{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QPHPLVWRVQJ5MGIGUPLODHQTJU","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":"9928316f5933e83d36729872888988c98582881488939d531f17b04bd67cdf1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-11T22:52:46Z","title_canon_sha256":"ee46e44aefc0a54994c80ac23ee67fb1c9e987c01de4badebea5ae40edcef5c4"},"schema_version":"1.0","source":{"id":"1706.03417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03417","created_at":"2026-05-18T00:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03417v1","created_at":"2026-05-18T00:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03417","created_at":"2026-05-18T00:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"QPHPLVWRVQJ5","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QPHPLVWRVQJ5MGIG","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QPHPLVWR","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:275636a354a314501f9ba82cbd26750152836ac1493214720ef150bd37e41005","target":"graph","created_at":"2026-05-18T00:42:35Z","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":"We study the action of the derived Hecke algebra on the space of weight one forms. By analogy with the topological case, we formulate a conjecture relating this to a certain Stark unit.\n  We verify the truth of the conjecture numerically, for the weight one forms of level $23$ and $31$, and many derived Hecke operators at primes less than $200$. Our computation depends in an essential way on Merel's evaluation of the pairing between the Shimura and cuspidal subgroups of $J_0(q)$.","authors_text":"Akshay Venkatesh, Michael Harris","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-11T22:52:46Z","title":"Derived Hecke algebra for weight one forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03417","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":"sha256:7a77d6852eca3ee581bf9d475724e3f3592beddfeb9dee429d0eba6183d21bd7","target":"record","created_at":"2026-05-18T00:42:35Z","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":"9928316f5933e83d36729872888988c98582881488939d531f17b04bd67cdf1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-06-11T22:52:46Z","title_canon_sha256":"ee46e44aefc0a54994c80ac23ee67fb1c9e987c01de4badebea5ae40edcef5c4"},"schema_version":"1.0","source":{"id":"1706.03417","kind":"arxiv","version":1}},"canonical_sha256":"83cef5d6d1ac13d61906a3d6e19e134d1f65d166eee6db10b152c77ebdc3d158","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83cef5d6d1ac13d61906a3d6e19e134d1f65d166eee6db10b152c77ebdc3d158","first_computed_at":"2026-05-18T00:42:35.732102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:35.732102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vGoh2eW7/eODFhuZSqATzrMYeMz26Mz7cSlW/ibcLekV2K7KB3Ay5nJb5PppffElcFZ2eke9o0A39yHk9W98DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:35.732640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a77d6852eca3ee581bf9d475724e3f3592beddfeb9dee429d0eba6183d21bd7","sha256:275636a354a314501f9ba82cbd26750152836ac1493214720ef150bd37e41005"],"state_sha256":"b76bbcf2cca7706e5737254d625ef8d0bc02f8b07a8c4e4c8dc5e10b6fc77f2d"}