{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HJ5QUZU7E57CSQNZOGZM3OMGFB","short_pith_number":"pith:HJ5QUZU7","schema_version":"1.0","canonical_sha256":"3a7b0a669f277e2941b971b2cdb986284b7d04ffde054306481b3d9a07f1553b","source":{"kind":"arxiv","id":"1511.07142","version":3},"attestation_state":"computed","paper":{"title":"Killing vectors of FLRW metric (in comoving coordinates) and zero modes of the scalar Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Harini Desiraju, N. D. Hari Dass","submitted_at":"2015-11-23T09:06:00Z","abstract_excerpt":"Based on an examination of the solutions to the Killing Vector equations for the FLRW-metric in co moving coordinates , it is conjectured and proved that the components(in these coordinates) of Killing Vectors, when suitably scaled by functions, are \\emph{zero modes} of the corresponding \\emph{scalar} Laplacian. The complete such set of zero modes(infinitely many) are explicitly constructed for the two-sphere. They are parametrised by an integer n. For $n\\,\\ge\\,2$, all the solutions are \\emph{irregular} (in the sense that they are neither well defined everywhere nor are \\emph{square-integrable"},"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":"1511.07142","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-11-23T09:06:00Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"99781b11a63a9175323180896dcc807c76795280edc15dea569765e1a589a68d","abstract_canon_sha256":"2aa26b6c2aafbcafbaa51ed5f42e254bc8459e54513353acf4e462102761f545"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:57.121836Z","signature_b64":"FNBHRdDyiQQU80JwtXpoHM1Genk8hIZ2zrIVSZExDvLASqNgaD6Kuvejf9qTn5jdZHxkOQ37mmyIFYYaz5vqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a7b0a669f277e2941b971b2cdb986284b7d04ffde054306481b3d9a07f1553b","last_reissued_at":"2026-05-18T01:19:57.121137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:57.121137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Killing vectors of FLRW metric (in comoving coordinates) and zero modes of the scalar Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Harini Desiraju, N. D. Hari Dass","submitted_at":"2015-11-23T09:06:00Z","abstract_excerpt":"Based on an examination of the solutions to the Killing Vector equations for the FLRW-metric in co moving coordinates , it is conjectured and proved that the components(in these coordinates) of Killing Vectors, when suitably scaled by functions, are \\emph{zero modes} of the corresponding \\emph{scalar} Laplacian. The complete such set of zero modes(infinitely many) are explicitly constructed for the two-sphere. They are parametrised by an integer n. For $n\\,\\ge\\,2$, all the solutions are \\emph{irregular} (in the sense that they are neither well defined everywhere nor are \\emph{square-integrable"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07142","kind":"arxiv","version":3},"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":"1511.07142","created_at":"2026-05-18T01:19:57.121234+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.07142v3","created_at":"2026-05-18T01:19:57.121234+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07142","created_at":"2026-05-18T01:19:57.121234+00:00"},{"alias_kind":"pith_short_12","alias_value":"HJ5QUZU7E57C","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HJ5QUZU7E57CSQNZ","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HJ5QUZU7","created_at":"2026-05-18T12:29:25.134429+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/HJ5QUZU7E57CSQNZOGZM3OMGFB","json":"https://pith.science/pith/HJ5QUZU7E57CSQNZOGZM3OMGFB.json","graph_json":"https://pith.science/api/pith-number/HJ5QUZU7E57CSQNZOGZM3OMGFB/graph.json","events_json":"https://pith.science/api/pith-number/HJ5QUZU7E57CSQNZOGZM3OMGFB/events.json","paper":"https://pith.science/paper/HJ5QUZU7"},"agent_actions":{"view_html":"https://pith.science/pith/HJ5QUZU7E57CSQNZOGZM3OMGFB","download_json":"https://pith.science/pith/HJ5QUZU7E57CSQNZOGZM3OMGFB.json","view_paper":"https://pith.science/paper/HJ5QUZU7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.07142&json=true","fetch_graph":"https://pith.science/api/pith-number/HJ5QUZU7E57CSQNZOGZM3OMGFB/graph.json","fetch_events":"https://pith.science/api/pith-number/HJ5QUZU7E57CSQNZOGZM3OMGFB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HJ5QUZU7E57CSQNZOGZM3OMGFB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HJ5QUZU7E57CSQNZOGZM3OMGFB/action/storage_attestation","attest_author":"https://pith.science/pith/HJ5QUZU7E57CSQNZOGZM3OMGFB/action/author_attestation","sign_citation":"https://pith.science/pith/HJ5QUZU7E57CSQNZOGZM3OMGFB/action/citation_signature","submit_replication":"https://pith.science/pith/HJ5QUZU7E57CSQNZOGZM3OMGFB/action/replication_record"}},"created_at":"2026-05-18T01:19:57.121234+00:00","updated_at":"2026-05-18T01:19:57.121234+00:00"}