{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:K6YF2342RFSZTLXBEE5VCNDQ6W","short_pith_number":"pith:K6YF2342","canonical_record":{"source":{"id":"0801.0856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-01-06T11:48:32Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"cbbf214de65d2b3c6e99b31e4a7d550be1db34720d167491b403fe8ffc04a31a","abstract_canon_sha256":"3e10c38bfefbdf98a8574defab682972d64c0a123150ab01db6430191d14d997"},"schema_version":"1.0"},"canonical_sha256":"57b05d6f9a896599aee1213b513470f59cb5961ffab1bb39fee94f8d587051f9","source":{"kind":"arxiv","id":"0801.0856","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.0856","created_at":"2026-05-18T02:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"0801.0856v2","created_at":"2026-05-18T02:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.0856","created_at":"2026-05-18T02:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"K6YF2342RFSZ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"K6YF2342RFSZTLXB","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"K6YF2342","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:K6YF2342RFSZTLXBEE5VCNDQ6W","target":"record","payload":{"canonical_record":{"source":{"id":"0801.0856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-01-06T11:48:32Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"cbbf214de65d2b3c6e99b31e4a7d550be1db34720d167491b403fe8ffc04a31a","abstract_canon_sha256":"3e10c38bfefbdf98a8574defab682972d64c0a123150ab01db6430191d14d997"},"schema_version":"1.0"},"canonical_sha256":"57b05d6f9a896599aee1213b513470f59cb5961ffab1bb39fee94f8d587051f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:02.219926Z","signature_b64":"sxLi6no1olR3EgKmHD4rCjnSiDXvtSmgThwePnrh0sDDal5ToebHMO09WL44D+2UBFLtne9Ct0jhh8OazqfiDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57b05d6f9a896599aee1213b513470f59cb5961ffab1bb39fee94f8d587051f9","last_reissued_at":"2026-05-18T02:16:02.219304Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:02.219304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.0856","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":"2026-05-18T02:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kCCFpIK3G+gNuxAxQlE2t18da1EwJ+fcPfswnOPVcXO4LJw+TcsQHTnf8HFWa03ruATgT6YF6Yc19rIAUmbHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:24:55.569932Z"},"content_sha256":"9865d2b99caf3dbf1955b3ded3cba5ee242f4897a0472f17c85f3aa7e5ed4967","schema_version":"1.0","event_id":"sha256:9865d2b99caf3dbf1955b3ded3cba5ee242f4897a0472f17c85f3aa7e5ed4967"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:K6YF2342RFSZTLXBEE5VCNDQ6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"nlin.SI","authors_text":"Ruoxia Yao, Shunli Zhang, S. Y. Lou, Xiaoyu Jiao","submitted_at":"2008-01-06T11:48:32Z","abstract_excerpt":"For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction equations of different orders enables series reduction solutions. For weak dissipation case, zero-order similarity solutions satisfy the Painlev\\'e II, Painlev\\'e I and Jacobi elliptic function equations. For weak dispersion case, zero-order similarity solutions are in the form of Kummer, Airy and hyperbolic tangent functions. Higher order similarity solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.0856","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":"2026-05-18T02:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qZyrbLMz/nHuBfYLuxbJTyD6Qdb1uQEK3RYwQxEX8t0c51DSQH8AyN7cbvsszmwkhIqab13Izu9VhGKpJLRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:24:55.570289Z"},"content_sha256":"16a6ec78468c9234dd12b1dd5c02244e051d0deffb82e67ece2b023f8dd775a5","schema_version":"1.0","event_id":"sha256:16a6ec78468c9234dd12b1dd5c02244e051d0deffb82e67ece2b023f8dd775a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6YF2342RFSZTLXBEE5VCNDQ6W/bundle.json","state_url":"https://pith.science/pith/K6YF2342RFSZTLXBEE5VCNDQ6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6YF2342RFSZTLXBEE5VCNDQ6W/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":"2026-06-05T02:24:55Z","links":{"resolver":"https://pith.science/pith/K6YF2342RFSZTLXBEE5VCNDQ6W","bundle":"https://pith.science/pith/K6YF2342RFSZTLXBEE5VCNDQ6W/bundle.json","state":"https://pith.science/pith/K6YF2342RFSZTLXBEE5VCNDQ6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6YF2342RFSZTLXBEE5VCNDQ6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:K6YF2342RFSZTLXBEE5VCNDQ6W","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":"3e10c38bfefbdf98a8574defab682972d64c0a123150ab01db6430191d14d997","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-01-06T11:48:32Z","title_canon_sha256":"cbbf214de65d2b3c6e99b31e4a7d550be1db34720d167491b403fe8ffc04a31a"},"schema_version":"1.0","source":{"id":"0801.0856","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.0856","created_at":"2026-05-18T02:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"0801.0856v2","created_at":"2026-05-18T02:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.0856","created_at":"2026-05-18T02:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"K6YF2342RFSZ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"K6YF2342RFSZTLXB","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"K6YF2342","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:16a6ec78468c9234dd12b1dd5c02244e051d0deffb82e67ece2b023f8dd775a5","target":"graph","created_at":"2026-05-18T02:16:02Z","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":"For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction equations of different orders enables series reduction solutions. For weak dissipation case, zero-order similarity solutions satisfy the Painlev\\'e II, Painlev\\'e I and Jacobi elliptic function equations. For weak dispersion case, zero-order similarity solutions are in the form of Kummer, Airy and hyperbolic tangent functions. Higher order similarity solutio","authors_text":"Ruoxia Yao, Shunli Zhang, S. Y. Lou, Xiaoyu Jiao","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-01-06T11:48:32Z","title":"Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.0856","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":"sha256:9865d2b99caf3dbf1955b3ded3cba5ee242f4897a0472f17c85f3aa7e5ed4967","target":"record","created_at":"2026-05-18T02:16:02Z","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":"3e10c38bfefbdf98a8574defab682972d64c0a123150ab01db6430191d14d997","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2008-01-06T11:48:32Z","title_canon_sha256":"cbbf214de65d2b3c6e99b31e4a7d550be1db34720d167491b403fe8ffc04a31a"},"schema_version":"1.0","source":{"id":"0801.0856","kind":"arxiv","version":2}},"canonical_sha256":"57b05d6f9a896599aee1213b513470f59cb5961ffab1bb39fee94f8d587051f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57b05d6f9a896599aee1213b513470f59cb5961ffab1bb39fee94f8d587051f9","first_computed_at":"2026-05-18T02:16:02.219304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:02.219304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sxLi6no1olR3EgKmHD4rCjnSiDXvtSmgThwePnrh0sDDal5ToebHMO09WL44D+2UBFLtne9Ct0jhh8OazqfiDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:02.219926Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.0856","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9865d2b99caf3dbf1955b3ded3cba5ee242f4897a0472f17c85f3aa7e5ed4967","sha256:16a6ec78468c9234dd12b1dd5c02244e051d0deffb82e67ece2b023f8dd775a5"],"state_sha256":"af142d9e0b75894b0df4d928b1a76e94a0c9cedb8fdf4d27a871c5205cd47815"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbiWOwgmdaQHn01QfI6q9Ifx0JEh08xnSjHs9i9IG/H4ekk81fn8RUxCBKXC8/vZphyD/k0mKMdHmXhiiXZ/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:24:55.572443Z","bundle_sha256":"89e95af31dcb47eefd7a4cb7cf2f8260f54d315d6ed72cd77522d56f585c2642"}}