{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:2ESOSNYO4JDZVSITAFZC5SLDJS","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":"2c5df46fa30e666e2531458695ecc028c3729d03e81f36ef8cf29db4c559c502","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-02-05T00:14:10Z","title_canon_sha256":"bbc15189adbaf3f4b1ffb78726d6b3b434ed13c76ca10719e9940cbfd8e474f4"},"schema_version":"1.0","source":{"id":"math/0702088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702088","created_at":"2026-07-04T15:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702088v1","created_at":"2026-07-04T15:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702088","created_at":"2026-07-04T15:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"2ESOSNYO4JDZ","created_at":"2026-07-04T15:14:59Z"},{"alias_kind":"pith_short_16","alias_value":"2ESOSNYO4JDZVSIT","created_at":"2026-07-04T15:14:59Z"},{"alias_kind":"pith_short_8","alias_value":"2ESOSNYO","created_at":"2026-07-04T15:14:59Z"}],"graph_snapshots":[{"event_id":"sha256:19a317b3c0d08ea154116cc029059dbcc0e59391a0f3226952d6ce522bfb1c17","target":"graph","created_at":"2026-07-04T15:14:59Z","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/math/0702088/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the paper, the large time behavior of solutions of the Cauchy problem for the one dimensional fractal Burgers equation $u_t+(-\\partial^2_x)^{\\alpha/2} u+uu_x=0$ with $\\alpha\\in (1,2)$ is studied. It is shown that if the nondecreasing initial datum approaches the constant states $u_\\pm$ ($u_-<u_+$) as $x\\to \\pm\\infty$, respectively, then the corresponding solution converges toward the rarefaction wave, {\\it i.e.} the unique entropy solution of the Riemann problem for the nonviscous Burgers equation.","authors_text":"Changxing Miao, Grzegorz Karch, Xiaojing Xu","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2007-02-05T00:14:10Z","title":"On convergence of solutions of fractal Burgers equation toward rarefaction waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702088","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":"sha256:5333d638c8909e6e39ebce0831add12a498d96f7a124d8a56f94ed3fe405974c","target":"record","created_at":"2026-07-04T15:14:59Z","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":"2c5df46fa30e666e2531458695ecc028c3729d03e81f36ef8cf29db4c559c502","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2007-02-05T00:14:10Z","title_canon_sha256":"bbc15189adbaf3f4b1ffb78726d6b3b434ed13c76ca10719e9940cbfd8e474f4"},"schema_version":"1.0","source":{"id":"math/0702088","kind":"arxiv","version":1}},"canonical_sha256":"d124e9370ee2479ac91301722ec9634c8c3a0138de6e039a33dbaf3a6e00117a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d124e9370ee2479ac91301722ec9634c8c3a0138de6e039a33dbaf3a6e00117a","first_computed_at":"2026-07-04T15:14:59.063926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:14:59.063926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zHQkYLiEP9Ej7R8FneJnfGVz3Yu26KaV24kkswe1SlDvnnNx8aSc/vJIMFHTX9qvd2idKJ1W88roJV3M00ziAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:14:59.064297Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5333d638c8909e6e39ebce0831add12a498d96f7a124d8a56f94ed3fe405974c","sha256:19a317b3c0d08ea154116cc029059dbcc0e59391a0f3226952d6ce522bfb1c17"],"state_sha256":"7989b264e474c78b9e4e3fc12103e99083a9590ca5dbd5fa3be869302db399a5"}