{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3QBV6M4HW2JS3JPOGSZSZAQYJK","short_pith_number":"pith:3QBV6M4H","canonical_record":{"source":{"id":"1809.09308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T03:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"66de10c1c80c0610a8e660a34e4e7cddeae2a5ecb2a5a08abdd9938100fd0591","abstract_canon_sha256":"4f8001e342e3a563d37308513541ba5c9af409818911a19e33ee5eec20966bae"},"schema_version":"1.0"},"canonical_sha256":"dc035f3387b6932da5ee34b32c82184abb9dbf26c21a30a92dc9b754275157b4","source":{"kind":"arxiv","id":"1809.09308","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09308","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09308v1","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09308","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"3QBV6M4HW2JS","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3QBV6M4HW2JS3JPO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3QBV6M4H","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3QBV6M4HW2JS3JPOGSZSZAQYJK","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T03:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"66de10c1c80c0610a8e660a34e4e7cddeae2a5ecb2a5a08abdd9938100fd0591","abstract_canon_sha256":"4f8001e342e3a563d37308513541ba5c9af409818911a19e33ee5eec20966bae"},"schema_version":"1.0"},"canonical_sha256":"dc035f3387b6932da5ee34b32c82184abb9dbf26c21a30a92dc9b754275157b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:53.730795Z","signature_b64":"5JuCcGh6bZ+++WytkxS9WJbsEf5exmpCEtbIDETeeKVbccFrhq0TBJV2Rz094I48i9qjiPh6AIzYwY+MEbkbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc035f3387b6932da5ee34b32c82184abb9dbf26c21a30a92dc9b754275157b4","last_reissued_at":"2026-05-18T00:04:53.730280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:53.730280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09308","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":"2026-05-18T00:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"31jqWXGQq/gpA1oV0uUPFm8LqZCpugttCZ6trfD40BCzr4kEppv0XI5RGoVdd7H/1IDBUNcHwGrwMiLxFAXcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:24:44.749479Z"},"content_sha256":"ba1d0d36f02665f8af365259e66ec0d1af09de87f570a0a20778a0d45b845841","schema_version":"1.0","event_id":"sha256:ba1d0d36f02665f8af365259e66ec0d1af09de87f570a0a20778a0d45b845841"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3QBV6M4HW2JS3JPOGSZSZAQYJK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic stability of shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar 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":"2018-09-25T03:54:16Z","abstract_excerpt":"In this paper we study large time behaviors toward shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws. The asymptotic stabilities and decay rates of shock waves and rarefaction waves under periodic perturbations are proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09308","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":"2026-05-18T00:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zUGCCudoFR8UtlP4GHbIhJpLjdq+CyvAIasKK6kNmUochKC/D1L/LGYeT6j1bXPwwBKM9tBQesO7D9VgVKrvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:24:44.749827Z"},"content_sha256":"9f5fb5acfe81c0ebcefbdd9ac9f75a5279b7c98a7ea9353b70382735a20e8a09","schema_version":"1.0","event_id":"sha256:9f5fb5acfe81c0ebcefbdd9ac9f75a5279b7c98a7ea9353b70382735a20e8a09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3QBV6M4HW2JS3JPOGSZSZAQYJK/bundle.json","state_url":"https://pith.science/pith/3QBV6M4HW2JS3JPOGSZSZAQYJK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3QBV6M4HW2JS3JPOGSZSZAQYJK/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":"2026-07-07T10:24:44Z","links":{"resolver":"https://pith.science/pith/3QBV6M4HW2JS3JPOGSZSZAQYJK","bundle":"https://pith.science/pith/3QBV6M4HW2JS3JPOGSZSZAQYJK/bundle.json","state":"https://pith.science/pith/3QBV6M4HW2JS3JPOGSZSZAQYJK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3QBV6M4HW2JS3JPOGSZSZAQYJK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3QBV6M4HW2JS3JPOGSZSZAQYJK","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":"4f8001e342e3a563d37308513541ba5c9af409818911a19e33ee5eec20966bae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T03:54:16Z","title_canon_sha256":"66de10c1c80c0610a8e660a34e4e7cddeae2a5ecb2a5a08abdd9938100fd0591"},"schema_version":"1.0","source":{"id":"1809.09308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09308","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09308v1","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09308","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"3QBV6M4HW2JS","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3QBV6M4HW2JS3JPO","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3QBV6M4H","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:9f5fb5acfe81c0ebcefbdd9ac9f75a5279b7c98a7ea9353b70382735a20e8a09","target":"graph","created_at":"2026-05-18T00:04:53Z","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":"In this paper we study large time behaviors toward shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws. The asymptotic stabilities and decay rates of shock waves and rarefaction waves under periodic perturbations are proved.","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":"2018-09-25T03:54:16Z","title":"Asymptotic stability of shock waves and rarefaction waves under periodic perturbations for 1-D convex scalar conservation laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09308","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:ba1d0d36f02665f8af365259e66ec0d1af09de87f570a0a20778a0d45b845841","target":"record","created_at":"2026-05-18T00:04:53Z","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":"4f8001e342e3a563d37308513541ba5c9af409818911a19e33ee5eec20966bae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-25T03:54:16Z","title_canon_sha256":"66de10c1c80c0610a8e660a34e4e7cddeae2a5ecb2a5a08abdd9938100fd0591"},"schema_version":"1.0","source":{"id":"1809.09308","kind":"arxiv","version":1}},"canonical_sha256":"dc035f3387b6932da5ee34b32c82184abb9dbf26c21a30a92dc9b754275157b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc035f3387b6932da5ee34b32c82184abb9dbf26c21a30a92dc9b754275157b4","first_computed_at":"2026-05-18T00:04:53.730280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:53.730280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5JuCcGh6bZ+++WytkxS9WJbsEf5exmpCEtbIDETeeKVbccFrhq0TBJV2Rz094I48i9qjiPh6AIzYwY+MEbkbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:53.730795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba1d0d36f02665f8af365259e66ec0d1af09de87f570a0a20778a0d45b845841","sha256:9f5fb5acfe81c0ebcefbdd9ac9f75a5279b7c98a7ea9353b70382735a20e8a09"],"state_sha256":"27ad5ceb71fc4693278570f5bd6e315e41a125cfc9b4b68e8dbb23191f20b824"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yVih2LaNFn6ddtcho0FspVklJdPCmOLFEVuNmuBZGks1NM9tVq68GoyUrfxQQmoeuAVT8nTLjeWVV/GwWjp8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T10:24:44.751772Z","bundle_sha256":"770b0b54b2d74525abb526a76098cdfd96547b6993b1dbe364f573f96314cab0"}}