{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BQRBIJ3UYZTBWG36KODA4ITOPA","short_pith_number":"pith:BQRBIJ3U","canonical_record":{"source":{"id":"2506.08152","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-09T18:59:02Z","cross_cats_sorted":["math-ph","math.MP","physics.flu-dyn"],"title_canon_sha256":"8340c9eb7b93192e827d4f16f5fce98c7a776c5eba5d1ac86629c09115ddb9a7","abstract_canon_sha256":"100428d8c796753965b486c94bf74cfa619d270cd22051f5868f9e3e27e3c9a3"},"schema_version":"1.0"},"canonical_sha256":"0c22142774c6661b1b7e53860e226e780bffa5bf3164a29b44a27bec3d0c4797","source":{"kind":"arxiv","id":"2506.08152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08152","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08152v1","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08152","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"BQRBIJ3UYZTB","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_16","alias_value":"BQRBIJ3UYZTBWG36","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_8","alias_value":"BQRBIJ3U","created_at":"2026-05-20T00:01:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BQRBIJ3UYZTBWG36KODA4ITOPA","target":"record","payload":{"canonical_record":{"source":{"id":"2506.08152","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-09T18:59:02Z","cross_cats_sorted":["math-ph","math.MP","physics.flu-dyn"],"title_canon_sha256":"8340c9eb7b93192e827d4f16f5fce98c7a776c5eba5d1ac86629c09115ddb9a7","abstract_canon_sha256":"100428d8c796753965b486c94bf74cfa619d270cd22051f5868f9e3e27e3c9a3"},"schema_version":"1.0"},"canonical_sha256":"0c22142774c6661b1b7e53860e226e780bffa5bf3164a29b44a27bec3d0c4797","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:34.466067Z","signature_b64":"FmJHpupFfP7GXuu0PvcL/lCJy2WC9aKlKGKZ5wtQ9e+G4oo3VNiWlIBKvV0ewRgzWHtlDHixNQDpMTMWZrZzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c22142774c6661b1b7e53860e226e780bffa5bf3164a29b44a27bec3d0c4797","last_reissued_at":"2026-05-20T00:01:34.465427Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:34.465427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.08152","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":"2026-05-20T00:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8CGKGJnRynxpF73Y1NaR4hrLRnTonK97pEGA2aa1lJXbPJDoFWC9paZ89LZKEOYIiGXinVlbOiA9o2SXUDygCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:13:47.698074Z"},"content_sha256":"1f95fd26d8b70f95880c90daea0ba5f3561ec02eb7573fc700165ad8477224e0","schema_version":"1.0","event_id":"sha256:1f95fd26d8b70f95880c90daea0ba5f3561ec02eb7573fc700165ad8477224e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BQRBIJ3UYZTBWG36KODA4ITOPA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Riemann problem for three-phase foam flow in porous media","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Dan Marchesin, Grigori Chapiro, Luis Fernando Lozano","submitted_at":"2025-06-09T18:59:02Z","abstract_excerpt":"Gas injection in the context of the three-phase flow in porous media appears in applications such as Enhanced Oil Recovery, aquifer remediation, and carbon capture, utilization, and storage (CCUS). In general, this technique suffers from a difficulty related to excessive gas mobility, which can be circumvented by using foam. This study addresses the non-linear system of differential equations describing the three-phase foam flow based on Corey relative permeability functions. A major obstacle is an umbilic point, where the characteristic wave velocities for different families coincide, complic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08152","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08152/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T00:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2uCOi76T+k/ZnA6VNLxvzUXgk7KLF4KDlWmqTV1Mh8Si/eMLKM9iDyYYOKQV0l4t8O4nIWwkHwO7pf6nGgxMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:13:47.698764Z"},"content_sha256":"2a0c85500f5784933e54bb65fcff1ae6efe00867ecbd043860d86180310dfeed","schema_version":"1.0","event_id":"sha256:2a0c85500f5784933e54bb65fcff1ae6efe00867ecbd043860d86180310dfeed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQRBIJ3UYZTBWG36KODA4ITOPA/bundle.json","state_url":"https://pith.science/pith/BQRBIJ3UYZTBWG36KODA4ITOPA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQRBIJ3UYZTBWG36KODA4ITOPA/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":"2026-06-10T13:13:47Z","links":{"resolver":"https://pith.science/pith/BQRBIJ3UYZTBWG36KODA4ITOPA","bundle":"https://pith.science/pith/BQRBIJ3UYZTBWG36KODA4ITOPA/bundle.json","state":"https://pith.science/pith/BQRBIJ3UYZTBWG36KODA4ITOPA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQRBIJ3UYZTBWG36KODA4ITOPA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BQRBIJ3UYZTBWG36KODA4ITOPA","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":"100428d8c796753965b486c94bf74cfa619d270cd22051f5868f9e3e27e3c9a3","cross_cats_sorted":["math-ph","math.MP","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-09T18:59:02Z","title_canon_sha256":"8340c9eb7b93192e827d4f16f5fce98c7a776c5eba5d1ac86629c09115ddb9a7"},"schema_version":"1.0","source":{"id":"2506.08152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.08152","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.08152v1","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08152","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"BQRBIJ3UYZTB","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_16","alias_value":"BQRBIJ3UYZTBWG36","created_at":"2026-05-20T00:01:34Z"},{"alias_kind":"pith_short_8","alias_value":"BQRBIJ3U","created_at":"2026-05-20T00:01:34Z"}],"graph_snapshots":[{"event_id":"sha256:2a0c85500f5784933e54bb65fcff1ae6efe00867ecbd043860d86180310dfeed","target":"graph","created_at":"2026-05-20T00:01:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.08152/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gas injection in the context of the three-phase flow in porous media appears in applications such as Enhanced Oil Recovery, aquifer remediation, and carbon capture, utilization, and storage (CCUS). In general, this technique suffers from a difficulty related to excessive gas mobility, which can be circumvented by using foam. This study addresses the non-linear system of differential equations describing the three-phase foam flow based on Corey relative permeability functions. A major obstacle is an umbilic point, where the characteristic wave velocities for different families coincide, complic","authors_text":"Dan Marchesin, Grigori Chapiro, Luis Fernando Lozano","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-09T18:59:02Z","title":"The Riemann problem for three-phase foam flow in porous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08152","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":"sha256:1f95fd26d8b70f95880c90daea0ba5f3561ec02eb7573fc700165ad8477224e0","target":"record","created_at":"2026-05-20T00:01:34Z","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":"100428d8c796753965b486c94bf74cfa619d270cd22051f5868f9e3e27e3c9a3","cross_cats_sorted":["math-ph","math.MP","physics.flu-dyn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-09T18:59:02Z","title_canon_sha256":"8340c9eb7b93192e827d4f16f5fce98c7a776c5eba5d1ac86629c09115ddb9a7"},"schema_version":"1.0","source":{"id":"2506.08152","kind":"arxiv","version":1}},"canonical_sha256":"0c22142774c6661b1b7e53860e226e780bffa5bf3164a29b44a27bec3d0c4797","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c22142774c6661b1b7e53860e226e780bffa5bf3164a29b44a27bec3d0c4797","first_computed_at":"2026-05-20T00:01:34.465427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:34.465427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FmJHpupFfP7GXuu0PvcL/lCJy2WC9aKlKGKZ5wtQ9e+G4oo3VNiWlIBKvV0ewRgzWHtlDHixNQDpMTMWZrZzAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:34.466067Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.08152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f95fd26d8b70f95880c90daea0ba5f3561ec02eb7573fc700165ad8477224e0","sha256:2a0c85500f5784933e54bb65fcff1ae6efe00867ecbd043860d86180310dfeed"],"state_sha256":"157c675e922050d09aca6b772079085fabb737577326fed4a5726c2af8a070b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZegJhGGBYzsr6VSmzlHMl5WD9TnQYo3/2co2aCKmD6hAP9/Mf4VLCYpvUfeWLvuVoAq8Vu1bfe/chMDj0WVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:13:47.702993Z","bundle_sha256":"4232b2fd63ba1f769a73e468bd18c6e2818e014c698998a7736c58988f8ce678"}}