{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ULXTFGLS2JOQ77P5AK5RWI547D","short_pith_number":"pith:ULXTFGLS","canonical_record":{"source":{"id":"1503.06684","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-23T15:26:29Z","cross_cats_sorted":[],"title_canon_sha256":"4417a8055a6de90d83b7686c68a61509e685edde5726d5795ac3300f1c225773","abstract_canon_sha256":"78ac75bb6220ea82bd7ea83a318d2df542d4cb6c91defc574a0ce6e498f98487"},"schema_version":"1.0"},"canonical_sha256":"a2ef329972d25d0ffdfd02bb1b23bcf8f3975dee0118a89e85cc2c209531a6b6","source":{"kind":"arxiv","id":"1503.06684","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06684","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06684v2","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06684","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"ULXTFGLS2JOQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"ULXTFGLS2JOQ77P5","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"ULXTFGLS","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ULXTFGLS2JOQ77P5AK5RWI547D","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06684","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-23T15:26:29Z","cross_cats_sorted":[],"title_canon_sha256":"4417a8055a6de90d83b7686c68a61509e685edde5726d5795ac3300f1c225773","abstract_canon_sha256":"78ac75bb6220ea82bd7ea83a318d2df542d4cb6c91defc574a0ce6e498f98487"},"schema_version":"1.0"},"canonical_sha256":"a2ef329972d25d0ffdfd02bb1b23bcf8f3975dee0118a89e85cc2c209531a6b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:40.616210Z","signature_b64":"6wzURZlFjHlu8vLcx+deWmgvlsx1IWUXCbbi1nopCvzZ5tITOUxmXgOfaLvT+O20M7TWupk0qfIpvmhOHyBoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2ef329972d25d0ffdfd02bb1b23bcf8f3975dee0118a89e85cc2c209531a6b6","last_reissued_at":"2026-05-18T00:53:40.615771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:40.615771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06684","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PB1NevE3yywNSGHztpb5RCZPsKwMKwLokpg1QvorudkmJuT0t7gFv7p4bt6J7eaoyXuvuYYsFckQKBwidqYqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:38:33.361620Z"},"content_sha256":"ec774268ec06fff2e8c1c79622abe3bf087a8b73832d3514b08a113979282dcd","schema_version":"1.0","event_id":"sha256:ec774268ec06fff2e8c1c79622abe3bf087a8b73832d3514b08a113979282dcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ULXTFGLS2JOQ77P5AK5RWI547D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incompressible limit for compressible fluids with stochastic forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dominic Breit, Eduard Feireisl, Martina Hofmanova","submitted_at":"2015-03-23T15:26:29Z","abstract_excerpt":"We study the asymptotic behavior of the isentropic Navier-Stokes system driven by a multiplicative stochastic forcing in the compressible regime, where the Mach number approaches zero. Our approach is based on the recently developed concept of weak martingale solution to the primitive system, uniform bounds derived from a stochastic analogue of the modulated energy inequality, and careful analysis of acoustic waves. A stochastic incompressible Navier-Stokes system is identified as the limit problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06684","kind":"arxiv","version":2},"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":"2026-05-18T00:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z647fSDJbJaPmEkkV5LVd72kRr6MYWzLmPkzVcvbAGhrRoQsRcz64g0O7bdEnxdO9P9x1ee9QYOkBR1Hfgj5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:38:33.362271Z"},"content_sha256":"a963a670fa5179d98656dcf3a31e86286a05444f497f8633a5e5709b1e42b1b3","schema_version":"1.0","event_id":"sha256:a963a670fa5179d98656dcf3a31e86286a05444f497f8633a5e5709b1e42b1b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULXTFGLS2JOQ77P5AK5RWI547D/bundle.json","state_url":"https://pith.science/pith/ULXTFGLS2JOQ77P5AK5RWI547D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULXTFGLS2JOQ77P5AK5RWI547D/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":"2026-05-27T02:38:33Z","links":{"resolver":"https://pith.science/pith/ULXTFGLS2JOQ77P5AK5RWI547D","bundle":"https://pith.science/pith/ULXTFGLS2JOQ77P5AK5RWI547D/bundle.json","state":"https://pith.science/pith/ULXTFGLS2JOQ77P5AK5RWI547D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULXTFGLS2JOQ77P5AK5RWI547D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ULXTFGLS2JOQ77P5AK5RWI547D","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":"78ac75bb6220ea82bd7ea83a318d2df542d4cb6c91defc574a0ce6e498f98487","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-23T15:26:29Z","title_canon_sha256":"4417a8055a6de90d83b7686c68a61509e685edde5726d5795ac3300f1c225773"},"schema_version":"1.0","source":{"id":"1503.06684","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06684","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06684v2","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06684","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"ULXTFGLS2JOQ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"ULXTFGLS2JOQ77P5","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"ULXTFGLS","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:a963a670fa5179d98656dcf3a31e86286a05444f497f8633a5e5709b1e42b1b3","target":"graph","created_at":"2026-05-18T00:53:40Z","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 study the asymptotic behavior of the isentropic Navier-Stokes system driven by a multiplicative stochastic forcing in the compressible regime, where the Mach number approaches zero. Our approach is based on the recently developed concept of weak martingale solution to the primitive system, uniform bounds derived from a stochastic analogue of the modulated energy inequality, and careful analysis of acoustic waves. A stochastic incompressible Navier-Stokes system is identified as the limit problem.","authors_text":"Dominic Breit, Eduard Feireisl, Martina Hofmanova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-23T15:26:29Z","title":"Incompressible limit for compressible fluids with stochastic forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06684","kind":"arxiv","version":2},"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:ec774268ec06fff2e8c1c79622abe3bf087a8b73832d3514b08a113979282dcd","target":"record","created_at":"2026-05-18T00:53:40Z","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":"78ac75bb6220ea82bd7ea83a318d2df542d4cb6c91defc574a0ce6e498f98487","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-23T15:26:29Z","title_canon_sha256":"4417a8055a6de90d83b7686c68a61509e685edde5726d5795ac3300f1c225773"},"schema_version":"1.0","source":{"id":"1503.06684","kind":"arxiv","version":2}},"canonical_sha256":"a2ef329972d25d0ffdfd02bb1b23bcf8f3975dee0118a89e85cc2c209531a6b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2ef329972d25d0ffdfd02bb1b23bcf8f3975dee0118a89e85cc2c209531a6b6","first_computed_at":"2026-05-18T00:53:40.615771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:40.615771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6wzURZlFjHlu8vLcx+deWmgvlsx1IWUXCbbi1nopCvzZ5tITOUxmXgOfaLvT+O20M7TWupk0qfIpvmhOHyBoAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:40.616210Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06684","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec774268ec06fff2e8c1c79622abe3bf087a8b73832d3514b08a113979282dcd","sha256:a963a670fa5179d98656dcf3a31e86286a05444f497f8633a5e5709b1e42b1b3"],"state_sha256":"47c3beb00587cbaeb8b0929e8b9b7063232cdd7b3643dc8fb62ab881d4789501"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YUI1t2S2hrid709rSWGW51CTD3WvtQ1r/XLNIPTVh7dNKB56oFTE6qX4mq4cs4Y7PgD9JfyipKrEGrLKdvxjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:38:33.365777Z","bundle_sha256":"61dd2c8c72d8e3d20cd8d3afcd30394bcc1433f6f02061f54b81b2860f7dcb6c"}}