{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EFLME6XFR4UTQMNR6VJHRECRM4","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":"ce614936555a227e19b62cc6b6969cdda94542a3f6b243596306ce86730ee329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-04-16T08:24:54Z","title_canon_sha256":"ca85b833ef94bf199207a92ac711bc482b32e7d1bb7ac5a56c8ade8fe75b885c"},"schema_version":"1.0","source":{"id":"1304.4359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4359","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4359v1","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4359","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"EFLME6XFR4UT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EFLME6XFR4UTQMNR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EFLME6XF","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:3582b72853b524369720fe0abcb5582f1b3001ac92ab8811960aad9262b376ff","target":"graph","created_at":"2026-05-18T02:57:24Z","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 consider the application of the theory of symmetries of coupled ordinary differential equations to the case of reparametrisation invariant Lagrangians quadratic in the velocities; such Lagrangians encompass all minisuperspace models. We find that, in order to acquire the maximum number of symmetry generators, one must (a) consider the lapse $N(t)$ among the degrees of freedom and (b) allow the action of the generator on the Lagrangian and/or the equations of motion to produce a multiple of the constraint, rather than strictly zero. The result of this necessary modification of the standard t","authors_text":"N. Dimakis, Petros A. Terzis, T. Christodoulakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-04-16T08:24:54Z","title":"Lie - point and variational symmetries in minisuperspace Einstein's gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4359","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":"sha256:1c0fe2c5fcbc865f2be770b18f81555c74c6f3edb3d915dc3db550acf6647068","target":"record","created_at":"2026-05-18T02:57:24Z","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":"ce614936555a227e19b62cc6b6969cdda94542a3f6b243596306ce86730ee329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-04-16T08:24:54Z","title_canon_sha256":"ca85b833ef94bf199207a92ac711bc482b32e7d1bb7ac5a56c8ade8fe75b885c"},"schema_version":"1.0","source":{"id":"1304.4359","kind":"arxiv","version":1}},"canonical_sha256":"2156c27ae58f293831b1f552789051671be6f9a34b27b9c6d6a56d64eccd9775","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2156c27ae58f293831b1f552789051671be6f9a34b27b9c6d6a56d64eccd9775","first_computed_at":"2026-05-18T02:57:24.016401Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:24.016401Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KMKidOQ3ZyS9a4qbwVRbZmsoOT+ZpzfXJAZtYk5bKds3HP8P3s2NVZrFOeTeg/51hJJjXwaKWzX6p0KuDYwgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:24.016889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c0fe2c5fcbc865f2be770b18f81555c74c6f3edb3d915dc3db550acf6647068","sha256:3582b72853b524369720fe0abcb5582f1b3001ac92ab8811960aad9262b376ff"],"state_sha256":"ceadcf7d53ca6e82f38e23bc9d84cb01119baf84f1660c620d24a33ec356c627"}