{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WIFS57RVGQLT5DEB3ZGWFBKY7G","short_pith_number":"pith:WIFS57RV","canonical_record":{"source":{"id":"1409.3817","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-12T18:47:41Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"2aa41908d40b707cf923abbb09d633fb8df4f6801ec8f605a425ece7fa5b84c0","abstract_canon_sha256":"f0289e66d64360a3bc1012894434d3a0abecb68b8d8eaf6187b83dd5a4658544"},"schema_version":"1.0"},"canonical_sha256":"b20b2efe3534173e8c81de4d628558f995852ae7ec828a7a93632c6577b17996","source":{"kind":"arxiv","id":"1409.3817","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3817","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3817v3","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3817","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"WIFS57RVGQLT","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WIFS57RVGQLT5DEB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WIFS57RV","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WIFS57RVGQLT5DEB3ZGWFBKY7G","target":"record","payload":{"canonical_record":{"source":{"id":"1409.3817","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-12T18:47:41Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"2aa41908d40b707cf923abbb09d633fb8df4f6801ec8f605a425ece7fa5b84c0","abstract_canon_sha256":"f0289e66d64360a3bc1012894434d3a0abecb68b8d8eaf6187b83dd5a4658544"},"schema_version":"1.0"},"canonical_sha256":"b20b2efe3534173e8c81de4d628558f995852ae7ec828a7a93632c6577b17996","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:52.072964Z","signature_b64":"rFDEj0DYoiWU36bE3yoa9WMFfUEWEZIfHBdKw5JSh6Isfl+KxQIxrXfFgxnNCaVnxolaIkgFHCWwWtyNWxsYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b20b2efe3534173e8c81de4d628558f995852ae7ec828a7a93632c6577b17996","last_reissued_at":"2026-05-18T00:42:52.072178Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:52.072178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.3817","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xmbc+R6hsJhWrlzI4iS1nyTK4UTeCrD9zAG7Wk3nL2kb05hXKCZlYr3Uzs8k1Ne2dQj/Pg5E8EK5zQVx8y9aBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:31:25.851376Z"},"content_sha256":"2b302f0e33bddeebd6fa32cb374bb49703b54c77e364dbf16b5fb13e9f0088db","schema_version":"1.0","event_id":"sha256:2b302f0e33bddeebd6fa32cb374bb49703b54c77e364dbf16b5fb13e9f0088db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WIFS57RVGQLT5DEB3ZGWFBKY7G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Alejandro Pozo, Liviu I. Ignat","submitted_at":"2014-09-12T18:47:41Z","abstract_excerpt":"In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1$-$L^p$ decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term $K*u_{xx}$ is the same as $u_{xx}$ for large times. Then, we propose a semi-discrete numerical scheme that preserves this asymptotic behavior, by introducing two correcting factors in the discretization of the non-local term. Numerical experiments illustrating the accuracy of the results of the paper are also present"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3817","kind":"arxiv","version":3},"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":"2026-05-18T00:42:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FX7mdyxgavmQJk89wIOy4u9mGFvuN7qXNySB9rAeOkiT483BpDQlaqKQGsQTEo5WJdfrRLOxaWNlBHP/sB3QCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:31:25.851722Z"},"content_sha256":"f824687c30a5ce6ecc04da71a68ecc1e2cff6b36b4c366aa5db866f6e28124f0","schema_version":"1.0","event_id":"sha256:f824687c30a5ce6ecc04da71a68ecc1e2cff6b36b4c366aa5db866f6e28124f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WIFS57RVGQLT5DEB3ZGWFBKY7G/bundle.json","state_url":"https://pith.science/pith/WIFS57RVGQLT5DEB3ZGWFBKY7G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WIFS57RVGQLT5DEB3ZGWFBKY7G/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":"2026-06-09T15:31:25Z","links":{"resolver":"https://pith.science/pith/WIFS57RVGQLT5DEB3ZGWFBKY7G","bundle":"https://pith.science/pith/WIFS57RVGQLT5DEB3ZGWFBKY7G/bundle.json","state":"https://pith.science/pith/WIFS57RVGQLT5DEB3ZGWFBKY7G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WIFS57RVGQLT5DEB3ZGWFBKY7G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WIFS57RVGQLT5DEB3ZGWFBKY7G","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":"f0289e66d64360a3bc1012894434d3a0abecb68b8d8eaf6187b83dd5a4658544","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-12T18:47:41Z","title_canon_sha256":"2aa41908d40b707cf923abbb09d633fb8df4f6801ec8f605a425ece7fa5b84c0"},"schema_version":"1.0","source":{"id":"1409.3817","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3817","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3817v3","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3817","created_at":"2026-05-18T00:42:52Z"},{"alias_kind":"pith_short_12","alias_value":"WIFS57RVGQLT","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WIFS57RVGQLT5DEB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WIFS57RV","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:f824687c30a5ce6ecc04da71a68ecc1e2cff6b36b4c366aa5db866f6e28124f0","target":"graph","created_at":"2026-05-18T00:42:52Z","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 analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1$-$L^p$ decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term $K*u_{xx}$ is the same as $u_{xx}$ for large times. Then, we propose a semi-discrete numerical scheme that preserves this asymptotic behavior, by introducing two correcting factors in the discretization of the non-local term. Numerical experiments illustrating the accuracy of the results of the paper are also present","authors_text":"Alejandro Pozo, Liviu I. Ignat","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-12T18:47:41Z","title":"A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3817","kind":"arxiv","version":3},"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":"sha256:2b302f0e33bddeebd6fa32cb374bb49703b54c77e364dbf16b5fb13e9f0088db","target":"record","created_at":"2026-05-18T00:42:52Z","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":"f0289e66d64360a3bc1012894434d3a0abecb68b8d8eaf6187b83dd5a4658544","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-12T18:47:41Z","title_canon_sha256":"2aa41908d40b707cf923abbb09d633fb8df4f6801ec8f605a425ece7fa5b84c0"},"schema_version":"1.0","source":{"id":"1409.3817","kind":"arxiv","version":3}},"canonical_sha256":"b20b2efe3534173e8c81de4d628558f995852ae7ec828a7a93632c6577b17996","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b20b2efe3534173e8c81de4d628558f995852ae7ec828a7a93632c6577b17996","first_computed_at":"2026-05-18T00:42:52.072178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:52.072178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rFDEj0DYoiWU36bE3yoa9WMFfUEWEZIfHBdKw5JSh6Isfl+KxQIxrXfFgxnNCaVnxolaIkgFHCWwWtyNWxsYAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:52.072964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3817","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b302f0e33bddeebd6fa32cb374bb49703b54c77e364dbf16b5fb13e9f0088db","sha256:f824687c30a5ce6ecc04da71a68ecc1e2cff6b36b4c366aa5db866f6e28124f0"],"state_sha256":"078ebe24b32109e32fbf922b12a085f353370a8ee75c54ca78f53b38b2272af2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TfMsPHtRtktTaksQhvJBPKEOPlOS1wcK+9wAizhmzEpUwGDX28F+6gP8zhS7uf0MD75PYxlWMSLPjUYsqU8lBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:31:25.853650Z","bundle_sha256":"9d8c05ada716c39d859ae4118788d792245b930618910b2e6ea49480ab74044c"}}