{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:64KD5UMDCKUDWFCCTBZFZGBYYO","short_pith_number":"pith:64KD5UMD","canonical_record":{"source":{"id":"2608.05940","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T12:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"d0cda85d95b151a5bf9bdcb40ea2c41d2849b55e89e8a1779f2a295cbf827a1b","abstract_canon_sha256":"59d4bdd53f0abe22d52e5c96db3ecf230b583f0298df45d64b351d71e00643a5"},"schema_version":"1.0"},"canonical_sha256":"f7143ed18312a83b144298725c9838c3bc2e4447ffd45ba9744c8ed86c3ecbd6","source":{"kind":"arxiv","id":"2608.05940","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.05940","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"2608.05940v1","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05940","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"64KD5UMDCKUD","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"pith_short_16","alias_value":"64KD5UMDCKUDWFCC","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"pith_short_8","alias_value":"64KD5UMD","created_at":"2026-08-07T00:53:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:64KD5UMDCKUDWFCCTBZFZGBYYO","target":"record","payload":{"canonical_record":{"source":{"id":"2608.05940","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T12:08:06Z","cross_cats_sorted":[],"title_canon_sha256":"d0cda85d95b151a5bf9bdcb40ea2c41d2849b55e89e8a1779f2a295cbf827a1b","abstract_canon_sha256":"59d4bdd53f0abe22d52e5c96db3ecf230b583f0298df45d64b351d71e00643a5"},"schema_version":"1.0"},"canonical_sha256":"f7143ed18312a83b144298725c9838c3bc2e4447ffd45ba9744c8ed86c3ecbd6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T00:53:45.136028Z","signature_b64":"XlxP6D08b4gA1AHJbdT9YwvExagme2x8M7HlKrgwdvPXJvSwGe0+KtAVsPrjC4n5Gu6bkNqqwqx+0sEzfSWVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7143ed18312a83b144298725c9838c3bc2e4447ffd45ba9744c8ed86c3ecbd6","last_reissued_at":"2026-08-07T00:53:45.134504Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T00:53:45.134504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.05940","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":"2026-08-07T00:53:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HjuvLfITX+sVpl3NZ6d33Ydp5Z1Im7nZp5jI1bk9nKB1n/GP9hLcExCjQrptHqnHlpASgeQ/D3zf6ykfuMNKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T03:16:22.662235Z"},"content_sha256":"b5b6bf1226ea9c4b0ad6be4b1290b22d675de67145b52ecb5bce45556d67896d","schema_version":"1.0","event_id":"sha256:b5b6bf1226ea9c4b0ad6be4b1290b22d675de67145b52ecb5bce45556d67896d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:64KD5UMDCKUDWFCCTBZFZGBYYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary layer analysis for the 2D chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part I: Well-posedness","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hui Wang, Lingling Zhao, Wendong Wang","submitted_at":"2026-08-06T12:08:06Z","abstract_excerpt":"This is the first part of a two-part work concerning the boundary layer convergence for chemotaxis-Navier-Stokes system in a two-dimensional half-space. In this paper, we investigate the chemotacxis-Navier-Stokes system with the logarithmic singularity under Navier-slip boundary conditions. More precisely, we perform an exact asymptotic expansion for the chemotaxis Navier-Stokes system with viscous coefficient $\\varepsilon>0$, and obtain partial boundary layer profiles, establishing the well-posedness of the corresponding boundary layer profiles. Specially, we also establish the local well-pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05940","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05940/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-08-07T00:53:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"06l6dXugv4PANaw8EeluWv7OjrkecGfR34NFFMWUHM8h48sVwWLG0s8Yspc5DoqJl1usbSUPZP1GZ86XfngzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T03:16:22.662757Z"},"content_sha256":"b2d51a0f4260c54adde1470558318fd638a66728378df61f6ac54290e918124d","schema_version":"1.0","event_id":"sha256:b2d51a0f4260c54adde1470558318fd638a66728378df61f6ac54290e918124d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64KD5UMDCKUDWFCCTBZFZGBYYO/bundle.json","state_url":"https://pith.science/pith/64KD5UMDCKUDWFCCTBZFZGBYYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64KD5UMDCKUDWFCCTBZFZGBYYO/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":"2026-08-12T03:16:22Z","links":{"resolver":"https://pith.science/pith/64KD5UMDCKUDWFCCTBZFZGBYYO","bundle":"https://pith.science/pith/64KD5UMDCKUDWFCCTBZFZGBYYO/bundle.json","state":"https://pith.science/pith/64KD5UMDCKUDWFCCTBZFZGBYYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64KD5UMDCKUDWFCCTBZFZGBYYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:64KD5UMDCKUDWFCCTBZFZGBYYO","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":"59d4bdd53f0abe22d52e5c96db3ecf230b583f0298df45d64b351d71e00643a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T12:08:06Z","title_canon_sha256":"d0cda85d95b151a5bf9bdcb40ea2c41d2849b55e89e8a1779f2a295cbf827a1b"},"schema_version":"1.0","source":{"id":"2608.05940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.05940","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"2608.05940v1","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05940","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"64KD5UMDCKUD","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"pith_short_16","alias_value":"64KD5UMDCKUDWFCC","created_at":"2026-08-07T00:53:45Z"},{"alias_kind":"pith_short_8","alias_value":"64KD5UMD","created_at":"2026-08-07T00:53:45Z"}],"graph_snapshots":[{"event_id":"sha256:b2d51a0f4260c54adde1470558318fd638a66728378df61f6ac54290e918124d","target":"graph","created_at":"2026-08-07T00:53:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.05940/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is the first part of a two-part work concerning the boundary layer convergence for chemotaxis-Navier-Stokes system in a two-dimensional half-space. In this paper, we investigate the chemotacxis-Navier-Stokes system with the logarithmic singularity under Navier-slip boundary conditions. More precisely, we perform an exact asymptotic expansion for the chemotaxis Navier-Stokes system with viscous coefficient $\\varepsilon>0$, and obtain partial boundary layer profiles, establishing the well-posedness of the corresponding boundary layer profiles. Specially, we also establish the local well-pos","authors_text":"Hui Wang, Lingling Zhao, Wendong Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T12:08:06Z","title":"Boundary layer analysis for the 2D chemotaxis-Navier-Stokes system with logarithmic sensitivity, Part I: Well-posedness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05940","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:b5b6bf1226ea9c4b0ad6be4b1290b22d675de67145b52ecb5bce45556d67896d","target":"record","created_at":"2026-08-07T00:53:45Z","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":"59d4bdd53f0abe22d52e5c96db3ecf230b583f0298df45d64b351d71e00643a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-08-06T12:08:06Z","title_canon_sha256":"d0cda85d95b151a5bf9bdcb40ea2c41d2849b55e89e8a1779f2a295cbf827a1b"},"schema_version":"1.0","source":{"id":"2608.05940","kind":"arxiv","version":1}},"canonical_sha256":"f7143ed18312a83b144298725c9838c3bc2e4447ffd45ba9744c8ed86c3ecbd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7143ed18312a83b144298725c9838c3bc2e4447ffd45ba9744c8ed86c3ecbd6","first_computed_at":"2026-08-07T00:53:45.134504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T00:53:45.134504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XlxP6D08b4gA1AHJbdT9YwvExagme2x8M7HlKrgwdvPXJvSwGe0+KtAVsPrjC4n5Gu6bkNqqwqx+0sEzfSWVDw==","signature_status":"signed_v1","signed_at":"2026-08-07T00:53:45.136028Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.05940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b6bf1226ea9c4b0ad6be4b1290b22d675de67145b52ecb5bce45556d67896d","sha256:b2d51a0f4260c54adde1470558318fd638a66728378df61f6ac54290e918124d"],"state_sha256":"6b158e19288779c797d479b4fe8a5ff9e3539b6fc81e230561b8b0dfc12b4db1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFt8ZAy4lO2IbmAvlBictc5nIO6Y+wr3EElgODWA/ueSoabXDJFD+M3XD2fGWIr3IIbXo4rOCQ0lprPaBAuaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T03:16:22.667958Z","bundle_sha256":"3a79c531abeb28a17c851a2b98183f4cf9c06caba1a494c55678af442adead2b"}}