{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:47KGCOIIW5O3N7XY2CNQXJZOHH","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":"96b326b6698aed9fa686f7f20fa732630b74430b1dccd19ffbdf738b68173837","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-10T08:24:51Z","title_canon_sha256":"17861c59e918b324416b551852d88a91604d6de0938a50c4ce09e9f96f07e7df"},"schema_version":"1.0","source":{"id":"1309.2407","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2407","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2407v1","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2407","created_at":"2026-05-18T01:47:43Z"},{"alias_kind":"pith_short_12","alias_value":"47KGCOIIW5O3","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"47KGCOIIW5O3N7XY","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"47KGCOII","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:a568dee0b5da8bbd0ca05af242696c2afaf4862752a7ac54c66f7c8752883e32","target":"graph","created_at":"2026-05-18T01:47:43Z","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":"When we consider a differential equation $\\Delta=0$ whose set of solutions is ${{\\cal S}}_\\Delta$, a Lie-point exact symmetry of this is a Lie-point invertible transformation $T$ such that $T({{\\cal S}}_\\Delta)={{\\cal S}}_\\Delta$, i.e. such that any solution to $\\Delta=0$ is tranformed into a (generally, different) solution to the same equation; here we define {\\it partial} symmetries of $\\Delta=0$ as Lie-point invertible transformations $T$ such that there is a nonempty subset ${{\\cal P}} \\subset {{\\cal S}}_\\Delta$ such that $T({{\\cal P}}) = {{\\cal P}}$, i.e. such that there is a subset of so","authors_text":"G. Cicogna, G. Gaeta","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-10T08:24:51Z","title":"Partial Lie-point symmetries of differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2407","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":"sha256:5798be7a7e90ee63e31d79570545ff7f563d63a64d34b51854427e31e03c79ca","target":"record","created_at":"2026-05-18T01:47:43Z","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":"96b326b6698aed9fa686f7f20fa732630b74430b1dccd19ffbdf738b68173837","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-10T08:24:51Z","title_canon_sha256":"17861c59e918b324416b551852d88a91604d6de0938a50c4ce09e9f96f07e7df"},"schema_version":"1.0","source":{"id":"1309.2407","kind":"arxiv","version":1}},"canonical_sha256":"e7d4613908b75db6fef8d09b0ba72e39ecda231ccaf22be4e677fd5fde8303ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7d4613908b75db6fef8d09b0ba72e39ecda231ccaf22be4e677fd5fde8303ee","first_computed_at":"2026-05-18T01:47:43.874731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:47:43.874731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+8UE5cEYW9Ameqq+HXGPW3a44bbRfxqVRoMMAR2MkWfteV1mNiili9mRHjD20F4vgzngyFN3xJy33dEcR7qZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:47:43.875244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2407","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5798be7a7e90ee63e31d79570545ff7f563d63a64d34b51854427e31e03c79ca","sha256:a568dee0b5da8bbd0ca05af242696c2afaf4862752a7ac54c66f7c8752883e32"],"state_sha256":"e9bd41aa30401f561a2cbf1ceee0a9ac6a95cabfd6701fae4e5c2a6de050f7b3"}