{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NSPQDKWEA35Q5LUE5FCWZQQAPI","short_pith_number":"pith:NSPQDKWE","canonical_record":{"source":{"id":"2212.13414","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-27T08:51:40Z","cross_cats_sorted":[],"title_canon_sha256":"67f79715db1bff71430fd3ccd4bc8f7d65ad758ab983f0635403774adb6af72e","abstract_canon_sha256":"01d7c684bbb4d0ae7d8e8be27f1045a6faea6b83d54493588decca7658528b8d"},"schema_version":"1.0"},"canonical_sha256":"6c9f01aac406fb0eae84e9456cc2007a09c7592ff0ecdebdaadbef16ea1b6008","source":{"kind":"arxiv","id":"2212.13414","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.13414","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"arxiv_version","alias_value":"2212.13414v4","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.13414","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"pith_short_12","alias_value":"NSPQDKWEA35Q","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"pith_short_16","alias_value":"NSPQDKWEA35Q5LUE","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"pith_short_8","alias_value":"NSPQDKWE","created_at":"2026-07-05T08:21:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NSPQDKWEA35Q5LUE5FCWZQQAPI","target":"record","payload":{"canonical_record":{"source":{"id":"2212.13414","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-27T08:51:40Z","cross_cats_sorted":[],"title_canon_sha256":"67f79715db1bff71430fd3ccd4bc8f7d65ad758ab983f0635403774adb6af72e","abstract_canon_sha256":"01d7c684bbb4d0ae7d8e8be27f1045a6faea6b83d54493588decca7658528b8d"},"schema_version":"1.0"},"canonical_sha256":"6c9f01aac406fb0eae84e9456cc2007a09c7592ff0ecdebdaadbef16ea1b6008","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:21:04.132002Z","signature_b64":"X3Ye/l2Zt4j33pxzGFIVGx/H/6G7uoTjIuqjKf7Yj8Uuxl5jOs2pEFXEXedwN9DZCfIUOys9K/DABe/M6ZoKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c9f01aac406fb0eae84e9456cc2007a09c7592ff0ecdebdaadbef16ea1b6008","last_reissued_at":"2026-07-05T08:21:04.131578Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:21:04.131578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.13414","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:21:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aaQfrn3qXGoU0Bn4PHnFWw7B+e/AOo+TLYa5PpvVETsOJXpMHKAVo2mSkJg/sMS2tFEP6OWOhoGlcIIXXBTPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T03:44:39.145987Z"},"content_sha256":"6d8d2fe5e5b80a08035106e23a69fa19903b95db99a6a3675ec922c670cb7dac","schema_version":"1.0","event_id":"sha256:6d8d2fe5e5b80a08035106e23a69fa19903b95db99a6a3675ec922c670cb7dac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NSPQDKWEA35Q5LUE5FCWZQQAPI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time-asymptotic stability of planar Navier-Stokes shocks with spatial oscillations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qian Yuan","submitted_at":"2022-12-27T08:51:40Z","abstract_excerpt":"This paper shows that for the three-dimensional compressible isentropic Navier-Stokes equations, the planar viscous shocks are time-asymptotically stable to suitably small initial perturbations with zero masses. In particular, the perturbations consist of not only $ H^3 $-perturbations, but also periodic ones that oscillate at spatial infinity. In the former case, the final shock locations can be predicted in terms of the initial conditions, while in the latter the locations are subject to the dynamics of the oscillations. The stability analysis is based on the $L^2$-energy method. The key poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.13414","kind":"arxiv","version":4},"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/2212.13414/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":"2026-07-05T08:21:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3m/tdITX71Dp6//2ovaE6tAyaD31x6ARV0tLyv8RpibCBe2fELDMyicZBafLNHKvm40Q22e9M3ihoFSgjCkqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T03:44:39.146383Z"},"content_sha256":"1d0599b194ff7dc6a6a0aaf360a7fdb133105647f358b74ddec8c620a37ac14f","schema_version":"1.0","event_id":"sha256:1d0599b194ff7dc6a6a0aaf360a7fdb133105647f358b74ddec8c620a37ac14f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSPQDKWEA35Q5LUE5FCWZQQAPI/bundle.json","state_url":"https://pith.science/pith/NSPQDKWEA35Q5LUE5FCWZQQAPI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSPQDKWEA35Q5LUE5FCWZQQAPI/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":"2026-07-07T03:44:39Z","links":{"resolver":"https://pith.science/pith/NSPQDKWEA35Q5LUE5FCWZQQAPI","bundle":"https://pith.science/pith/NSPQDKWEA35Q5LUE5FCWZQQAPI/bundle.json","state":"https://pith.science/pith/NSPQDKWEA35Q5LUE5FCWZQQAPI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSPQDKWEA35Q5LUE5FCWZQQAPI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NSPQDKWEA35Q5LUE5FCWZQQAPI","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":"01d7c684bbb4d0ae7d8e8be27f1045a6faea6b83d54493588decca7658528b8d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-27T08:51:40Z","title_canon_sha256":"67f79715db1bff71430fd3ccd4bc8f7d65ad758ab983f0635403774adb6af72e"},"schema_version":"1.0","source":{"id":"2212.13414","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.13414","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"arxiv_version","alias_value":"2212.13414v4","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.13414","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"pith_short_12","alias_value":"NSPQDKWEA35Q","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"pith_short_16","alias_value":"NSPQDKWEA35Q5LUE","created_at":"2026-07-05T08:21:04Z"},{"alias_kind":"pith_short_8","alias_value":"NSPQDKWE","created_at":"2026-07-05T08:21:04Z"}],"graph_snapshots":[{"event_id":"sha256:1d0599b194ff7dc6a6a0aaf360a7fdb133105647f358b74ddec8c620a37ac14f","target":"graph","created_at":"2026-07-05T08:21:04Z","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/2212.13414/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper shows that for the three-dimensional compressible isentropic Navier-Stokes equations, the planar viscous shocks are time-asymptotically stable to suitably small initial perturbations with zero masses. In particular, the perturbations consist of not only $ H^3 $-perturbations, but also periodic ones that oscillate at spatial infinity. In the former case, the final shock locations can be predicted in terms of the initial conditions, while in the latter the locations are subject to the dynamics of the oscillations. The stability analysis is based on the $L^2$-energy method. The key poi","authors_text":"Qian Yuan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-27T08:51:40Z","title":"Time-asymptotic stability of planar Navier-Stokes shocks with spatial oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.13414","kind":"arxiv","version":4},"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":"sha256:6d8d2fe5e5b80a08035106e23a69fa19903b95db99a6a3675ec922c670cb7dac","target":"record","created_at":"2026-07-05T08:21:04Z","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":"01d7c684bbb4d0ae7d8e8be27f1045a6faea6b83d54493588decca7658528b8d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-12-27T08:51:40Z","title_canon_sha256":"67f79715db1bff71430fd3ccd4bc8f7d65ad758ab983f0635403774adb6af72e"},"schema_version":"1.0","source":{"id":"2212.13414","kind":"arxiv","version":4}},"canonical_sha256":"6c9f01aac406fb0eae84e9456cc2007a09c7592ff0ecdebdaadbef16ea1b6008","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c9f01aac406fb0eae84e9456cc2007a09c7592ff0ecdebdaadbef16ea1b6008","first_computed_at":"2026-07-05T08:21:04.131578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:21:04.131578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X3Ye/l2Zt4j33pxzGFIVGx/H/6G7uoTjIuqjKf7Yj8Uuxl5jOs2pEFXEXedwN9DZCfIUOys9K/DABe/M6ZoKCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:21:04.132002Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.13414","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d8d2fe5e5b80a08035106e23a69fa19903b95db99a6a3675ec922c670cb7dac","sha256:1d0599b194ff7dc6a6a0aaf360a7fdb133105647f358b74ddec8c620a37ac14f"],"state_sha256":"3af695c0e63acad1c363b7423b9780cd73345b62ef33419637b83eadb6a16fb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IaYg46GRkpXW0eq0avXrv3+sp94B9XK4WeBGJgM3uQcJdgPxYWcLVEwsLw597l7JqYMsa9xQBOYIhydIRF6rAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T03:44:39.148625Z","bundle_sha256":"9d8a943c606c77a8010c112653071719d2693b0ddfcc613f3735237c33f3ae03"}}