{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ATG4PMEJ7UYLUW3TMB34JR5UMS","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":"f87c2046da7fa95195778fcde492bf0f6f04e4f6d61de99357293e8133657df6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.hist-ph","submitted_at":"2005-03-08T22:21:40Z","title_canon_sha256":"90ce14e09f9a3ff6cb0921a95f6a6fef7c5c28ef375afcfca9e647c270f7c80c"},"schema_version":"1.0","source":{"id":"physics/0503066","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0503066","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0503066v3","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0503066","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"ATG4PMEJ7UYL","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ATG4PMEJ7UYLUW3T","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ATG4PMEJ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:65157471144101b763c1fe0c8989bffc9f82212112c3f94d82be4c9e7b5dbf90","target":"graph","created_at":"2026-05-18T00:14:29Z","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 problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in Section 1 and proved in following sections. Concerning these differential equations that arise from problems of variation, far more precise statements can be made than about arbitrary differential equations admitting of a group, which are the subject of Lie's researches. What is to follow, therefore, represents a combination of the methods of the formal calcul","authors_text":"Emmy Noether, M. A. Tavel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.hist-ph","submitted_at":"2005-03-08T22:21:40Z","title":"Invariant Variation Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0503066","kind":"arxiv","version":3},"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:df3bd2db479142a881d7309816f12b10d32a8760da157eb51dab86e4e5e41a80","target":"record","created_at":"2026-05-18T00:14:29Z","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":"f87c2046da7fa95195778fcde492bf0f6f04e4f6d61de99357293e8133657df6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.hist-ph","submitted_at":"2005-03-08T22:21:40Z","title_canon_sha256":"90ce14e09f9a3ff6cb0921a95f6a6fef7c5c28ef375afcfca9e647c270f7c80c"},"schema_version":"1.0","source":{"id":"physics/0503066","kind":"arxiv","version":3}},"canonical_sha256":"04cdc7b089fd30ba5b736077c4c7b46487b559f3a3d9955ecae41a7705b54419","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04cdc7b089fd30ba5b736077c4c7b46487b559f3a3d9955ecae41a7705b54419","first_computed_at":"2026-05-18T00:14:29.855403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.855403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rEbZsyYo8ok4IsbZ7gfxpnYFfMISBbuVFQKx4DNLLlc1w4ab7uSxUOYiBqneEICb9wu5WrqFHUeNa0PAOGwGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.856102Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0503066","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df3bd2db479142a881d7309816f12b10d32a8760da157eb51dab86e4e5e41a80","sha256:65157471144101b763c1fe0c8989bffc9f82212112c3f94d82be4c9e7b5dbf90"],"state_sha256":"c0aad6a358afac8d05b38927ead12abb23bef3f2a3591a8afc87458d58a75f36"}