{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RXEXMI4XESOROTKDU3FFRA4KBS","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":"81c256c96459efa40343290be75fd0fdb11b21826970fc51b99ec56ba470dbfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-26T14:04:06Z","title_canon_sha256":"fc764a1ad0260a7f3d06b1eb3c9e93fa9d00b53a76debda7ed9812b5c06218a9"},"schema_version":"1.0","source":{"id":"1809.10004","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10004","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10004v2","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10004","created_at":"2026-05-17T23:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"RXEXMI4XESOR","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RXEXMI4XESOROTKD","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RXEXMI4X","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:b1aa067aae3338f643d9947fff7abb9a50dcf5139e9cb2117c99f70c43144d6c","target":"graph","created_at":"2026-05-17T23:44:30Z","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":"Let $p\\ge 7$ be a prime number and $f$ a normalized eigen-newform with good reduction at $p$ such that its $p$-th Fourier coefficient vanishes. We construct a rank-two Euler system attached to the $p$-adic realization of the symmetric square motive of $f$. Furthermore, we show that the non-triviality is guaranteed by the non-vanishing of the leading term of the relevant $L$-value and the non-vanishing of a certain $p$-adic period modulo $p$.","authors_text":"Antonio Lei, K\\^az{\\i}m B\\\"uy\\\"ukboduk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-26T14:04:06Z","title":"Rank--two Euler systems for symmetric squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10004","kind":"arxiv","version":2},"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":"sha256:417a886c510a2de9c80560ea585cb60e388225aa11621b5674c25660709cd13c","target":"record","created_at":"2026-05-17T23:44:30Z","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":"81c256c96459efa40343290be75fd0fdb11b21826970fc51b99ec56ba470dbfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-26T14:04:06Z","title_canon_sha256":"fc764a1ad0260a7f3d06b1eb3c9e93fa9d00b53a76debda7ed9812b5c06218a9"},"schema_version":"1.0","source":{"id":"1809.10004","kind":"arxiv","version":2}},"canonical_sha256":"8dc9762397249d174d43a6ca58838a0c9b4c220102ca387151dd146e463391a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dc9762397249d174d43a6ca58838a0c9b4c220102ca387151dd146e463391a1","first_computed_at":"2026-05-17T23:44:30.183569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:30.183569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2vZSqcUyqm8c6tlXGQeqaNv9YnrTaBI9d/bFjfY6A8OGXM/HwMA8sdOzkk9wAgB0EzHWriFw0bhHYyFczfYMBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:30.184261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10004","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:417a886c510a2de9c80560ea585cb60e388225aa11621b5674c25660709cd13c","sha256:b1aa067aae3338f643d9947fff7abb9a50dcf5139e9cb2117c99f70c43144d6c"],"state_sha256":"3a177ba8da986b7e78c8ec8d334b9c707d0b2171ae28454a5d1fd386607ae861"}