{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:P3DMMOGIOLNNMGOUTL2D3DFL2O","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":"6a5a591d63633d5e4ffe0c7ec07e58d1923d0478193e35315786998a46247a49","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-06-13T07:11:38Z","title_canon_sha256":"d7acf7a2f67e5acea288ebaf7b827663676e4c2febe26c4b70d1acac6161c5b3"},"schema_version":"1.0","source":{"id":"2306.07582","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.07582","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"2306.07582v4","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.07582","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"P3DMMOGIOLNN","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_16","alias_value":"P3DMMOGIOLNNMGOU","created_at":"2026-06-19T16:11:07Z"},{"alias_kind":"pith_short_8","alias_value":"P3DMMOGI","created_at":"2026-06-19T16:11:07Z"}],"graph_snapshots":[{"event_id":"sha256:7665035107132f142d89a697d7684bb5882914b5cb7b2f5e124521d25e3a196d","target":"graph","created_at":"2026-06-19T16:11:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2306.07582/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f$ be a primitive form of weight $2k+j-2$ for $SL_2(Z)$, and let $P$ be a prime ideal of the Hecke field of $f$. We denote by $Sp_m(Z)$ the Siegel modular group of degree $m$. Suppose that $k$ is congruent to $0$ modulo $4$, $j$ is congruent to $0$ modulo $4$, and that $P$ divides the algebraic part of $L(k+j,f)$. Put ${\\bf k}=(k+j/2,k+j/2,j/2+4,j/2+4)$. Then under certain easily checkable conditions, we prove that there exists a Hecke eigenform $F$ in the space of modular forms of weight $(k+j,k)$ for $Sp_2(Z)$ such that $[I_2(f)]^{\\bf k}$ is congruent to $A^{(I)}_4(F)$ modulo $P$. Here,","authors_text":"Hidenori Katsurada, Hiraku Atobe, Masataka Chida, Takuya Yamauchi, Tomoyoshi Ibukiyama","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-06-13T07:11:38Z","title":"Harder's conjecture II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07582","kind":"arxiv","version":4},"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:b15969c3a93ce2948399eaf22da54fcb25e1fee9bb0dff02cac834adc97bc9e2","target":"record","created_at":"2026-06-19T16:11:07Z","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":"6a5a591d63633d5e4ffe0c7ec07e58d1923d0478193e35315786998a46247a49","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2023-06-13T07:11:38Z","title_canon_sha256":"d7acf7a2f67e5acea288ebaf7b827663676e4c2febe26c4b70d1acac6161c5b3"},"schema_version":"1.0","source":{"id":"2306.07582","kind":"arxiv","version":4}},"canonical_sha256":"7ec6c638c872dad619d49af43d8cabd3ac19b801f2fa07d5b36a50b5ae4d8501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ec6c638c872dad619d49af43d8cabd3ac19b801f2fa07d5b36a50b5ae4d8501","first_computed_at":"2026-06-19T16:11:07.619263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:07.619263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wRGemmWsLH57/q9UJU+oDG4jFM8naS7c7ezVOwV/9S66PbIrlMnIWxcUyqaxPKPp24xFoAwD+wop1aXcs7BNBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:07.619646Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.07582","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b15969c3a93ce2948399eaf22da54fcb25e1fee9bb0dff02cac834adc97bc9e2","sha256:7665035107132f142d89a697d7684bb5882914b5cb7b2f5e124521d25e3a196d"],"state_sha256":"be0f0f658ad272ef6b5dd20b2b730d7dcdf671e83f91deb41b347a1a079331dc"}