{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RXEXMI4XESOROTKDU3FFRA4KBS","short_pith_number":"pith:RXEXMI4X","schema_version":"1.0","canonical_sha256":"8dc9762397249d174d43a6ca58838a0c9b4c220102ca387151dd146e463391a1","source":{"kind":"arxiv","id":"1809.10004","version":2},"attestation_state":"computed","paper":{"title":"Rank--two Euler systems for symmetric squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonio Lei, K\\^az{\\i}m B\\\"uy\\\"ukboduk","submitted_at":"2018-09-26T14:04:06Z","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 $p$."},"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":"1809.10004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-26T14:04:06Z","cross_cats_sorted":[],"title_canon_sha256":"fc764a1ad0260a7f3d06b1eb3c9e93fa9d00b53a76debda7ed9812b5c06218a9","abstract_canon_sha256":"81c256c96459efa40343290be75fd0fdb11b21826970fc51b99ec56ba470dbfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:30.184261Z","signature_b64":"2vZSqcUyqm8c6tlXGQeqaNv9YnrTaBI9d/bFjfY6A8OGXM/HwMA8sdOzkk9wAgB0EzHWriFw0bhHYyFczfYMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dc9762397249d174d43a6ca58838a0c9b4c220102ca387151dd146e463391a1","last_reissued_at":"2026-05-17T23:44:30.183569Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:30.183569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank--two Euler systems for symmetric squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonio Lei, K\\^az{\\i}m B\\\"uy\\\"ukboduk","submitted_at":"2018-09-26T14:04:06Z","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 $p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10004","kind":"arxiv","version":2},"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":"1809.10004","created_at":"2026-05-17T23:44:30.183678+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.10004v2","created_at":"2026-05-17T23:44:30.183678+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10004","created_at":"2026-05-17T23:44:30.183678+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXEXMI4XESOR","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXEXMI4XESOROTKD","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXEXMI4X","created_at":"2026-05-18T12:32:50.500415+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/RXEXMI4XESOROTKDU3FFRA4KBS","json":"https://pith.science/pith/RXEXMI4XESOROTKDU3FFRA4KBS.json","graph_json":"https://pith.science/api/pith-number/RXEXMI4XESOROTKDU3FFRA4KBS/graph.json","events_json":"https://pith.science/api/pith-number/RXEXMI4XESOROTKDU3FFRA4KBS/events.json","paper":"https://pith.science/paper/RXEXMI4X"},"agent_actions":{"view_html":"https://pith.science/pith/RXEXMI4XESOROTKDU3FFRA4KBS","download_json":"https://pith.science/pith/RXEXMI4XESOROTKDU3FFRA4KBS.json","view_paper":"https://pith.science/paper/RXEXMI4X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.10004&json=true","fetch_graph":"https://pith.science/api/pith-number/RXEXMI4XESOROTKDU3FFRA4KBS/graph.json","fetch_events":"https://pith.science/api/pith-number/RXEXMI4XESOROTKDU3FFRA4KBS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXEXMI4XESOROTKDU3FFRA4KBS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXEXMI4XESOROTKDU3FFRA4KBS/action/storage_attestation","attest_author":"https://pith.science/pith/RXEXMI4XESOROTKDU3FFRA4KBS/action/author_attestation","sign_citation":"https://pith.science/pith/RXEXMI4XESOROTKDU3FFRA4KBS/action/citation_signature","submit_replication":"https://pith.science/pith/RXEXMI4XESOROTKDU3FFRA4KBS/action/replication_record"}},"created_at":"2026-05-17T23:44:30.183678+00:00","updated_at":"2026-05-17T23:44:30.183678+00:00"}