{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GXTD5HI4NGDJXOCSY7ASAKZ53Z","short_pith_number":"pith:GXTD5HI4","canonical_record":{"source":{"id":"1307.3647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-13T13:45:12Z","cross_cats_sorted":[],"title_canon_sha256":"9442c75154410d8c395f6eea937d8581f0c84ad2c43a386a99554b67b787ac71","abstract_canon_sha256":"4f577b45d68093d63b3c92afb380e2e85351e0814db7b7fd4c6e93aa39b2abc8"},"schema_version":"1.0"},"canonical_sha256":"35e63e9d1c69869bb852c7c1202b3dde5b474bcaa6b0680e3c0a92d0327ed20e","source":{"kind":"arxiv","id":"1307.3647","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3647","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3647v1","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3647","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"GXTD5HI4NGDJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"GXTD5HI4NGDJXOCS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"GXTD5HI4","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GXTD5HI4NGDJXOCSY7ASAKZ53Z","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-13T13:45:12Z","cross_cats_sorted":[],"title_canon_sha256":"9442c75154410d8c395f6eea937d8581f0c84ad2c43a386a99554b67b787ac71","abstract_canon_sha256":"4f577b45d68093d63b3c92afb380e2e85351e0814db7b7fd4c6e93aa39b2abc8"},"schema_version":"1.0"},"canonical_sha256":"35e63e9d1c69869bb852c7c1202b3dde5b474bcaa6b0680e3c0a92d0327ed20e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:28.291217Z","signature_b64":"0RfbKPfirFCt5Q+86KcX6VIi1A39Tupf59s+QCyhqMTncSg5lVbpJSUHkkS3F3yBJTGtVYl0r2rIv3JgtY1bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e63e9d1c69869bb852c7c1202b3dde5b474bcaa6b0680e3c0a92d0327ed20e","last_reissued_at":"2026-05-18T03:18:28.290510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:28.290510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3647","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":"2026-05-18T03:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h8vDU34SC0eOAojP+3ODUtMoxt+1ygF3HcTpsgpNUAOnzMZI4AfMovWqF1aWa8ZWyqsOAlOHHe8nFJvCfEqKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:01:19.780476Z"},"content_sha256":"a8e15aff6cc6f8bb57e9708d389df5f9dd34a13fec6675152ed1fddb044fbbe6","schema_version":"1.0","event_id":"sha256:a8e15aff6cc6f8bb57e9708d389df5f9dd34a13fec6675152ed1fddb044fbbe6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GXTD5HI4NGDJXOCSY7ASAKZ53Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffuse planar phase boundaries in a two-phase fluid with one very dense phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Heinrich Freistuhler, Matthias Kotschote","submitted_at":"2013-07-13T13:45:12Z","abstract_excerpt":"This note studies Navier-Stokes-Allen-Cahn models for compressible fluids that are mixtures of two incompressible phases whose density ratio eps=rho_1/rho_2 is very small. Under a natural assumption on the mixing energy, it shows the existence of diffuse planar phase boundaries for all 0=eps<eps_0. For eps=0, one recovers the Navier-Stokes-Korteweg model and its well-known diffuse phase boundaries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3647","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":"2026-05-18T03:18:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pr3SRxIOwBJKHno+FlCov2vFeadGajMNTNELLhwdk1OR/5DHZ3HV6WyPq+Eu7+lb1ve+CmHenIobs8hiAY+LCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:01:19.780815Z"},"content_sha256":"49dbb357659bfb1908e9d3188e62ccec1f8453b238ff58ba7612e88234961d4e","schema_version":"1.0","event_id":"sha256:49dbb357659bfb1908e9d3188e62ccec1f8453b238ff58ba7612e88234961d4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXTD5HI4NGDJXOCSY7ASAKZ53Z/bundle.json","state_url":"https://pith.science/pith/GXTD5HI4NGDJXOCSY7ASAKZ53Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXTD5HI4NGDJXOCSY7ASAKZ53Z/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":"2026-06-23T03:01:19Z","links":{"resolver":"https://pith.science/pith/GXTD5HI4NGDJXOCSY7ASAKZ53Z","bundle":"https://pith.science/pith/GXTD5HI4NGDJXOCSY7ASAKZ53Z/bundle.json","state":"https://pith.science/pith/GXTD5HI4NGDJXOCSY7ASAKZ53Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXTD5HI4NGDJXOCSY7ASAKZ53Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GXTD5HI4NGDJXOCSY7ASAKZ53Z","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":"4f577b45d68093d63b3c92afb380e2e85351e0814db7b7fd4c6e93aa39b2abc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-13T13:45:12Z","title_canon_sha256":"9442c75154410d8c395f6eea937d8581f0c84ad2c43a386a99554b67b787ac71"},"schema_version":"1.0","source":{"id":"1307.3647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3647","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3647v1","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3647","created_at":"2026-05-18T03:18:28Z"},{"alias_kind":"pith_short_12","alias_value":"GXTD5HI4NGDJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"GXTD5HI4NGDJXOCS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"GXTD5HI4","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:49dbb357659bfb1908e9d3188e62ccec1f8453b238ff58ba7612e88234961d4e","target":"graph","created_at":"2026-05-18T03:18:28Z","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":"This note studies Navier-Stokes-Allen-Cahn models for compressible fluids that are mixtures of two incompressible phases whose density ratio eps=rho_1/rho_2 is very small. Under a natural assumption on the mixing energy, it shows the existence of diffuse planar phase boundaries for all 0=eps<eps_0. For eps=0, one recovers the Navier-Stokes-Korteweg model and its well-known diffuse phase boundaries.","authors_text":"Heinrich Freistuhler, Matthias Kotschote","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-13T13:45:12Z","title":"Diffuse planar phase boundaries in a two-phase fluid with one very dense phase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3647","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:a8e15aff6cc6f8bb57e9708d389df5f9dd34a13fec6675152ed1fddb044fbbe6","target":"record","created_at":"2026-05-18T03:18:28Z","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":"4f577b45d68093d63b3c92afb380e2e85351e0814db7b7fd4c6e93aa39b2abc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-13T13:45:12Z","title_canon_sha256":"9442c75154410d8c395f6eea937d8581f0c84ad2c43a386a99554b67b787ac71"},"schema_version":"1.0","source":{"id":"1307.3647","kind":"arxiv","version":1}},"canonical_sha256":"35e63e9d1c69869bb852c7c1202b3dde5b474bcaa6b0680e3c0a92d0327ed20e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35e63e9d1c69869bb852c7c1202b3dde5b474bcaa6b0680e3c0a92d0327ed20e","first_computed_at":"2026-05-18T03:18:28.290510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:28.290510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0RfbKPfirFCt5Q+86KcX6VIi1A39Tupf59s+QCyhqMTncSg5lVbpJSUHkkS3F3yBJTGtVYl0r2rIv3JgtY1bDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:28.291217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8e15aff6cc6f8bb57e9708d389df5f9dd34a13fec6675152ed1fddb044fbbe6","sha256:49dbb357659bfb1908e9d3188e62ccec1f8453b238ff58ba7612e88234961d4e"],"state_sha256":"5396d0cee3b678c5b84aaffbe366ec5f7b84cf2f9c72c41a413af815355fe207"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jivVDwA1TjiPAmLEWRuYviMw7HrpLy6hBwBo+gsZLYkGaw9u1MH2zsDvBL+9tQ3cJle51X1OXX5sXPrEe9yyDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:01:19.782699Z","bundle_sha256":"13375d6d95587c3b5b10a2dfbf9dd98f9785de876d28716fd714f84b7be32336"}}