{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6VVGW5SHC7BG6H5AEDO2FUYQCF","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":"f654c05130c32a3fd548a99761517d860ad29e5f5c29b8a11dde2cd4f34553ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-10T01:43:53Z","title_canon_sha256":"6ef923623303b26e8d611c73aaba378921640df75648246df2f4810910307cd6"},"schema_version":"1.0","source":{"id":"1706.03166","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03166","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03166v1","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03166","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"6VVGW5SHC7BG","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6VVGW5SHC7BG6H5A","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6VVGW5SH","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:19be8a2818831dcfc1d833578205cf79fedfd0ae5c5de8871c64739f47bee40b","target":"graph","created_at":"2026-05-18T00:42:38Z","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":"In this paper, we provide combinatorial proofs for certain partition identities which arise naturally in the context of Langlands' beyond endoscopy proposal. These partition identities motivate an explicit plethysm expansion of $\\mathrm{Sym}^j(\\mathrm{Sym}^kV)$ for $\\mathrm{GL}_2$ in the case $k=3$. We compute the plethysm explicitly for the cases $k=3, 4$. Moreover, we use these expansions to explicitly compute the basic function attached to the symmetric power $L$-function of $\\mathrm{GL}_2$ for these two cases.","authors_text":"Eunsung Lim, Heekyoung Hahn, Jaebum Sohn, JiSun Huh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-10T01:43:53Z","title":"From partition identities to a combinatorial approach to explicit Satake inversion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03166","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:fff420db0389e08a9dbb7d7946549b2149edf0131bb94d0e43f5ef5389180254","target":"record","created_at":"2026-05-18T00:42:38Z","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":"f654c05130c32a3fd548a99761517d860ad29e5f5c29b8a11dde2cd4f34553ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-10T01:43:53Z","title_canon_sha256":"6ef923623303b26e8d611c73aaba378921640df75648246df2f4810910307cd6"},"schema_version":"1.0","source":{"id":"1706.03166","kind":"arxiv","version":1}},"canonical_sha256":"f56a6b764717c26f1fa020dda2d31011439311230cc886a7c370327a8fa04fe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f56a6b764717c26f1fa020dda2d31011439311230cc886a7c370327a8fa04fe5","first_computed_at":"2026-05-18T00:42:38.309925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:38.309925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4+ocpj44PXDeJ/Apodze4A0xDATQ8mHfMDPEgFcxJmAkLMxz+98mTduiKdSL3rUAWSI89WPMNvBH2Vprr0vpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:38.310642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03166","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fff420db0389e08a9dbb7d7946549b2149edf0131bb94d0e43f5ef5389180254","sha256:19be8a2818831dcfc1d833578205cf79fedfd0ae5c5de8871c64739f47bee40b"],"state_sha256":"e12a3b81290a49d7782915788767f93a5e64745793168e3fc8bbd3bda0f3b745"}