{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:F7TSXJN5CQVIQ4J4WJ5LN555AE","short_pith_number":"pith:F7TSXJN5","canonical_record":{"source":{"id":"1409.7563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-09-26T13:16:35Z","cross_cats_sorted":[],"title_canon_sha256":"7ab28046c301e416914ea33a12268abf81bf380f1d53b0063d4e710f0cee9da7","abstract_canon_sha256":"67f7fab09478999107e34230b71e31d782ff8dc7198ac0ffefbc56609ff401d4"},"schema_version":"1.0"},"canonical_sha256":"2fe72ba5bd142a88713cb27ab6f7bd013141b59d132c160049d68725b93d0b76","source":{"kind":"arxiv","id":"1409.7563","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7563","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7563v1","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7563","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"F7TSXJN5CQVI","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F7TSXJN5CQVIQ4J4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F7TSXJN5","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:F7TSXJN5CQVIQ4J4WJ5LN555AE","target":"record","payload":{"canonical_record":{"source":{"id":"1409.7563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-09-26T13:16:35Z","cross_cats_sorted":[],"title_canon_sha256":"7ab28046c301e416914ea33a12268abf81bf380f1d53b0063d4e710f0cee9da7","abstract_canon_sha256":"67f7fab09478999107e34230b71e31d782ff8dc7198ac0ffefbc56609ff401d4"},"schema_version":"1.0"},"canonical_sha256":"2fe72ba5bd142a88713cb27ab6f7bd013141b59d132c160049d68725b93d0b76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:52.410618Z","signature_b64":"/TFNkYotpHJBP2yHA6y00wymuxecpOh0AFsXk9XCZS4x/dWDw/cUNT53cEaCUmUity9TPAdHyUinMOf4bh1BCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fe72ba5bd142a88713cb27ab6f7bd013141b59d132c160049d68725b93d0b76","last_reissued_at":"2026-05-18T02:41:52.410095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:52.410095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.7563","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":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82sza4GbyUIi/+Io3036gJoaJG1S5FWTIk1/CmNzRdBdB0J8njUSbJyD/l7rQ/8SBgBNvVtupdvnric3dH3OCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:11:21.887909Z"},"content_sha256":"020a1fbce0045c60201c8e67d6d26ada5cca7f519949b0ae7fbde94ac3347315","schema_version":"1.0","event_id":"sha256:020a1fbce0045c60201c8e67d6d26ada5cca7f519949b0ae7fbde94ac3347315"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:F7TSXJN5CQVIQ4J4WJ5LN555AE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-exact solutions of nonlinear differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Mark B. Kochanov, Nikolay A. Kudryashov","submitted_at":"2014-09-26T13:16:35Z","abstract_excerpt":"The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7563","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":"2026-05-18T02:41:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V7ZmXDQ8PcbEK8E+a/kvglq+cw8riMovpWxSn+wCg3fTEKMzoOvoxbub8MyZPeF0zAxpzBsvzWKHOv0fHpKSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:11:21.888252Z"},"content_sha256":"4cbf6bed304af98c1bd89bc1798d53810e3b0984e21fb0b83e206b8efb0d1099","schema_version":"1.0","event_id":"sha256:4cbf6bed304af98c1bd89bc1798d53810e3b0984e21fb0b83e206b8efb0d1099"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F7TSXJN5CQVIQ4J4WJ5LN555AE/bundle.json","state_url":"https://pith.science/pith/F7TSXJN5CQVIQ4J4WJ5LN555AE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F7TSXJN5CQVIQ4J4WJ5LN555AE/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":"2026-06-23T15:11:21Z","links":{"resolver":"https://pith.science/pith/F7TSXJN5CQVIQ4J4WJ5LN555AE","bundle":"https://pith.science/pith/F7TSXJN5CQVIQ4J4WJ5LN555AE/bundle.json","state":"https://pith.science/pith/F7TSXJN5CQVIQ4J4WJ5LN555AE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F7TSXJN5CQVIQ4J4WJ5LN555AE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F7TSXJN5CQVIQ4J4WJ5LN555AE","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":"67f7fab09478999107e34230b71e31d782ff8dc7198ac0ffefbc56609ff401d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-09-26T13:16:35Z","title_canon_sha256":"7ab28046c301e416914ea33a12268abf81bf380f1d53b0063d4e710f0cee9da7"},"schema_version":"1.0","source":{"id":"1409.7563","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7563","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7563v1","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7563","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"F7TSXJN5CQVI","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F7TSXJN5CQVIQ4J4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F7TSXJN5","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:4cbf6bed304af98c1bd89bc1798d53810e3b0984e21fb0b83e206b8efb0d1099","target":"graph","created_at":"2026-05-18T02:41:52Z","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":"The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.","authors_text":"Mark B. Kochanov, Nikolay A. Kudryashov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-09-26T13:16:35Z","title":"Quasi-exact solutions of nonlinear differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7563","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":"sha256:020a1fbce0045c60201c8e67d6d26ada5cca7f519949b0ae7fbde94ac3347315","target":"record","created_at":"2026-05-18T02:41:52Z","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":"67f7fab09478999107e34230b71e31d782ff8dc7198ac0ffefbc56609ff401d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2014-09-26T13:16:35Z","title_canon_sha256":"7ab28046c301e416914ea33a12268abf81bf380f1d53b0063d4e710f0cee9da7"},"schema_version":"1.0","source":{"id":"1409.7563","kind":"arxiv","version":1}},"canonical_sha256":"2fe72ba5bd142a88713cb27ab6f7bd013141b59d132c160049d68725b93d0b76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fe72ba5bd142a88713cb27ab6f7bd013141b59d132c160049d68725b93d0b76","first_computed_at":"2026-05-18T02:41:52.410095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:52.410095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/TFNkYotpHJBP2yHA6y00wymuxecpOh0AFsXk9XCZS4x/dWDw/cUNT53cEaCUmUity9TPAdHyUinMOf4bh1BCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:52.410618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7563","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:020a1fbce0045c60201c8e67d6d26ada5cca7f519949b0ae7fbde94ac3347315","sha256:4cbf6bed304af98c1bd89bc1798d53810e3b0984e21fb0b83e206b8efb0d1099"],"state_sha256":"dff8a5d1fe1ad3f2f58efa9bb9eaf50aea4ffac413ca4cc3dbda86de6889ff33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJKk1Yhv0LuTAqNrlWjfUz4GuZxAYnB0QKmTBWvtnsd72LNDFWxwy5YWqt9t6xbP0TCcvVqBn8uv2Bz+zmm0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:11:21.890175Z","bundle_sha256":"9bcb27a79e3e8fd12a986d4c2210c64be959ad0f5edca1cd880736055a207869"}}