{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:BV2N3ULKADCCUVHCBF4ECYLW64","short_pith_number":"pith:BV2N3ULK","canonical_record":{"source":{"id":"2105.11534","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MS","submitted_at":"2021-05-07T11:22:13Z","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"title_canon_sha256":"28c518615d635bff9fce2831b3bbcdc2e2bdc138dde808bb60661ea85b34e56f","abstract_canon_sha256":"3e6764e77bec2956df44157fa86b506cf2c2316df3c736a3bd482d750f55f321"},"schema_version":"1.0"},"canonical_sha256":"0d74ddd16a00c42a54e20978416176f731481c4a3228b7b03b6a70fbd09b2b5b","source":{"kind":"arxiv","id":"2105.11534","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.11534","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"2105.11534v1","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.11534","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"BV2N3ULKADCC","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"pith_short_16","alias_value":"BV2N3ULKADCCUVHC","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"pith_short_8","alias_value":"BV2N3ULK","created_at":"2026-07-05T02:42:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:BV2N3ULKADCCUVHCBF4ECYLW64","target":"record","payload":{"canonical_record":{"source":{"id":"2105.11534","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MS","submitted_at":"2021-05-07T11:22:13Z","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"title_canon_sha256":"28c518615d635bff9fce2831b3bbcdc2e2bdc138dde808bb60661ea85b34e56f","abstract_canon_sha256":"3e6764e77bec2956df44157fa86b506cf2c2316df3c736a3bd482d750f55f321"},"schema_version":"1.0"},"canonical_sha256":"0d74ddd16a00c42a54e20978416176f731481c4a3228b7b03b6a70fbd09b2b5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:42:53.461341Z","signature_b64":"HZnRLpc+xKBHbqCfE5TuXqrs7FDb/aqEhQ88hT/jPTc3mnEk7XwIYkyTS2J6kKyyJCRhM3v3OCW6Vm4C8CEGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d74ddd16a00c42a54e20978416176f731481c4a3228b7b03b6a70fbd09b2b5b","last_reissued_at":"2026-07-05T02:42:53.460716Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:42:53.460716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.11534","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":"2026-07-05T02:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QEnOjDBn6Pliu4f4M+kYLH/61jPZlf2g/yQqa0xKFqZHgMtsaJJmB/un6A88SKUAf0v1lKjdSeTHtN7pjN8aBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:40:47.019213Z"},"content_sha256":"3f9426bf907e1dc174d6750e22037e39e412f1d2666a6a4a2cc65eb9b33d8960","schema_version":"1.0","event_id":"sha256:3f9426bf907e1dc174d6750e22037e39e412f1d2666a6a4a2cc65eb9b33d8960"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:BV2N3ULKADCCUVHCBF4ECYLW64","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"ReLie: a Reduce program for Lie group analysis of differential equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"primary_cat":"cs.MS","authors_text":"Francesco Oliveri","submitted_at":"2021-05-07T11:22:13Z","abstract_excerpt":"Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many computer algebra packages have been developed along the years to automate the computation. In this paper, we describe the program ReLie, written in the Computer Algebra System Reduce, which since 2008 is an open source program (http://www.reduce-algebra.com) and is available for all platforms. \\relie is able to perform almost automatically the needed computations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.11534","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.11534/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:42:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A91bBVI8/246QY+F0+usJBYZk2rlHrlA5AYbyIItt3R5oxfIfo6GqYrVD4hq5oa0RLUFEQCxfp5kGwatRo8+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T03:40:47.019721Z"},"content_sha256":"34dac596f4dceda4d12d2bf5c95a4f17715a9ef35cb3f703206576cf312fd0eb","schema_version":"1.0","event_id":"sha256:34dac596f4dceda4d12d2bf5c95a4f17715a9ef35cb3f703206576cf312fd0eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BV2N3ULKADCCUVHCBF4ECYLW64/bundle.json","state_url":"https://pith.science/pith/BV2N3ULKADCCUVHCBF4ECYLW64/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BV2N3ULKADCCUVHCBF4ECYLW64/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":"2026-08-08T03:40:47Z","links":{"resolver":"https://pith.science/pith/BV2N3ULKADCCUVHCBF4ECYLW64","bundle":"https://pith.science/pith/BV2N3ULKADCCUVHCBF4ECYLW64/bundle.json","state":"https://pith.science/pith/BV2N3ULKADCCUVHCBF4ECYLW64/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BV2N3ULKADCCUVHCBF4ECYLW64/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BV2N3ULKADCCUVHCBF4ECYLW64","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":"3e6764e77bec2956df44157fa86b506cf2c2316df3c736a3bd482d750f55f321","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MS","submitted_at":"2021-05-07T11:22:13Z","title_canon_sha256":"28c518615d635bff9fce2831b3bbcdc2e2bdc138dde808bb60661ea85b34e56f"},"schema_version":"1.0","source":{"id":"2105.11534","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.11534","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"arxiv_version","alias_value":"2105.11534v1","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.11534","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"pith_short_12","alias_value":"BV2N3ULKADCC","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"pith_short_16","alias_value":"BV2N3ULKADCCUVHC","created_at":"2026-07-05T02:42:53Z"},{"alias_kind":"pith_short_8","alias_value":"BV2N3ULK","created_at":"2026-07-05T02:42:53Z"}],"graph_snapshots":[{"event_id":"sha256:34dac596f4dceda4d12d2bf5c95a4f17715a9ef35cb3f703206576cf312fd0eb","target":"graph","created_at":"2026-07-05T02:42:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.11534/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many computer algebra packages have been developed along the years to automate the computation. In this paper, we describe the program ReLie, written in the Computer Algebra System Reduce, which since 2008 is an open source program (http://www.reduce-algebra.com) and is available for all platforms. \\relie is able to perform almost automatically the needed computations","authors_text":"Francesco Oliveri","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MS","submitted_at":"2021-05-07T11:22:13Z","title":"ReLie: a Reduce program for Lie group analysis of differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.11534","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":"sha256:3f9426bf907e1dc174d6750e22037e39e412f1d2666a6a4a2cc65eb9b33d8960","target":"record","created_at":"2026-07-05T02:42:53Z","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":"3e6764e77bec2956df44157fa86b506cf2c2316df3c736a3bd482d750f55f321","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MS","submitted_at":"2021-05-07T11:22:13Z","title_canon_sha256":"28c518615d635bff9fce2831b3bbcdc2e2bdc138dde808bb60661ea85b34e56f"},"schema_version":"1.0","source":{"id":"2105.11534","kind":"arxiv","version":1}},"canonical_sha256":"0d74ddd16a00c42a54e20978416176f731481c4a3228b7b03b6a70fbd09b2b5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d74ddd16a00c42a54e20978416176f731481c4a3228b7b03b6a70fbd09b2b5b","first_computed_at":"2026-07-05T02:42:53.460716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:42:53.460716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZnRLpc+xKBHbqCfE5TuXqrs7FDb/aqEhQ88hT/jPTc3mnEk7XwIYkyTS2J6kKyyJCRhM3v3OCW6Vm4C8CEGAg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:42:53.461341Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.11534","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f9426bf907e1dc174d6750e22037e39e412f1d2666a6a4a2cc65eb9b33d8960","sha256:34dac596f4dceda4d12d2bf5c95a4f17715a9ef35cb3f703206576cf312fd0eb"],"state_sha256":"85f87d27b3cf080247dc686c7016cfce4cbd948a58fe4eb40770c391d2c285eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3HBSOe5eQQeMXKrW5SASpYdddc3LUfEHv14E/94IjUTu75LZ9a1XhJAAldwqR7SSAkDEzwxIbx2IFxKhxk+wDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T03:40:47.024732Z","bundle_sha256":"5c6a1e7995985c63756136e6f03fc744001faf06748fac3f594ec3742acc582f"}}