{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GT7KC7KKT42K4STYVRPU6P4JGI","short_pith_number":"pith:GT7KC7KK","canonical_record":{"source":{"id":"1302.2765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-12T11:54:49Z","cross_cats_sorted":[],"title_canon_sha256":"12ce545d5543ca9590628c4270d6fad707bc62452c3e726baf7830d4f3a7fd00","abstract_canon_sha256":"069a2084c175553d9c3129b203446f3f4e7939d4ed8b60f413a197b29318bd05"},"schema_version":"1.0"},"canonical_sha256":"34fea17d4a9f34ae4a78ac5f4f3f89321398944d2bef1edecae8b4b5b5748a26","source":{"kind":"arxiv","id":"1302.2765","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2765","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2765v1","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2765","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"GT7KC7KKT42K","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GT7KC7KKT42K4STY","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GT7KC7KK","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GT7KC7KKT42K4STYVRPU6P4JGI","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2765","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-12T11:54:49Z","cross_cats_sorted":[],"title_canon_sha256":"12ce545d5543ca9590628c4270d6fad707bc62452c3e726baf7830d4f3a7fd00","abstract_canon_sha256":"069a2084c175553d9c3129b203446f3f4e7939d4ed8b60f413a197b29318bd05"},"schema_version":"1.0"},"canonical_sha256":"34fea17d4a9f34ae4a78ac5f4f3f89321398944d2bef1edecae8b4b5b5748a26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:50.941547Z","signature_b64":"IUkOArm+98HLGfyOc5axokspNb1f3p2onTwJvGF0kBycSGEH8VCT5CFTskNhd3+HOCytniHBUjWvncswDrlnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34fea17d4a9f34ae4a78ac5f4f3f89321398944d2bef1edecae8b4b5b5748a26","last_reissued_at":"2026-05-18T03:33:50.940516Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:50.940516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2765","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":"2026-05-18T03:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKpuOTJzU7/DEZtWC7n4cbTk+4Mlkl8RSl3HVvPGnhwD8pIpUjFk+1oJBg/tOrPDkvOZoQoxLq0aFS3ryaKRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:35:16.132994Z"},"content_sha256":"9a7d5906ab31d9792d1f8da56b51427ba87fc4e6dbf3223ae209473d4d76df1c","schema_version":"1.0","event_id":"sha256:9a7d5906ab31d9792d1f8da56b51427ba87fc4e6dbf3223ae209473d4d76df1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GT7KC7KKT42K4STYVRPU6P4JGI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factorization method for nonlinear evolution equations Factorization method for nonlinear evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Aparna Saha, Benoy Talukdar, Debabrata Pal, Swapan K. Ghosh","submitted_at":"2013-02-12T11:54:49Z","abstract_excerpt":"The traditional method of factorization can be used to obtain only the particular solutions of the Li\\'enard type ordinary differential equations. We suggest a modification of the approach that can be used to construct general solutions . We first demonstrate the effectiveness of our method by dealing with a solvable form of the modified Emden-type equation and subsequently employ it to obtain the solitary wave solutions of the KdV, mKdV, Rosenau-Hyman (RH) and NLS equations. The solution of the mKdV equation, via the so-called Muira transform, leads to a singular solution of the KdV equation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2765","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":"2026-05-18T03:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TjwX1BvaTHOXvuaxRTA4wUTRKgqxJKgP52WDs/gGt5Y9FmMVspd5x9Uu1JRA9zBMDA3AwCOFqM87NH+dtufsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:35:16.133610Z"},"content_sha256":"ec81ed476c4d364563366d14eb27b9720f7a2e7ebf89c6f9c6863cb4c80fbd57","schema_version":"1.0","event_id":"sha256:ec81ed476c4d364563366d14eb27b9720f7a2e7ebf89c6f9c6863cb4c80fbd57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GT7KC7KKT42K4STYVRPU6P4JGI/bundle.json","state_url":"https://pith.science/pith/GT7KC7KKT42K4STYVRPU6P4JGI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GT7KC7KKT42K4STYVRPU6P4JGI/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":"2026-05-22T18:35:16Z","links":{"resolver":"https://pith.science/pith/GT7KC7KKT42K4STYVRPU6P4JGI","bundle":"https://pith.science/pith/GT7KC7KKT42K4STYVRPU6P4JGI/bundle.json","state":"https://pith.science/pith/GT7KC7KKT42K4STYVRPU6P4JGI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GT7KC7KKT42K4STYVRPU6P4JGI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GT7KC7KKT42K4STYVRPU6P4JGI","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":"069a2084c175553d9c3129b203446f3f4e7939d4ed8b60f413a197b29318bd05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-12T11:54:49Z","title_canon_sha256":"12ce545d5543ca9590628c4270d6fad707bc62452c3e726baf7830d4f3a7fd00"},"schema_version":"1.0","source":{"id":"1302.2765","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2765","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2765v1","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2765","created_at":"2026-05-18T03:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"GT7KC7KKT42K","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GT7KC7KKT42K4STY","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GT7KC7KK","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:ec81ed476c4d364563366d14eb27b9720f7a2e7ebf89c6f9c6863cb4c80fbd57","target":"graph","created_at":"2026-05-18T03:33:50Z","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 traditional method of factorization can be used to obtain only the particular solutions of the Li\\'enard type ordinary differential equations. We suggest a modification of the approach that can be used to construct general solutions . We first demonstrate the effectiveness of our method by dealing with a solvable form of the modified Emden-type equation and subsequently employ it to obtain the solitary wave solutions of the KdV, mKdV, Rosenau-Hyman (RH) and NLS equations. The solution of the mKdV equation, via the so-called Muira transform, leads to a singular solution of the KdV equation ","authors_text":"Aparna Saha, Benoy Talukdar, Debabrata Pal, Swapan K. Ghosh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-12T11:54:49Z","title":"Factorization method for nonlinear evolution equations Factorization method for nonlinear evolution equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2765","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":"sha256:9a7d5906ab31d9792d1f8da56b51427ba87fc4e6dbf3223ae209473d4d76df1c","target":"record","created_at":"2026-05-18T03:33:50Z","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":"069a2084c175553d9c3129b203446f3f4e7939d4ed8b60f413a197b29318bd05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-02-12T11:54:49Z","title_canon_sha256":"12ce545d5543ca9590628c4270d6fad707bc62452c3e726baf7830d4f3a7fd00"},"schema_version":"1.0","source":{"id":"1302.2765","kind":"arxiv","version":1}},"canonical_sha256":"34fea17d4a9f34ae4a78ac5f4f3f89321398944d2bef1edecae8b4b5b5748a26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34fea17d4a9f34ae4a78ac5f4f3f89321398944d2bef1edecae8b4b5b5748a26","first_computed_at":"2026-05-18T03:33:50.940516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:50.940516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IUkOArm+98HLGfyOc5axokspNb1f3p2onTwJvGF0kBycSGEH8VCT5CFTskNhd3+HOCytniHBUjWvncswDrlnDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:50.941547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2765","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a7d5906ab31d9792d1f8da56b51427ba87fc4e6dbf3223ae209473d4d76df1c","sha256:ec81ed476c4d364563366d14eb27b9720f7a2e7ebf89c6f9c6863cb4c80fbd57"],"state_sha256":"852cf6d8b1e2f0b9d950c7658f0ad1c38dd24fb9450f27dd0de1f88f299798e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l/Z+pN5iyPMOYDsmL84StKczeLGFgiYu6574Y8nFE9erBcbvTdl1fW4fGIMgvpnzpT67lPGqdH6Cx1y3zLqoAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T18:35:16.135955Z","bundle_sha256":"c70f089b738f8128c2c05e5e0c7fb01f31635681aff16c8c0edd57655003ff4c"}}