Hele-Shaw model of enhanced oil recovery. A nonlinear transformation is introduced which allows reformulation of the non-standard eigenvalue problem as a boundary value problem for Kummer's equation when the viscous profile of the middle layer is linear. Using the existing body of works on Kummer's equation, we construct an exact solution of the eigenvalue problem and provide the dispersion relation implicitly through the existence criterion for the non-trivial solution. We also discuss the conver","authors_text":"Oscar Orellana, Prabir Daripa, Rodrigo Meneses","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-02-02T07:07:21Z","title":"On a three-layer Hele-Shaw model of enhanced oil recovery with a linear viscous profile"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00380","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:be79e0fdfd4cb0c129d3a9ceadac098eea67585cf27baf600ccb32bba4a1cac5","target":"record","created_at":"2026-05-18T02:28:06Z","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":"924aa30270a4c5f057515e6fe423452272c95e0cfa8d3fcf38749220d4bc631d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2015-02-02T07:07:21Z","title_canon_sha256":"80dbb4abb283335eee55ce0edcd73cb4242be18c93257a985f5c84d385272417"},"schema_version":"1.0","source":{"id":"1502.00380","kind":"arxiv","version":1}},"canonical_sha256":"b222b28ad88ba7efb8845bc046c0637fdff0c111f7eb57a6f6630c6e3376254b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b222b28ad88ba7efb8845bc046c0637fdff0c111f7eb57a6f6630c6e3376254b","first_computed_at":"2026-05-18T02:28:06.092495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:06.092495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z6gMTgrnwziPMkAW1PftQzLygQQ9AAl714sHzsErr3WeSVdO1bbOqMbGRaa1j/y0KSeO3/wiEELuf3S01hmNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:06.092911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be79e0fdfd4cb0c129d3a9ceadac098eea67585cf27baf600ccb32bba4a1cac5","sha256:28de216f1924c358d2fb9e6610388a25dd6eaf67e0a7f7df0af8a4b65d2adad9"],"state_sha256":"d7fa4dae1b3f2b4417865ad76d9966e52de34e31cbb3df0309820cd9e692d3ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hr5zsKici4J197ekQkHSmaRfSxxYKgqxfyEWAK6xEtBHi/0MlphRPk4n+cplTppU3JFMEiDf5MNSiSGm9M7sBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:58:01.019123Z","bundle_sha256":"f5e8f0659cbf0165c42702963a68c76f4a8ce3b6496223d81b8825d06196f379"}}