{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6XEUTXKN6SY3DXAQIOLTH3N5FN","short_pith_number":"pith:6XEUTXKN","canonical_record":{"source":{"id":"1210.3626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-12T20:02:31Z","cross_cats_sorted":[],"title_canon_sha256":"7b5e3176725ca354c03cd0f9442b232a5eaaf2a9baf8a5257a5bd5f0c0d7ad33","abstract_canon_sha256":"e6a0b3c3c156458549f775be3385351c0b4c1b2443a1c5159403f344ceb2fbe5"},"schema_version":"1.0"},"canonical_sha256":"f5c949dd4df4b1b1dc10439733edbd2b5981f5c339744bb743648f51db6d5771","source":{"kind":"arxiv","id":"1210.3626","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3626","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3626v2","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3626","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"6XEUTXKN6SY3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6XEUTXKN6SY3DXAQ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6XEUTXKN","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6XEUTXKN6SY3DXAQIOLTH3N5FN","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3626","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-12T20:02:31Z","cross_cats_sorted":[],"title_canon_sha256":"7b5e3176725ca354c03cd0f9442b232a5eaaf2a9baf8a5257a5bd5f0c0d7ad33","abstract_canon_sha256":"e6a0b3c3c156458549f775be3385351c0b4c1b2443a1c5159403f344ceb2fbe5"},"schema_version":"1.0"},"canonical_sha256":"f5c949dd4df4b1b1dc10439733edbd2b5981f5c339744bb743648f51db6d5771","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:43.837735Z","signature_b64":"trTKn/YrH+OvXltWRMjGTs9eYbQAykMusNq+41KyPLLykPFdpK0P4TN9No/vAjWbQr0hczxf2PLO7cf4zxkjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5c949dd4df4b1b1dc10439733edbd2b5981f5c339744bb743648f51db6d5771","last_reissued_at":"2026-05-18T03:42:43.836902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:43.836902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3626","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":"2026-05-18T03:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tS7J57d5uBPpJxAc2cNQxhF8Jr2EP+VhwX2ptgVL3STVYaJQ+zosSYHLPyAc71ntge/D0T2auDhK5I8yI1yxCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T11:32:54.791076Z"},"content_sha256":"c20781cb24829284d08c42ce23c5a74e7c7fabd882dd7fb5776a7b3d61db6e02","schema_version":"1.0","event_id":"sha256:c20781cb24829284d08c42ce23c5a74e7c7fabd882dd7fb5776a7b3d61db6e02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6XEUTXKN6SY3DXAQIOLTH3N5FN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pointwise stability estimates for periodic traveling wave solutions of systems of viscous conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Soyeun Jung","submitted_at":"2012-10-12T20:02:31Z","abstract_excerpt":"In the previous paper \\cite{J1}, we established pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves $\\bar u$ of a system of reaction diffusion equations, and also obtained pointwise nonlinear stability and behavior of $\\bar u$ under small perturbations. In this paper, using periodic resolvent kernels and the Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with periodic standing waves $\\bar u$ of a system of conservation laws. We also show pointwise nonlinear stabili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3626","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":"2026-05-18T03:42:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ck8vN/KIol8dajdC1D93ScQ4BadiYr3mXNYbjvWgiDWyGW5wGQcsy3RMm5tLBMXTc2kc4FSRwnuUu6grf5Y8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T11:32:54.791431Z"},"content_sha256":"a4845af44dd0e484af249abbf42f9d84f0c3fb37fdaa2f3e13fc6968d7bffaad","schema_version":"1.0","event_id":"sha256:a4845af44dd0e484af249abbf42f9d84f0c3fb37fdaa2f3e13fc6968d7bffaad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XEUTXKN6SY3DXAQIOLTH3N5FN/bundle.json","state_url":"https://pith.science/pith/6XEUTXKN6SY3DXAQIOLTH3N5FN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XEUTXKN6SY3DXAQIOLTH3N5FN/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":"2026-06-28T11:32:54Z","links":{"resolver":"https://pith.science/pith/6XEUTXKN6SY3DXAQIOLTH3N5FN","bundle":"https://pith.science/pith/6XEUTXKN6SY3DXAQIOLTH3N5FN/bundle.json","state":"https://pith.science/pith/6XEUTXKN6SY3DXAQIOLTH3N5FN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XEUTXKN6SY3DXAQIOLTH3N5FN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6XEUTXKN6SY3DXAQIOLTH3N5FN","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":"e6a0b3c3c156458549f775be3385351c0b4c1b2443a1c5159403f344ceb2fbe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-12T20:02:31Z","title_canon_sha256":"7b5e3176725ca354c03cd0f9442b232a5eaaf2a9baf8a5257a5bd5f0c0d7ad33"},"schema_version":"1.0","source":{"id":"1210.3626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3626","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3626v2","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3626","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"6XEUTXKN6SY3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6XEUTXKN6SY3DXAQ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6XEUTXKN","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:a4845af44dd0e484af249abbf42f9d84f0c3fb37fdaa2f3e13fc6968d7bffaad","target":"graph","created_at":"2026-05-18T03:42:43Z","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 the previous paper \\cite{J1}, we established pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves $\\bar u$ of a system of reaction diffusion equations, and also obtained pointwise nonlinear stability and behavior of $\\bar u$ under small perturbations. In this paper, using periodic resolvent kernels and the Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with periodic standing waves $\\bar u$ of a system of conservation laws. We also show pointwise nonlinear stabili","authors_text":"Soyeun Jung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-12T20:02:31Z","title":"Pointwise stability estimates for periodic traveling wave solutions of systems of viscous conservation laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3626","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:c20781cb24829284d08c42ce23c5a74e7c7fabd882dd7fb5776a7b3d61db6e02","target":"record","created_at":"2026-05-18T03:42:43Z","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":"e6a0b3c3c156458549f775be3385351c0b4c1b2443a1c5159403f344ceb2fbe5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-12T20:02:31Z","title_canon_sha256":"7b5e3176725ca354c03cd0f9442b232a5eaaf2a9baf8a5257a5bd5f0c0d7ad33"},"schema_version":"1.0","source":{"id":"1210.3626","kind":"arxiv","version":2}},"canonical_sha256":"f5c949dd4df4b1b1dc10439733edbd2b5981f5c339744bb743648f51db6d5771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5c949dd4df4b1b1dc10439733edbd2b5981f5c339744bb743648f51db6d5771","first_computed_at":"2026-05-18T03:42:43.836902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:43.836902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"trTKn/YrH+OvXltWRMjGTs9eYbQAykMusNq+41KyPLLykPFdpK0P4TN9No/vAjWbQr0hczxf2PLO7cf4zxkjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:43.837735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c20781cb24829284d08c42ce23c5a74e7c7fabd882dd7fb5776a7b3d61db6e02","sha256:a4845af44dd0e484af249abbf42f9d84f0c3fb37fdaa2f3e13fc6968d7bffaad"],"state_sha256":"452a9bc6a2e4ead3266b592829f4f212503b83cc75368868d552f291a7454500"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iZmAKSwcnmqXfgI6N1lCtyyIWHFl97bKdKMD3JgWd+EiAUJkCyJskJxNGX/FMUeqH19VP0EdG4WKyhfb4q08AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T11:32:54.793326Z","bundle_sha256":"c4aadbf861fbd28e9566b23bef1880f7a1dc6d703769c35415b2de1c7bca5237"}}