{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:H7LDQNTH3E7IT5MXWEQIC3DIBK","short_pith_number":"pith:H7LDQNTH","schema_version":"1.0","canonical_sha256":"3fd6383667d93e89f597b120816c680ab9faeea7ab405f05cbffe1342d101fb4","source":{"kind":"arxiv","id":"2605.20736","version":1},"attestation_state":"computed","paper":{"title":"Addition Theorems for Real Vector Spherical Harmonics and Explicit Matrix Representations of the Quasi-Periodic Elastic Single Layer Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"primary_cat":"math.AP","authors_text":"Xin Feng","submitted_at":"2026-05-20T05:41:57Z","abstract_excerpt":"This paper develops a multipole expansion method for the quasi-periodic elastic single layer potential $\\mathcal{S}_D^{\\alpha,0}$ associated with the Kelvin tensor in one-dimensional periodic arrays. A key step in this approach is the derivation of translation addition theorems for the real vector spherical harmonics $V_{lm}$, $W_{lm}$, and $X_{lm}$. These addition theorems enable the exact calculation of all matrix entries of $\\mathcal{S}_D^{\\alpha,0}$ in closed form. By working entirely within the spherical harmonic basis, the proposed analytical method overcomes the poor convergence and mes"},"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":"2605.20736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-20T05:41:57Z","cross_cats_sorted":["cs.NA","math-ph","math.MP","math.NA"],"title_canon_sha256":"57b9c3523578ea77438bcfc252f3dcf6f9b34c0fc0a374e47208f6324a2ed5d4","abstract_canon_sha256":"a557a06b4304a6f94f239161ff47e0aa54feae61387495bf925b88d84696002f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:51.406584Z","signature_b64":"jEPVvNPm2b/u9AJHEjs++LkXlSAJASGX/n09oBxs4aYAfAaK9D4CdJksgOI9A39hV1HgSSWdkdo1CA0N7j52AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fd6383667d93e89f597b120816c680ab9faeea7ab405f05cbffe1342d101fb4","last_reissued_at":"2026-05-21T01:04:51.405861Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:51.405861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Addition Theorems for Real Vector Spherical Harmonics and Explicit Matrix Representations of the Quasi-Periodic Elastic Single Layer Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math-ph","math.MP","math.NA"],"primary_cat":"math.AP","authors_text":"Xin Feng","submitted_at":"2026-05-20T05:41:57Z","abstract_excerpt":"This paper develops a multipole expansion method for the quasi-periodic elastic single layer potential $\\mathcal{S}_D^{\\alpha,0}$ associated with the Kelvin tensor in one-dimensional periodic arrays. A key step in this approach is the derivation of translation addition theorems for the real vector spherical harmonics $V_{lm}$, $W_{lm}$, and $X_{lm}$. These addition theorems enable the exact calculation of all matrix entries of $\\mathcal{S}_D^{\\alpha,0}$ in closed form. By working entirely within the spherical harmonic basis, the proposed analytical method overcomes the poor convergence and mes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20736","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20736/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2605.20736","created_at":"2026-05-21T01:04:51.405989+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20736v1","created_at":"2026-05-21T01:04:51.405989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20736","created_at":"2026-05-21T01:04:51.405989+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7LDQNTH3E7I","created_at":"2026-05-21T01:04:51.405989+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7LDQNTH3E7IT5MX","created_at":"2026-05-21T01:04:51.405989+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7LDQNTH","created_at":"2026-05-21T01:04:51.405989+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/H7LDQNTH3E7IT5MXWEQIC3DIBK","json":"https://pith.science/pith/H7LDQNTH3E7IT5MXWEQIC3DIBK.json","graph_json":"https://pith.science/api/pith-number/H7LDQNTH3E7IT5MXWEQIC3DIBK/graph.json","events_json":"https://pith.science/api/pith-number/H7LDQNTH3E7IT5MXWEQIC3DIBK/events.json","paper":"https://pith.science/paper/H7LDQNTH"},"agent_actions":{"view_html":"https://pith.science/pith/H7LDQNTH3E7IT5MXWEQIC3DIBK","download_json":"https://pith.science/pith/H7LDQNTH3E7IT5MXWEQIC3DIBK.json","view_paper":"https://pith.science/paper/H7LDQNTH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20736&json=true","fetch_graph":"https://pith.science/api/pith-number/H7LDQNTH3E7IT5MXWEQIC3DIBK/graph.json","fetch_events":"https://pith.science/api/pith-number/H7LDQNTH3E7IT5MXWEQIC3DIBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7LDQNTH3E7IT5MXWEQIC3DIBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7LDQNTH3E7IT5MXWEQIC3DIBK/action/storage_attestation","attest_author":"https://pith.science/pith/H7LDQNTH3E7IT5MXWEQIC3DIBK/action/author_attestation","sign_citation":"https://pith.science/pith/H7LDQNTH3E7IT5MXWEQIC3DIBK/action/citation_signature","submit_replication":"https://pith.science/pith/H7LDQNTH3E7IT5MXWEQIC3DIBK/action/replication_record"}},"created_at":"2026-05-21T01:04:51.405989+00:00","updated_at":"2026-05-21T01:04:51.405989+00:00"}