{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:4IMHUJGMHFEIAM5A2CJXESKR7U","short_pith_number":"pith:4IMHUJGM","canonical_record":{"source":{"id":"math/0701007","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-12-30T07:17:50Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"15b8edd64533af1578fc12b9d0e07da1573f182afbbd02247f320b07eb771d44","abstract_canon_sha256":"4e449e6e764f621e2fe17563f25f6ad5940d6f601587a98ceb019286d233408e"},"schema_version":"1.0"},"canonical_sha256":"e2187a24cc39488033a0d093724951fd2b4ec6615af0626e2ad9eaf82def9e79","source":{"kind":"arxiv","id":"math/0701007","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701007","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701007v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701007","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"4IMHUJGMHFEI","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"4IMHUJGMHFEIAM5A","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"4IMHUJGM","created_at":"2026-06-03T22:06:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:4IMHUJGMHFEIAM5A2CJXESKR7U","target":"record","payload":{"canonical_record":{"source":{"id":"math/0701007","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-12-30T07:17:50Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"15b8edd64533af1578fc12b9d0e07da1573f182afbbd02247f320b07eb771d44","abstract_canon_sha256":"4e449e6e764f621e2fe17563f25f6ad5940d6f601587a98ceb019286d233408e"},"schema_version":"1.0"},"canonical_sha256":"e2187a24cc39488033a0d093724951fd2b4ec6615af0626e2ad9eaf82def9e79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:21.654798Z","signature_b64":"TT9R0Yfgts5BspgumkYzOYKl3h4YUpibn09xvXYxHCAQYr0xMfXcKiVLrjb15IZljyv3FPSrF9rQcXU4F1LsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2187a24cc39488033a0d093724951fd2b4ec6615af0626e2ad9eaf82def9e79","last_reissued_at":"2026-06-03T22:06:21.654443Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:21.654443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0701007","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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"125GEIC+Ej+0uGfrnH7NEtCsuyrCswjqMTCj1CrvMyA8hMi3rZ9rF/O2IX6q3y8T7ETKYoXzRmEe6YSOvBU2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:29:21.077042Z"},"content_sha256":"4a62d87a95083d664afdd8b9d1ffa5c44c37958e53acd615c14fb0bc016fe2e8","schema_version":"1.0","event_id":"sha256:4a62d87a95083d664afdd8b9d1ffa5c44c37958e53acd615c14fb0bc016fe2e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:4IMHUJGMHFEIAM5A2CJXESKR7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular limits in phase dynamics with physical viscosity and capillarity","license":"","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"K.T. Joseph, Philippe G. LeFloch","submitted_at":"2006-12-30T07:17:50Z","abstract_excerpt":"Following pioneering work by Fan and Slemrod who studied the effect of artificial viscosity terms, we consider the system of conservation laws arising in liquid-vapor phase dynamics with {\\sl physical} viscosity and capillarity effects taken into account. Following Dafermos we consider self-similar solutions to the Riemann problem and establish uniform total variation bounds, allowing us to deduce new existence results. Our analysis cover both the hyperbolic and the hyperbolic-elliptic regimes and apply to arbitrarily large Riemann data.\n  The proofs rely on a new technique of reduction to two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701007","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/math/0701007/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":"2026-06-03T22:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPnwVAV1/r5v5wktGqkqTzF+NdpDpCg9QKv20tTOENgi3y8TC4IcoByxuSI5MdPQo4F9NF6qcxEvwnthGNO4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:29:21.077943Z"},"content_sha256":"71c949e02d7a505dd87b339928048f8eceaf28adac31b3af39d73cbf46c68795","schema_version":"1.0","event_id":"sha256:71c949e02d7a505dd87b339928048f8eceaf28adac31b3af39d73cbf46c68795"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4IMHUJGMHFEIAM5A2CJXESKR7U/bundle.json","state_url":"https://pith.science/pith/4IMHUJGMHFEIAM5A2CJXESKR7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4IMHUJGMHFEIAM5A2CJXESKR7U/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":"2026-06-11T21:29:21Z","links":{"resolver":"https://pith.science/pith/4IMHUJGMHFEIAM5A2CJXESKR7U","bundle":"https://pith.science/pith/4IMHUJGMHFEIAM5A2CJXESKR7U/bundle.json","state":"https://pith.science/pith/4IMHUJGMHFEIAM5A2CJXESKR7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4IMHUJGMHFEIAM5A2CJXESKR7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4IMHUJGMHFEIAM5A2CJXESKR7U","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":"4e449e6e764f621e2fe17563f25f6ad5940d6f601587a98ceb019286d233408e","cross_cats_sorted":["cs.NA","math.NA"],"license":"","primary_cat":"math.AP","submitted_at":"2006-12-30T07:17:50Z","title_canon_sha256":"15b8edd64533af1578fc12b9d0e07da1573f182afbbd02247f320b07eb771d44"},"schema_version":"1.0","source":{"id":"math/0701007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701007","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701007v1","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701007","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"4IMHUJGMHFEI","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_16","alias_value":"4IMHUJGMHFEIAM5A","created_at":"2026-06-03T22:06:21Z"},{"alias_kind":"pith_short_8","alias_value":"4IMHUJGM","created_at":"2026-06-03T22:06:21Z"}],"graph_snapshots":[{"event_id":"sha256:71c949e02d7a505dd87b339928048f8eceaf28adac31b3af39d73cbf46c68795","target":"graph","created_at":"2026-06-03T22:06:21Z","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/math/0701007/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Following pioneering work by Fan and Slemrod who studied the effect of artificial viscosity terms, we consider the system of conservation laws arising in liquid-vapor phase dynamics with {\\sl physical} viscosity and capillarity effects taken into account. Following Dafermos we consider self-similar solutions to the Riemann problem and establish uniform total variation bounds, allowing us to deduce new existence results. Our analysis cover both the hyperbolic and the hyperbolic-elliptic regimes and apply to arbitrarily large Riemann data.\n  The proofs rely on a new technique of reduction to two","authors_text":"K.T. Joseph, Philippe G. LeFloch","cross_cats":["cs.NA","math.NA"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-12-30T07:17:50Z","title":"Singular limits in phase dynamics with physical viscosity and capillarity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701007","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":"sha256:4a62d87a95083d664afdd8b9d1ffa5c44c37958e53acd615c14fb0bc016fe2e8","target":"record","created_at":"2026-06-03T22:06:21Z","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":"4e449e6e764f621e2fe17563f25f6ad5940d6f601587a98ceb019286d233408e","cross_cats_sorted":["cs.NA","math.NA"],"license":"","primary_cat":"math.AP","submitted_at":"2006-12-30T07:17:50Z","title_canon_sha256":"15b8edd64533af1578fc12b9d0e07da1573f182afbbd02247f320b07eb771d44"},"schema_version":"1.0","source":{"id":"math/0701007","kind":"arxiv","version":1}},"canonical_sha256":"e2187a24cc39488033a0d093724951fd2b4ec6615af0626e2ad9eaf82def9e79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2187a24cc39488033a0d093724951fd2b4ec6615af0626e2ad9eaf82def9e79","first_computed_at":"2026-06-03T22:06:21.654443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:21.654443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TT9R0Yfgts5BspgumkYzOYKl3h4YUpibn09xvXYxHCAQYr0xMfXcKiVLrjb15IZljyv3FPSrF9rQcXU4F1LsCQ==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:21.654798Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a62d87a95083d664afdd8b9d1ffa5c44c37958e53acd615c14fb0bc016fe2e8","sha256:71c949e02d7a505dd87b339928048f8eceaf28adac31b3af39d73cbf46c68795"],"state_sha256":"80c5e9769aa5eb9169981c89f72dcb25462174755bdf1c1b712ccad2be13a0a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pz3bL8OR+zbh/oB9SJUZB9r2x3CCXoMJxMNzLSXL+PXU4DT31NcUW1s5OFpq1hM0iTrB/q61/I27VurF3xChAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:29:21.081029Z","bundle_sha256":"26711be40ae2ece740e84d362ebf7a7513390a99fd9cff2cf8e74a9eab6d1a27"}}