{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:EAVJV7FIHXOWD4X5MBBNESJ6F2","short_pith_number":"pith:EAVJV7FI","schema_version":"1.0","canonical_sha256":"202a9afca83ddd61f2fd6042d2493e2e9201ba4fc62412cf2600dea1b8540bdb","source":{"kind":"arxiv","id":"1310.7084","version":1},"attestation_state":"computed","paper":{"title":"The reduction of Laplace equation in certain Riemannian spaces and the resulting Type II hidden symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Andronikos Paliathanasis, Michael Tsamparlis","submitted_at":"2013-10-26T08:51:20Z","abstract_excerpt":"We prove a general theorem which allows the determination of Lie symmetries of Laplace equation in a general Riemannian space using the conformal group of the space. Algebraic computing is not necessary. We apply the theorem in the study of the reduction of Laplace equation in certain classes of Riemannian spaces which admit a gradient Killing vector, a gradient Homothetic vector and a special Conformal Killing vector. In each reduction we identify the source of Type II hidden symmetries. We find that in general the Type II hidden symmetries of Laplace equation are directly related to the tran"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.7084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-26T08:51:20Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"326af0ed2106e0e4d34b2f9da2ff36ab65dd4231ecf88ebf7a9d3715a757b3e9","abstract_canon_sha256":"ec3132983d4a22e363f013b7f2e7f6760f8c6500c77bd528d77dc18707fa965f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:32.802959Z","signature_b64":"B3NRcnAnwpAhc6jm5gs61Dk2t4g2AFEHU9zadnk1bnoYJhUZsR+2MW5OP5xODVd1h/LyvSkXwPdSQgJCGXp4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"202a9afca83ddd61f2fd6042d2493e2e9201ba4fc62412cf2600dea1b8540bdb","last_reissued_at":"2026-05-18T02:25:32.802555Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:32.802555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The reduction of Laplace equation in certain Riemannian spaces and the resulting Type II hidden symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Andronikos Paliathanasis, Michael Tsamparlis","submitted_at":"2013-10-26T08:51:20Z","abstract_excerpt":"We prove a general theorem which allows the determination of Lie symmetries of Laplace equation in a general Riemannian space using the conformal group of the space. Algebraic computing is not necessary. We apply the theorem in the study of the reduction of Laplace equation in certain classes of Riemannian spaces which admit a gradient Killing vector, a gradient Homothetic vector and a special Conformal Killing vector. In each reduction we identify the source of Type II hidden symmetries. We find that in general the Type II hidden symmetries of Laplace equation are directly related to the tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7084","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.7084","created_at":"2026-05-18T02:25:32.802627+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.7084v1","created_at":"2026-05-18T02:25:32.802627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7084","created_at":"2026-05-18T02:25:32.802627+00:00"},{"alias_kind":"pith_short_12","alias_value":"EAVJV7FIHXOW","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EAVJV7FIHXOWD4X5","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EAVJV7FI","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2","json":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2.json","graph_json":"https://pith.science/api/pith-number/EAVJV7FIHXOWD4X5MBBNESJ6F2/graph.json","events_json":"https://pith.science/api/pith-number/EAVJV7FIHXOWD4X5MBBNESJ6F2/events.json","paper":"https://pith.science/paper/EAVJV7FI"},"agent_actions":{"view_html":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2","download_json":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2.json","view_paper":"https://pith.science/paper/EAVJV7FI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.7084&json=true","fetch_graph":"https://pith.science/api/pith-number/EAVJV7FIHXOWD4X5MBBNESJ6F2/graph.json","fetch_events":"https://pith.science/api/pith-number/EAVJV7FIHXOWD4X5MBBNESJ6F2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2/action/storage_attestation","attest_author":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2/action/author_attestation","sign_citation":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2/action/citation_signature","submit_replication":"https://pith.science/pith/EAVJV7FIHXOWD4X5MBBNESJ6F2/action/replication_record"}},"created_at":"2026-05-18T02:25:32.802627+00:00","updated_at":"2026-05-18T02:25:32.802627+00:00"}