{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE","short_pith_number":"pith:ZZ7F6NNM","canonical_record":{"source":{"id":"1809.07265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-19T16:03:30Z","cross_cats_sorted":[],"title_canon_sha256":"af7017c352f284cc03c0223e367f6270655a86f98096bf42ab619eafe57b4267","abstract_canon_sha256":"2ba63d42218b43f41cb617f1b0f276f38d55d8a21c42fd4cb57debf6dae8d916"},"schema_version":"1.0"},"canonical_sha256":"ce7e5f35ac06f30f2632c0359e89eeb9108f68efb9660dd0d324e5ff1b7c34bb","source":{"kind":"arxiv","id":"1809.07265","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07265","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07265v1","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07265","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZZ7F6NNMA3ZQ","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZZ7F6NNMA3ZQ6JRS","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZZ7F6NNM","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07265","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-19T16:03:30Z","cross_cats_sorted":[],"title_canon_sha256":"af7017c352f284cc03c0223e367f6270655a86f98096bf42ab619eafe57b4267","abstract_canon_sha256":"2ba63d42218b43f41cb617f1b0f276f38d55d8a21c42fd4cb57debf6dae8d916"},"schema_version":"1.0"},"canonical_sha256":"ce7e5f35ac06f30f2632c0359e89eeb9108f68efb9660dd0d324e5ff1b7c34bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:20.212359Z","signature_b64":"noMrLi6V5GQSaqbG1IqqXhcfa1Uckz8job1LQB4U8K0Aed99hwobgWs+FVR22fH9Ta1jzsolGONw/1F6/OiMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce7e5f35ac06f30f2632c0359e89eeb9108f68efb9660dd0d324e5ff1b7c34bb","last_reissued_at":"2026-05-18T00:05:20.211710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:20.211710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07265","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":"2026-05-18T00:05:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhNV/wroP9tr+Rh9frFiNjFVICB6zkOQjRa/B7bSpFT0Z56qdIOZkbkcLOki/3HoG21fjPDr8nmP7wAkjZeyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:12:06.009255Z"},"content_sha256":"22d14bb8d6e462dcdb154a257b57c866f5879257e501046f2adf127eae48e799","schema_version":"1.0","event_id":"sha256:22d14bb8d6e462dcdb154a257b57c866f5879257e501046f2adf127eae48e799"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markov selection for the stochastic compressible Navier--Stokes system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dominic Breit, Eduard Feireisl, Martina Hofmanova","submitted_at":"2018-09-19T16:03:30Z","abstract_excerpt":"We analyze the Markov property of solutions to the compressible Navier--Stokes system perturbed by a general multiplicative stochastic forcing. We show the existence of an almost sure Markov selection to the associated martingale problem. Our proof is based on the abstract framework introduced in [F. Flandoli, M. Romito: Markov selections for the 3D stochastic Navier--Stokes equations. Probab. Theory Relat. Fields 140, 407--458. (2008)]. A major difficulty arises from the fact, different from the incompressible case, that the velocity field is not continuous in time. In addition, it cannot be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07265","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":"2026-05-18T00:05:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmibV+q46xEn0Jz0FW36MuHj/zkNbisWWmGzXgjJ7tcST/RxndFNHsl1qB8l+54DyAJns2g60OnofoP3gpCuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:12:06.009810Z"},"content_sha256":"aa9ccdc684f0bb23a8cb09a29424ddc9171384e74793ec7a145ccea92a2efd81","schema_version":"1.0","event_id":"sha256:aa9ccdc684f0bb23a8cb09a29424ddc9171384e74793ec7a145ccea92a2efd81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE/bundle.json","state_url":"https://pith.science/pith/ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE/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":"2026-05-26T16:12:06Z","links":{"resolver":"https://pith.science/pith/ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE","bundle":"https://pith.science/pith/ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE/bundle.json","state":"https://pith.science/pith/ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZZ7F6NNMA3ZQ6JRSYA2Z5CPOXE","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":"2ba63d42218b43f41cb617f1b0f276f38d55d8a21c42fd4cb57debf6dae8d916","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-19T16:03:30Z","title_canon_sha256":"af7017c352f284cc03c0223e367f6270655a86f98096bf42ab619eafe57b4267"},"schema_version":"1.0","source":{"id":"1809.07265","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07265","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07265v1","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07265","created_at":"2026-05-18T00:05:20Z"},{"alias_kind":"pith_short_12","alias_value":"ZZ7F6NNMA3ZQ","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZZ7F6NNMA3ZQ6JRS","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZZ7F6NNM","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:aa9ccdc684f0bb23a8cb09a29424ddc9171384e74793ec7a145ccea92a2efd81","target":"graph","created_at":"2026-05-18T00:05:20Z","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":"We analyze the Markov property of solutions to the compressible Navier--Stokes system perturbed by a general multiplicative stochastic forcing. We show the existence of an almost sure Markov selection to the associated martingale problem. Our proof is based on the abstract framework introduced in [F. Flandoli, M. Romito: Markov selections for the 3D stochastic Navier--Stokes equations. Probab. Theory Relat. Fields 140, 407--458. (2008)]. A major difficulty arises from the fact, different from the incompressible case, that the velocity field is not continuous in time. In addition, it cannot be ","authors_text":"Dominic Breit, Eduard Feireisl, Martina Hofmanova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-19T16:03:30Z","title":"Markov selection for the stochastic compressible Navier--Stokes system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07265","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":"sha256:22d14bb8d6e462dcdb154a257b57c866f5879257e501046f2adf127eae48e799","target":"record","created_at":"2026-05-18T00:05:20Z","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":"2ba63d42218b43f41cb617f1b0f276f38d55d8a21c42fd4cb57debf6dae8d916","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-19T16:03:30Z","title_canon_sha256":"af7017c352f284cc03c0223e367f6270655a86f98096bf42ab619eafe57b4267"},"schema_version":"1.0","source":{"id":"1809.07265","kind":"arxiv","version":1}},"canonical_sha256":"ce7e5f35ac06f30f2632c0359e89eeb9108f68efb9660dd0d324e5ff1b7c34bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce7e5f35ac06f30f2632c0359e89eeb9108f68efb9660dd0d324e5ff1b7c34bb","first_computed_at":"2026-05-18T00:05:20.211710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:20.211710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"noMrLi6V5GQSaqbG1IqqXhcfa1Uckz8job1LQB4U8K0Aed99hwobgWs+FVR22fH9Ta1jzsolGONw/1F6/OiMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:20.212359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07265","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22d14bb8d6e462dcdb154a257b57c866f5879257e501046f2adf127eae48e799","sha256:aa9ccdc684f0bb23a8cb09a29424ddc9171384e74793ec7a145ccea92a2efd81"],"state_sha256":"4235e63c9071dfe4aa8e8d0cb1104d05b9d2b8f0b189681bda7b03e19b683863"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DouQ6xax2GNNedP8sZnzMdOqkcOBxtSz1IP1kDU2F79GAuqJQ3PAenZoBnCyTWNWJGfXgJSDyRNrBKQoIW6bCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:12:06.013050Z","bundle_sha256":"d41a3f33ad2cc02a11b356dbcbe8e811ce662e4a5db78ef16c561761a87a0768"}}