{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:LEBDEFKMXSRPEPL76D7WJASMTB","short_pith_number":"pith:LEBDEFKM","canonical_record":{"source":{"id":"1902.09772","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-26T07:27:41Z","cross_cats_sorted":[],"title_canon_sha256":"f6342b569f3e3ba809e2fa914665610cc7620f1d11a56cac803418155588609e","abstract_canon_sha256":"277dd5072a7352eef11d36ef45b99844780c597816cfb50ca4eab23088d7fc28"},"schema_version":"1.0"},"canonical_sha256":"590232154cbca2f23d7ff0ff64824c9852306a1ef5fdd5e5ec8398ed69b190e1","source":{"kind":"arxiv","id":"1902.09772","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09772","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09772v2","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09772","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"pith_short_12","alias_value":"LEBDEFKMXSRP","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"pith_short_16","alias_value":"LEBDEFKMXSRPEPL7","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"pith_short_8","alias_value":"LEBDEFKM","created_at":"2026-07-04T23:50:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:LEBDEFKMXSRPEPL76D7WJASMTB","target":"record","payload":{"canonical_record":{"source":{"id":"1902.09772","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-26T07:27:41Z","cross_cats_sorted":[],"title_canon_sha256":"f6342b569f3e3ba809e2fa914665610cc7620f1d11a56cac803418155588609e","abstract_canon_sha256":"277dd5072a7352eef11d36ef45b99844780c597816cfb50ca4eab23088d7fc28"},"schema_version":"1.0"},"canonical_sha256":"590232154cbca2f23d7ff0ff64824c9852306a1ef5fdd5e5ec8398ed69b190e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:50:54.417733Z","signature_b64":"Dv+r4GQpIZwIfUtV/zfZr8oPKrCe6ieXtDuXu3R+9ejbwRYMkyDGJGsOR4Cd8a4dDQSFLTrHDtJd3m3IZU6xDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"590232154cbca2f23d7ff0ff64824c9852306a1ef5fdd5e5ec8398ed69b190e1","last_reissued_at":"2026-07-04T23:50:54.417228Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:50:54.417228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.09772","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":"2026-07-04T23:50:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BTvBN9FxKGJ4xFtoEjbJbck7YCEA3PrluBB5pteJz0W6jbtrwrQ6UCCmApkoyAkS7uYgqrbzu+GuN70LyBdMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:42:18.496652Z"},"content_sha256":"bf10a0998841a7fa96f65aedd3b8bff336d0260ce8901742df2f794d2ef648f5","schema_version":"1.0","event_id":"sha256:bf10a0998841a7fa96f65aedd3b8bff336d0260ce8901742df2f794d2ef648f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:LEBDEFKMXSRPEPL76D7WJASMTB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-d convex scalar viscous conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qian Yuan, Yuan Yuan, Zhouping Xin","submitted_at":"2019-02-26T07:27:41Z","abstract_excerpt":"This paper studies the asymptotic stability of shock profiles and rarefaction waves under space-periodic perturbations for one-dimensional convex scalar viscous conservation laws. For the shock profile, we show that the solution approaches the background shock profile with a constant shift in the $ L^\\infty(\\mathbb{R}) $ norm at exponential rates. The new phenomena contrasting to the case of localized perturbations is that the constant shift cannot be determined by the initial excessive mass in general, which indicates that the periodic oscillations at infinities make contributions to this shi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09772","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.09772/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":"2026-07-04T23:50:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vlTodJs9jFkrBT6+kM1YG+aqWBroFan1AJDfLv709BfgNkPACUcgtBpBb0wrk2WKS+ZLAX497NOi9j8V2MWgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:42:18.497015Z"},"content_sha256":"8cf2681c6e30fff1db601d4cd4f3e6d82b1c374ed018a2e98e2024f1a1af1314","schema_version":"1.0","event_id":"sha256:8cf2681c6e30fff1db601d4cd4f3e6d82b1c374ed018a2e98e2024f1a1af1314"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LEBDEFKMXSRPEPL76D7WJASMTB/bundle.json","state_url":"https://pith.science/pith/LEBDEFKMXSRPEPL76D7WJASMTB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LEBDEFKMXSRPEPL76D7WJASMTB/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":"2026-07-06T20:42:18Z","links":{"resolver":"https://pith.science/pith/LEBDEFKMXSRPEPL76D7WJASMTB","bundle":"https://pith.science/pith/LEBDEFKMXSRPEPL76D7WJASMTB/bundle.json","state":"https://pith.science/pith/LEBDEFKMXSRPEPL76D7WJASMTB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LEBDEFKMXSRPEPL76D7WJASMTB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LEBDEFKMXSRPEPL76D7WJASMTB","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":"277dd5072a7352eef11d36ef45b99844780c597816cfb50ca4eab23088d7fc28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-26T07:27:41Z","title_canon_sha256":"f6342b569f3e3ba809e2fa914665610cc7620f1d11a56cac803418155588609e"},"schema_version":"1.0","source":{"id":"1902.09772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09772","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09772v2","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09772","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"pith_short_12","alias_value":"LEBDEFKMXSRP","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"pith_short_16","alias_value":"LEBDEFKMXSRPEPL7","created_at":"2026-07-04T23:50:54Z"},{"alias_kind":"pith_short_8","alias_value":"LEBDEFKM","created_at":"2026-07-04T23:50:54Z"}],"graph_snapshots":[{"event_id":"sha256:8cf2681c6e30fff1db601d4cd4f3e6d82b1c374ed018a2e98e2024f1a1af1314","target":"graph","created_at":"2026-07-04T23:50:54Z","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/1902.09772/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the asymptotic stability of shock profiles and rarefaction waves under space-periodic perturbations for one-dimensional convex scalar viscous conservation laws. For the shock profile, we show that the solution approaches the background shock profile with a constant shift in the $ L^\\infty(\\mathbb{R}) $ norm at exponential rates. The new phenomena contrasting to the case of localized perturbations is that the constant shift cannot be determined by the initial excessive mass in general, which indicates that the periodic oscillations at infinities make contributions to this shi","authors_text":"Qian Yuan, Yuan Yuan, Zhouping Xin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-26T07:27:41Z","title":"Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-d convex scalar viscous conservation laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09772","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:bf10a0998841a7fa96f65aedd3b8bff336d0260ce8901742df2f794d2ef648f5","target":"record","created_at":"2026-07-04T23:50:54Z","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":"277dd5072a7352eef11d36ef45b99844780c597816cfb50ca4eab23088d7fc28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-26T07:27:41Z","title_canon_sha256":"f6342b569f3e3ba809e2fa914665610cc7620f1d11a56cac803418155588609e"},"schema_version":"1.0","source":{"id":"1902.09772","kind":"arxiv","version":2}},"canonical_sha256":"590232154cbca2f23d7ff0ff64824c9852306a1ef5fdd5e5ec8398ed69b190e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"590232154cbca2f23d7ff0ff64824c9852306a1ef5fdd5e5ec8398ed69b190e1","first_computed_at":"2026-07-04T23:50:54.417228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:50:54.417228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dv+r4GQpIZwIfUtV/zfZr8oPKrCe6ieXtDuXu3R+9ejbwRYMkyDGJGsOR4Cd8a4dDQSFLTrHDtJd3m3IZU6xDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:50:54.417733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf10a0998841a7fa96f65aedd3b8bff336d0260ce8901742df2f794d2ef648f5","sha256:8cf2681c6e30fff1db601d4cd4f3e6d82b1c374ed018a2e98e2024f1a1af1314"],"state_sha256":"9e0f093616f7c4b7259aa9811f57b971a7a23da64140e8d87fb43a3ca1fd0bce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1lq5K/1XtkStN0aNunV8glMjIANPnib0oCbORdUK7fZQsaXnnkKOyQOrJh6Tl8JB2E6qcMKFbSmAcfR6m10Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:42:18.498956Z","bundle_sha256":"f37cbd44e2d741d2fc148cb67d1308f7dfc914536d62e12897db4405ff0162f4"}}