{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:EEFUH42DS4BW3D6FSREDL2OEQE","short_pith_number":"pith:EEFUH42D","canonical_record":{"source":{"id":"1105.6189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-05-31T07:36:38Z","cross_cats_sorted":["math.AP","math.CA","math.NA"],"title_canon_sha256":"5f22c83bd7e083caca2f80e21d6b9efd7aadceec6735f7c64c8a950488d71cf4","abstract_canon_sha256":"adbbcafc4b6b74ae08ab8cd750df9dfac3057c4925dea6470dbd95186f2051a6"},"schema_version":"1.0"},"canonical_sha256":"210b43f34397036d8fc5944835e9c4811e527c145d704d8df0e86fe54015d299","source":{"kind":"arxiv","id":"1105.6189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6189","created_at":"2026-05-18T02:01:45Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6189v1","created_at":"2026-05-18T02:01:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6189","created_at":"2026-05-18T02:01:45Z"},{"alias_kind":"pith_short_12","alias_value":"EEFUH42DS4BW","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EEFUH42DS4BW3D6F","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EEFUH42D","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:EEFUH42DS4BW3D6FSREDL2OEQE","target":"record","payload":{"canonical_record":{"source":{"id":"1105.6189","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-05-31T07:36:38Z","cross_cats_sorted":["math.AP","math.CA","math.NA"],"title_canon_sha256":"5f22c83bd7e083caca2f80e21d6b9efd7aadceec6735f7c64c8a950488d71cf4","abstract_canon_sha256":"adbbcafc4b6b74ae08ab8cd750df9dfac3057c4925dea6470dbd95186f2051a6"},"schema_version":"1.0"},"canonical_sha256":"210b43f34397036d8fc5944835e9c4811e527c145d704d8df0e86fe54015d299","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:45.744221Z","signature_b64":"UXhULTjH3gxrvIY04Osi2p9rEl508cuIZGHwJlAcsWi2XqMQuGgHnLkfMcIx0FoMXkeGGalRAMkR0auSmur+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"210b43f34397036d8fc5944835e9c4811e527c145d704d8df0e86fe54015d299","last_reissued_at":"2026-05-18T02:01:45.743282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:45.743282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.6189","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":"2026-05-18T02:01:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5bNfJKVzyMB6+nzsKW7ZKyRdCC0lesVYxlfU0n93cEhReo2hHGsh1PePZaeUGu7bIN5x1sPtppUyfZLNC3bDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:26:46.440288Z"},"content_sha256":"ba9424ceb68f7afbda42866e2f7bbd0a0d1d9a5eee0d008f3e98540eb43de4a6","schema_version":"1.0","event_id":"sha256:ba9424ceb68f7afbda42866e2f7bbd0a0d1d9a5eee0d008f3e98540eb43de4a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:EEFUH42DS4BW3D6FSREDL2OEQE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparison of a general series expansion method and the homotopy analysis method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA","math.NA"],"primary_cat":"nlin.SI","authors_text":"Cheng-shi Liu, Y Liu","submitted_at":"2011-05-31T07:36:38Z","abstract_excerpt":"A simple analytic tool namely the general series expansion method is proposed to find the solutions for nonlinear differential equations. By choosing a set of suitable basis functions $\\{e_n(t,t_0)\\}_{n=0}^{+\\infty}$ such that the solution to the equation can be expressed by $u(t)=\\sum_{n=0}^{+\\infty}c_ne_n(t,t_0)$. In general, $t_0$ can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is more simple and clear. As a result, we show that the secret parameter $h$ in the homot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6189","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":"2026-05-18T02:01:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"03kOgfh9kTQMK7/6ApjnXyS43q+9QLurynKuNP/LfKryaRRfLyz0ipkwaek9JmW0n2fSTvnDGoCOStSFNRKpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:26:46.440650Z"},"content_sha256":"9f5aec655d9db5ae4956d5e5260460fda4ac7b478754da5a21e81ebe8223e71f","schema_version":"1.0","event_id":"sha256:9f5aec655d9db5ae4956d5e5260460fda4ac7b478754da5a21e81ebe8223e71f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EEFUH42DS4BW3D6FSREDL2OEQE/bundle.json","state_url":"https://pith.science/pith/EEFUH42DS4BW3D6FSREDL2OEQE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EEFUH42DS4BW3D6FSREDL2OEQE/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":"2026-06-02T20:26:46Z","links":{"resolver":"https://pith.science/pith/EEFUH42DS4BW3D6FSREDL2OEQE","bundle":"https://pith.science/pith/EEFUH42DS4BW3D6FSREDL2OEQE/bundle.json","state":"https://pith.science/pith/EEFUH42DS4BW3D6FSREDL2OEQE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EEFUH42DS4BW3D6FSREDL2OEQE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EEFUH42DS4BW3D6FSREDL2OEQE","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":"adbbcafc4b6b74ae08ab8cd750df9dfac3057c4925dea6470dbd95186f2051a6","cross_cats_sorted":["math.AP","math.CA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-05-31T07:36:38Z","title_canon_sha256":"5f22c83bd7e083caca2f80e21d6b9efd7aadceec6735f7c64c8a950488d71cf4"},"schema_version":"1.0","source":{"id":"1105.6189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6189","created_at":"2026-05-18T02:01:45Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6189v1","created_at":"2026-05-18T02:01:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6189","created_at":"2026-05-18T02:01:45Z"},{"alias_kind":"pith_short_12","alias_value":"EEFUH42DS4BW","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EEFUH42DS4BW3D6F","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EEFUH42D","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:9f5aec655d9db5ae4956d5e5260460fda4ac7b478754da5a21e81ebe8223e71f","target":"graph","created_at":"2026-05-18T02:01:45Z","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":"A simple analytic tool namely the general series expansion method is proposed to find the solutions for nonlinear differential equations. By choosing a set of suitable basis functions $\\{e_n(t,t_0)\\}_{n=0}^{+\\infty}$ such that the solution to the equation can be expressed by $u(t)=\\sum_{n=0}^{+\\infty}c_ne_n(t,t_0)$. In general, $t_0$ can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is more simple and clear. As a result, we show that the secret parameter $h$ in the homot","authors_text":"Cheng-shi Liu, Y Liu","cross_cats":["math.AP","math.CA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-05-31T07:36:38Z","title":"Comparison of a general series expansion method and the homotopy analysis method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6189","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:ba9424ceb68f7afbda42866e2f7bbd0a0d1d9a5eee0d008f3e98540eb43de4a6","target":"record","created_at":"2026-05-18T02:01:45Z","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":"adbbcafc4b6b74ae08ab8cd750df9dfac3057c4925dea6470dbd95186f2051a6","cross_cats_sorted":["math.AP","math.CA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2011-05-31T07:36:38Z","title_canon_sha256":"5f22c83bd7e083caca2f80e21d6b9efd7aadceec6735f7c64c8a950488d71cf4"},"schema_version":"1.0","source":{"id":"1105.6189","kind":"arxiv","version":1}},"canonical_sha256":"210b43f34397036d8fc5944835e9c4811e527c145d704d8df0e86fe54015d299","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"210b43f34397036d8fc5944835e9c4811e527c145d704d8df0e86fe54015d299","first_computed_at":"2026-05-18T02:01:45.743282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:45.743282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UXhULTjH3gxrvIY04Osi2p9rEl508cuIZGHwJlAcsWi2XqMQuGgHnLkfMcIx0FoMXkeGGalRAMkR0auSmur+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:45.744221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.6189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba9424ceb68f7afbda42866e2f7bbd0a0d1d9a5eee0d008f3e98540eb43de4a6","sha256:9f5aec655d9db5ae4956d5e5260460fda4ac7b478754da5a21e81ebe8223e71f"],"state_sha256":"2b23b25b91b99fa7d2544916a9b807afac0333706f236871676ad9faad8698a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"avJoQSKiJsl3oJPetWrZDAbmMIAMk4XhPx+OqQ9bR+3fpTd7Frl264Gv/x7ek2kbdr7O4O0OWIGvH3VnrgPZAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:26:46.442541Z","bundle_sha256":"27eb4115b8e5cc258bac1e8025963df504c179be93175e9999cd9c202b9fb38d"}}