{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZYBJIUDRHW6ZTXFOX5OZNI4BTS","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":"4eee08b5f716e4657b49fc42d7303a9edd27433cbd8e2f834ca94f4c9f683d41","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-07T11:44:45Z","title_canon_sha256":"c048261f05deda912e3a9812ed8b26e90d712804e7f07bee8218178265f5fd3f"},"schema_version":"1.0","source":{"id":"1012.1477","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.1477","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"arxiv_version","alias_value":"1012.1477v2","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.1477","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZYBJIUDRHW6Z","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZYBJIUDRHW6ZTXFO","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZYBJIUDR","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:b46bd64acb05a6f3c5f5f18431a4de75aefb11679a4555df1b633e72fd80116b","target":"graph","created_at":"2026-05-18T03:07:41Z","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":"The moduli space of twisted stable maps into the stack $B(\\Z/m\\Z)^2$ carries a natural $S_n$-action and so its cohomology may be decomposed into irreducible $S_n$-representations. Working over $\\Spec \\Z[1/m]$ we show that the alternating part of the cohomology of one of its connected components is exactly the cohomology associated to cusp forms for $\\Gamma(m)$. In particular this offers an alternative to Scholl's construction of the Chow motive associated to such cusp forms. This answers in the affirmative a question of Manin on whether one can replace the Kuga-Sato varieties used by Scholl wi","authors_text":"Dan Petersen","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-07T11:44:45Z","title":"Cusp form motives and admissible $G$-covers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1477","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:b53f0c7a1c509b22ee2504176b73b32ccb3093fec1615c79e8a3d48ea9f15efe","target":"record","created_at":"2026-05-18T03:07:41Z","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":"4eee08b5f716e4657b49fc42d7303a9edd27433cbd8e2f834ca94f4c9f683d41","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-12-07T11:44:45Z","title_canon_sha256":"c048261f05deda912e3a9812ed8b26e90d712804e7f07bee8218178265f5fd3f"},"schema_version":"1.0","source":{"id":"1012.1477","kind":"arxiv","version":2}},"canonical_sha256":"ce029450713dbd99dcaebf5d96a3819c91f9d63a3626eab2d08b0ee97f63b0a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce029450713dbd99dcaebf5d96a3819c91f9d63a3626eab2d08b0ee97f63b0a3","first_computed_at":"2026-05-18T03:07:41.570672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:41.570672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TaAtzjT2QmDAR6rh4BnadovnTnHqpo2kyGDSPFKy9d/utH9Od7mo5UnDA6DrPY3oH+IXnOWhAcUhQMFk1LbPCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:41.571166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.1477","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b53f0c7a1c509b22ee2504176b73b32ccb3093fec1615c79e8a3d48ea9f15efe","sha256:b46bd64acb05a6f3c5f5f18431a4de75aefb11679a4555df1b633e72fd80116b"],"state_sha256":"8f0015abfcbf92c899e232f0c4277f74f79a902de5954fd8be0e8c2f8f4c4391"}