{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VLGSFDKWU6HZPWX3YGTLRK7ZDY","short_pith_number":"pith:VLGSFDKW","canonical_record":{"source":{"id":"1004.3339","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-20T03:56:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0e5d9f12447998ee763e388c3f04093279bd405da69b9d2de4bd959a55c8a3b3","abstract_canon_sha256":"d74a09bc2286bb161ce597c272fa92b73c3d0985991a591bffa923d5aba72c3f"},"schema_version":"1.0"},"canonical_sha256":"aacd228d56a78f97dafbc1a6b8abf91e3fdeccc92f93ddf660c76ec024c91c68","source":{"kind":"arxiv","id":"1004.3339","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3339","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3339v2","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3339","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"VLGSFDKWU6HZ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VLGSFDKWU6HZPWX3","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VLGSFDKW","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VLGSFDKWU6HZPWX3YGTLRK7ZDY","target":"record","payload":{"canonical_record":{"source":{"id":"1004.3339","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-20T03:56:08Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"0e5d9f12447998ee763e388c3f04093279bd405da69b9d2de4bd959a55c8a3b3","abstract_canon_sha256":"d74a09bc2286bb161ce597c272fa92b73c3d0985991a591bffa923d5aba72c3f"},"schema_version":"1.0"},"canonical_sha256":"aacd228d56a78f97dafbc1a6b8abf91e3fdeccc92f93ddf660c76ec024c91c68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:56.459565Z","signature_b64":"JRdyn/0YEdwM73soCoaUUkTfdSqy/c30NI+fBc94jmAMDcWNarrD9wVLYRUdMc4eX9obMFigK921Z1Yl7FFkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aacd228d56a78f97dafbc1a6b8abf91e3fdeccc92f93ddf660c76ec024c91c68","last_reissued_at":"2026-05-18T02:07:56.458783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:56.458783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.3339","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":"2026-05-18T02:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOE9UIm183veIkVEojSUKDdNludXtJLwpzJ9z70ZnI0BqZZaefd86ASn5PUjHRlEovqRpcq7sARAzJvqp0fIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:13:37.618560Z"},"content_sha256":"3b33422318cbe88296afaa2244d0aceb15fb29cf39558e543d6ade028c32fb3b","schema_version":"1.0","event_id":"sha256:3b33422318cbe88296afaa2244d0aceb15fb29cf39558e543d6ade028c32fb3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VLGSFDKWU6HZPWX3YGTLRK7ZDY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"[SADE] A Maple package for the Symmetry Analysis of Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Annibal Figueiredo, Tarc\\'i sio M. Rocha Filho","submitted_at":"2010-04-20T03:56:08Z","abstract_excerpt":"We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\\\"acklund and potential symmetries, invariant solutions, first-integrals, N\\\"other theorem for both discrete and continuous systems, solution of ordinary differential equations, reduction of order or dimension using Lie symmetries, classification of differential equations, Casimir invariants, and the quasi-polynomial formalism for ODE's (previously implemented in the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3339","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":"2026-05-18T02:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9VDgd5QrIiyW9Ru8LHz+eNjYqpNkA/xiWohacMISTY4lb8CgJKFmHz8sM4xqbrCpXIic+c2m7kyeKW1M3h/DBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:13:37.618910Z"},"content_sha256":"8a9d628ea69c807db704abb0139ccfd58a864a9128f63134587294d29a9c440a","schema_version":"1.0","event_id":"sha256:8a9d628ea69c807db704abb0139ccfd58a864a9128f63134587294d29a9c440a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VLGSFDKWU6HZPWX3YGTLRK7ZDY/bundle.json","state_url":"https://pith.science/pith/VLGSFDKWU6HZPWX3YGTLRK7ZDY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VLGSFDKWU6HZPWX3YGTLRK7ZDY/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":"2026-06-20T23:13:37Z","links":{"resolver":"https://pith.science/pith/VLGSFDKWU6HZPWX3YGTLRK7ZDY","bundle":"https://pith.science/pith/VLGSFDKWU6HZPWX3YGTLRK7ZDY/bundle.json","state":"https://pith.science/pith/VLGSFDKWU6HZPWX3YGTLRK7ZDY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VLGSFDKWU6HZPWX3YGTLRK7ZDY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VLGSFDKWU6HZPWX3YGTLRK7ZDY","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":"d74a09bc2286bb161ce597c272fa92b73c3d0985991a591bffa923d5aba72c3f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-20T03:56:08Z","title_canon_sha256":"0e5d9f12447998ee763e388c3f04093279bd405da69b9d2de4bd959a55c8a3b3"},"schema_version":"1.0","source":{"id":"1004.3339","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3339","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3339v2","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3339","created_at":"2026-05-18T02:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"VLGSFDKWU6HZ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VLGSFDKWU6HZPWX3","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VLGSFDKW","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:8a9d628ea69c807db704abb0139ccfd58a864a9128f63134587294d29a9c440a","target":"graph","created_at":"2026-05-18T02:07:56Z","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":"We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie-B\\\"acklund and potential symmetries, invariant solutions, first-integrals, N\\\"other theorem for both discrete and continuous systems, solution of ordinary differential equations, reduction of order or dimension using Lie symmetries, classification of differential equations, Casimir invariants, and the quasi-polynomial formalism for ODE's (previously implemented in the p","authors_text":"Annibal Figueiredo, Tarc\\'i sio M. Rocha Filho","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-20T03:56:08Z","title":"[SADE] A Maple package for the Symmetry Analysis of Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3339","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":"sha256:3b33422318cbe88296afaa2244d0aceb15fb29cf39558e543d6ade028c32fb3b","target":"record","created_at":"2026-05-18T02:07:56Z","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":"d74a09bc2286bb161ce597c272fa92b73c3d0985991a591bffa923d5aba72c3f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-20T03:56:08Z","title_canon_sha256":"0e5d9f12447998ee763e388c3f04093279bd405da69b9d2de4bd959a55c8a3b3"},"schema_version":"1.0","source":{"id":"1004.3339","kind":"arxiv","version":2}},"canonical_sha256":"aacd228d56a78f97dafbc1a6b8abf91e3fdeccc92f93ddf660c76ec024c91c68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aacd228d56a78f97dafbc1a6b8abf91e3fdeccc92f93ddf660c76ec024c91c68","first_computed_at":"2026-05-18T02:07:56.458783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:56.458783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JRdyn/0YEdwM73soCoaUUkTfdSqy/c30NI+fBc94jmAMDcWNarrD9wVLYRUdMc4eX9obMFigK921Z1Yl7FFkCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:56.459565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3339","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b33422318cbe88296afaa2244d0aceb15fb29cf39558e543d6ade028c32fb3b","sha256:8a9d628ea69c807db704abb0139ccfd58a864a9128f63134587294d29a9c440a"],"state_sha256":"f0f332cc0d8ec94d81b3cd85044c2c1e3df9069475eb39371a4144e947493dd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDI1Xz9uNceMojFpVwGJI+372Yj1fvq64NGbMSTuGY3vcThXXiyX00ox/uLfMCT2kuqe2683X1/E4/okjfQfAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T23:13:37.620906Z","bundle_sha256":"9b6161b4a07fb7e5f9e14193b0b269bcdd5fb0837a749367917644836290cd12"}}