{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZYZU6EMLJKKIO5O26PTO42BR3S","short_pith_number":"pith:ZYZU6EML","canonical_record":{"source":{"id":"1904.04778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-09T16:39:59Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4b3cacd282582c54c47c25c54323a0ef9bea09bb0aa553010ede874fe128225d","abstract_canon_sha256":"406e4e47ddc2f96c0efbf5a5b51d80433ccc1504615b36e0215419e6e5c98466"},"schema_version":"1.0"},"canonical_sha256":"ce334f118b4a948775daf3e6ee6831dcab1a2c2ef1e83e95aa0578523ae7ca62","source":{"kind":"arxiv","id":"1904.04778","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04778","created_at":"2026-05-17T23:42:20Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04778v1","created_at":"2026-05-17T23:42:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04778","created_at":"2026-05-17T23:42:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZYZU6EMLJKKI","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZYZU6EMLJKKIO5O2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZYZU6EML","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZYZU6EMLJKKIO5O26PTO42BR3S","target":"record","payload":{"canonical_record":{"source":{"id":"1904.04778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-09T16:39:59Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4b3cacd282582c54c47c25c54323a0ef9bea09bb0aa553010ede874fe128225d","abstract_canon_sha256":"406e4e47ddc2f96c0efbf5a5b51d80433ccc1504615b36e0215419e6e5c98466"},"schema_version":"1.0"},"canonical_sha256":"ce334f118b4a948775daf3e6ee6831dcab1a2c2ef1e83e95aa0578523ae7ca62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:20.003942Z","signature_b64":"VF3/Clo57zjxn/vbp2CuxkNBILmGv/2QfpAjVx1C6H00FnieFKUvCuHUJpWPUSsHHufvkXBvG1j8teFl4GshDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce334f118b4a948775daf3e6ee6831dcab1a2c2ef1e83e95aa0578523ae7ca62","last_reissued_at":"2026-05-17T23:42:20.003561Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:20.003561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.04778","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":"2026-05-17T23:42:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZUj3awtzizWcmXOPuvjuGLk3FI9F5m6DxNM5uqwHSJDWE+HeOJn8Li7u66q74dFcpQ3R8MtRbytXBLeT13UXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:20:03.758160Z"},"content_sha256":"fd74b2da13ce37b7a7f157fb10cc5330ca0639402d423787ee51ff134969f866","schema_version":"1.0","event_id":"sha256:fd74b2da13ce37b7a7f157fb10cc5330ca0639402d423787ee51ff134969f866"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZYZU6EMLJKKIO5O26PTO42BR3S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase transitions in filtration of Redlich-Kwong gases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Mikhail Roop, Valentin Lychagin","submitted_at":"2019-04-09T16:39:59Z","abstract_excerpt":"In this paper we study a 3-dimensional filtration of real gases described by Redlich-Kwong equations of state. Thermodynamical states are considered as Legendrian (Lagrangian) submanifolds in contact (symplectic) space. Connection between singularities of their projection on the space of intensive variables and phase transitions is shown. Explicit formulae for the Dirichlet boundary problem are given and the distribution of phases in space is shown."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04778","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":"2026-05-17T23:42:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opQzdKCEB1yleDuERF7DuJrC/zRZRovbX5Dfc4/7jERsrTnG9ajEWw/ydvKhNCRyFLBmQQb2O5mGsitnrxnLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:20:03.758528Z"},"content_sha256":"b0268aad4c11f8480b58589e09522474db7120b0371bae5a85749e814da5cc77","schema_version":"1.0","event_id":"sha256:b0268aad4c11f8480b58589e09522474db7120b0371bae5a85749e814da5cc77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYZU6EMLJKKIO5O26PTO42BR3S/bundle.json","state_url":"https://pith.science/pith/ZYZU6EMLJKKIO5O26PTO42BR3S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYZU6EMLJKKIO5O26PTO42BR3S/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":"2026-06-24T19:20:03Z","links":{"resolver":"https://pith.science/pith/ZYZU6EMLJKKIO5O26PTO42BR3S","bundle":"https://pith.science/pith/ZYZU6EMLJKKIO5O26PTO42BR3S/bundle.json","state":"https://pith.science/pith/ZYZU6EMLJKKIO5O26PTO42BR3S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYZU6EMLJKKIO5O26PTO42BR3S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZYZU6EMLJKKIO5O26PTO42BR3S","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":"406e4e47ddc2f96c0efbf5a5b51d80433ccc1504615b36e0215419e6e5c98466","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-09T16:39:59Z","title_canon_sha256":"4b3cacd282582c54c47c25c54323a0ef9bea09bb0aa553010ede874fe128225d"},"schema_version":"1.0","source":{"id":"1904.04778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04778","created_at":"2026-05-17T23:42:20Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04778v1","created_at":"2026-05-17T23:42:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04778","created_at":"2026-05-17T23:42:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZYZU6EMLJKKI","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZYZU6EMLJKKIO5O2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZYZU6EML","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:b0268aad4c11f8480b58589e09522474db7120b0371bae5a85749e814da5cc77","target":"graph","created_at":"2026-05-17T23:42:20Z","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":"In this paper we study a 3-dimensional filtration of real gases described by Redlich-Kwong equations of state. Thermodynamical states are considered as Legendrian (Lagrangian) submanifolds in contact (symplectic) space. Connection between singularities of their projection on the space of intensive variables and phase transitions is shown. Explicit formulae for the Dirichlet boundary problem are given and the distribution of phases in space is shown.","authors_text":"Mikhail Roop, Valentin Lychagin","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-09T16:39:59Z","title":"Phase transitions in filtration of Redlich-Kwong gases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04778","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:fd74b2da13ce37b7a7f157fb10cc5330ca0639402d423787ee51ff134969f866","target":"record","created_at":"2026-05-17T23:42:20Z","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":"406e4e47ddc2f96c0efbf5a5b51d80433ccc1504615b36e0215419e6e5c98466","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-04-09T16:39:59Z","title_canon_sha256":"4b3cacd282582c54c47c25c54323a0ef9bea09bb0aa553010ede874fe128225d"},"schema_version":"1.0","source":{"id":"1904.04778","kind":"arxiv","version":1}},"canonical_sha256":"ce334f118b4a948775daf3e6ee6831dcab1a2c2ef1e83e95aa0578523ae7ca62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce334f118b4a948775daf3e6ee6831dcab1a2c2ef1e83e95aa0578523ae7ca62","first_computed_at":"2026-05-17T23:42:20.003561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:20.003561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VF3/Clo57zjxn/vbp2CuxkNBILmGv/2QfpAjVx1C6H00FnieFKUvCuHUJpWPUSsHHufvkXBvG1j8teFl4GshDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:20.003942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd74b2da13ce37b7a7f157fb10cc5330ca0639402d423787ee51ff134969f866","sha256:b0268aad4c11f8480b58589e09522474db7120b0371bae5a85749e814da5cc77"],"state_sha256":"7e284ffbc8404a94f529029b3d28c130cd99960aa6ae40d6a9c750075dfc32a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kxbkJr1HpgayEppzKjrIR4Syq+8o2Dlxpiv4ushQICyHmMV7eWSIcrm6Mot9+skIp7GdwWKt8goXs7ynMfl+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:20:03.760471Z","bundle_sha256":"ea5ab35382a976093af21845c55fcf87a47b6ebed5e8b8ed7eaefd3a09780ed7"}}