{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZEUZIODJLVKN5RVIIKDNMHCYNX","short_pith_number":"pith:ZEUZIODJ","canonical_record":{"source":{"id":"1304.3302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-11T14:00:39Z","cross_cats_sorted":[],"title_canon_sha256":"45ad9746f71a09974061e91c5f239a5897a454fae8fe7fb686139e778ca54336","abstract_canon_sha256":"42016387f158e94fedb7dcd9dc2ba753c1ad74d1fce098c6fdd878c6912da929"},"schema_version":"1.0"},"canonical_sha256":"c9299438695d54dec6a84286d61c586dee7828e05076c45f93a548c2e4bb4f37","source":{"kind":"arxiv","id":"1304.3302","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3302","created_at":"2026-05-18T03:28:18Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3302v1","created_at":"2026-05-18T03:28:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3302","created_at":"2026-05-18T03:28:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZEUZIODJLVKN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZEUZIODJLVKN5RVI","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZEUZIODJ","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZEUZIODJLVKN5RVIIKDNMHCYNX","target":"record","payload":{"canonical_record":{"source":{"id":"1304.3302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-11T14:00:39Z","cross_cats_sorted":[],"title_canon_sha256":"45ad9746f71a09974061e91c5f239a5897a454fae8fe7fb686139e778ca54336","abstract_canon_sha256":"42016387f158e94fedb7dcd9dc2ba753c1ad74d1fce098c6fdd878c6912da929"},"schema_version":"1.0"},"canonical_sha256":"c9299438695d54dec6a84286d61c586dee7828e05076c45f93a548c2e4bb4f37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:18.029126Z","signature_b64":"AQM1V57f0Utscc5nOULY3jh8b5ERCriA0twvUQzx0bmdBVu0NWhvHX0vaS03F+CwC/6JaGPbPYhy8qhbJjurDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9299438695d54dec6a84286d61c586dee7828e05076c45f93a548c2e4bb4f37","last_reissued_at":"2026-05-18T03:28:18.028455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:18.028455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.3302","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":"2026-05-18T03:28:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0s3XG7wrD32WSEE1Sd+beAVEh20tQ+1z2x0VAh702eKpzXKXD6fqNFFxcnzHRSBELbdqCXdJ4/nLkqEePZGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:46:01.388874Z"},"content_sha256":"f64dc64cd4919ec0abcd3233cb086ade043ddcc18b7bdca4b32a34f5771b0ad4","schema_version":"1.0","event_id":"sha256:f64dc64cd4919ec0abcd3233cb086ade043ddcc18b7bdca4b32a34f5771b0ad4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZEUZIODJLVKN5RVIIKDNMHCYNX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Qualitative behaviour of incompressible two-phase flows with phase transitions: The case of non-equal densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jan Pruess, Mathias Wilke, Senjo Shimizu","submitted_at":"2013-04-11T14:00:39Z","abstract_excerpt":"Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our well-posedness result to general geometries, study the stability of the equilibria of the problem, and show that a solution which does not develop singularities exists globally. If its limit set contains a stable equilibrium it converges to this equilibrium as time goes to infinity, in the natural state manifold for the problem in an Lp-setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3302","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":"2026-05-18T03:28:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fNFQKMwWnP12rMPDigZ8/vbZEKR9Xt/nBw+w9uJwrEgwh0y03Nb4llwHdIsWhWFL6i+ihKtx8n8yKKJkrH11Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:46:01.389364Z"},"content_sha256":"e66597fee98af169ef6bc064b04cc7cd4189f1917fc563ff4cccfaa3b93d6c77","schema_version":"1.0","event_id":"sha256:e66597fee98af169ef6bc064b04cc7cd4189f1917fc563ff4cccfaa3b93d6c77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZEUZIODJLVKN5RVIIKDNMHCYNX/bundle.json","state_url":"https://pith.science/pith/ZEUZIODJLVKN5RVIIKDNMHCYNX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZEUZIODJLVKN5RVIIKDNMHCYNX/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":"2026-05-26T13:46:01Z","links":{"resolver":"https://pith.science/pith/ZEUZIODJLVKN5RVIIKDNMHCYNX","bundle":"https://pith.science/pith/ZEUZIODJLVKN5RVIIKDNMHCYNX/bundle.json","state":"https://pith.science/pith/ZEUZIODJLVKN5RVIIKDNMHCYNX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZEUZIODJLVKN5RVIIKDNMHCYNX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZEUZIODJLVKN5RVIIKDNMHCYNX","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":"42016387f158e94fedb7dcd9dc2ba753c1ad74d1fce098c6fdd878c6912da929","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-11T14:00:39Z","title_canon_sha256":"45ad9746f71a09974061e91c5f239a5897a454fae8fe7fb686139e778ca54336"},"schema_version":"1.0","source":{"id":"1304.3302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3302","created_at":"2026-05-18T03:28:18Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3302v1","created_at":"2026-05-18T03:28:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3302","created_at":"2026-05-18T03:28:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZEUZIODJLVKN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZEUZIODJLVKN5RVI","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZEUZIODJ","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:e66597fee98af169ef6bc064b04cc7cd4189f1917fc563ff4cccfaa3b93d6c77","target":"graph","created_at":"2026-05-18T03:28:18Z","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":"Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our well-posedness result to general geometries, study the stability of the equilibria of the problem, and show that a solution which does not develop singularities exists globally. If its limit set contains a stable equilibrium it converges to this equilibrium as time goes to infinity, in the natural state manifold for the problem in an Lp-setting.","authors_text":"Jan Pruess, Mathias Wilke, Senjo Shimizu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-11T14:00:39Z","title":"Qualitative behaviour of incompressible two-phase flows with phase transitions: The case of non-equal densities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3302","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:f64dc64cd4919ec0abcd3233cb086ade043ddcc18b7bdca4b32a34f5771b0ad4","target":"record","created_at":"2026-05-18T03:28:18Z","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":"42016387f158e94fedb7dcd9dc2ba753c1ad74d1fce098c6fdd878c6912da929","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-11T14:00:39Z","title_canon_sha256":"45ad9746f71a09974061e91c5f239a5897a454fae8fe7fb686139e778ca54336"},"schema_version":"1.0","source":{"id":"1304.3302","kind":"arxiv","version":1}},"canonical_sha256":"c9299438695d54dec6a84286d61c586dee7828e05076c45f93a548c2e4bb4f37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9299438695d54dec6a84286d61c586dee7828e05076c45f93a548c2e4bb4f37","first_computed_at":"2026-05-18T03:28:18.028455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:18.028455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AQM1V57f0Utscc5nOULY3jh8b5ERCriA0twvUQzx0bmdBVu0NWhvHX0vaS03F+CwC/6JaGPbPYhy8qhbJjurDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:18.029126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f64dc64cd4919ec0abcd3233cb086ade043ddcc18b7bdca4b32a34f5771b0ad4","sha256:e66597fee98af169ef6bc064b04cc7cd4189f1917fc563ff4cccfaa3b93d6c77"],"state_sha256":"fd31d3a27cdae95c542a4b828caff84f7776c3ec0305291e83ab8beb522ca322"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWWUl5CCICbI1UV6pnHmImxJ5N6CVnbCp5yLfDtUS5uvqOYB0O/W5VM/0tojXcjNUjONY7aIBQ1s8gya3xRWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:46:01.393036Z","bundle_sha256":"7fccffc847e77aff8bc37982940ba981cded8b03945fc4a74a3629df1419294f"}}