{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HPJX4NZUPVSLOKGKA7EK6OGGLR","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":"dd52c45f40dde373e09c92ff7e07639f981cc2d4d67ae2d1d0caf6b719620232","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-27T17:10:33Z","title_canon_sha256":"74d149b61c8057013be37d8f52a849478b976a043995f2de2cac26d9605ff9b3"},"schema_version":"1.0","source":{"id":"1503.08789","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08789","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08789v1","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08789","created_at":"2026-05-18T02:20:00Z"},{"alias_kind":"pith_short_12","alias_value":"HPJX4NZUPVSL","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HPJX4NZUPVSLOKGK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HPJX4NZU","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:09499359dcea261761121d3b40a463e5cf8c7c0cea2dbe040fca3167e632e5d1","target":"graph","created_at":"2026-05-18T02:20:00Z","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, the invariant subspace method is applied to the time fractional modified Kuramoto-Sivashinsky partial differential equation. The obtained reduced system of nonlinear ordinary fractional equations is solved by the Laplace transform method and with using of some useful properties of Mittag-Leffler function. Then, some exact solutions of the time fractional nonlinear studied equation are found.","authors_text":"A. Ouhadan, E. H. El Kinani","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-27T17:10:33Z","title":"Invariant Subspace Method and Fractional Modified Kuramoto-Sivashinsky Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08789","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:a5ff831b3a01ea90ba1ec69e717a659c4ce71122e2a3ab9beeab799cc049f6e4","target":"record","created_at":"2026-05-18T02:20:00Z","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":"dd52c45f40dde373e09c92ff7e07639f981cc2d4d67ae2d1d0caf6b719620232","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-27T17:10:33Z","title_canon_sha256":"74d149b61c8057013be37d8f52a849478b976a043995f2de2cac26d9605ff9b3"},"schema_version":"1.0","source":{"id":"1503.08789","kind":"arxiv","version":1}},"canonical_sha256":"3bd37e37347d64b728ca07c8af38c65c5223b2180dc95a23016585863eb644cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bd37e37347d64b728ca07c8af38c65c5223b2180dc95a23016585863eb644cf","first_computed_at":"2026-05-18T02:20:00.930357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:00.930357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6tgkDUUrHHM0Mrh2yn1BcFVe05AczgErZY8IuGXLThELIGHmKpmQNwp61FEXp2P9uu0vyha7XJsqj3H14F2/Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:00.931014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08789","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5ff831b3a01ea90ba1ec69e717a659c4ce71122e2a3ab9beeab799cc049f6e4","sha256:09499359dcea261761121d3b40a463e5cf8c7c0cea2dbe040fca3167e632e5d1"],"state_sha256":"19651c030f9ffecd652c3344dd06708d39eb9264e5c41e1ac2c328680b6d823b"}