{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DJWSN4DOTGGWV4LQ7H7SF233LK","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":"1d08bb0b04f87535d2ee2403d41f71962a64a65358c6a186de5c6b19d049bca6","cross_cats_sorted":["math.AT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-05T17:12:24Z","title_canon_sha256":"10bb1c8376788ab4aa60dc06ae064f228904ef3cc823a726884cb728f1895c4b"},"schema_version":"1.0","source":{"id":"1904.03162","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03162","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03162v2","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03162","created_at":"2026-05-17T23:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"DJWSN4DOTGGW","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DJWSN4DOTGGWV4LQ","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DJWSN4DO","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:7a2b7fd49520b953df4320c5f7e68c05ad095e5df7bec67b2c706f0ac489151c","target":"graph","created_at":"2026-05-17T23:48:04Z","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 develop a basic theory of affine group dg-schemes, their Lie algebraic counterparts and linear representations. We prove Tannaka type reconstruction theorems that an affine group dg-scheme can be recovered from the dg-tensor category of its linear representations as well as from the rigid dg-tensor category of its finite dimensional linear representations along with the forgetful functors to the underlying dg-tensor category of cochain complexes.","authors_text":"Jaehyeok Lee, Jae-Suk Park","cross_cats":["math.AT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-05T17:12:24Z","title":"Affine group dg-schemes and linear representations I - Basic theory and Tannakian reconstructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03162","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:eb15e074556c83e4eb6a1f4c63f28f68bd6e02309cfd857f5f51a206d88cb6fd","target":"record","created_at":"2026-05-17T23:48:04Z","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":"1d08bb0b04f87535d2ee2403d41f71962a64a65358c6a186de5c6b19d049bca6","cross_cats_sorted":["math.AT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-05T17:12:24Z","title_canon_sha256":"10bb1c8376788ab4aa60dc06ae064f228904ef3cc823a726884cb728f1895c4b"},"schema_version":"1.0","source":{"id":"1904.03162","kind":"arxiv","version":2}},"canonical_sha256":"1a6d26f06e998d6af170f9ff22eb7b5a8dd3dac9387e5f0cb0958461f5ce6b33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a6d26f06e998d6af170f9ff22eb7b5a8dd3dac9387e5f0cb0958461f5ce6b33","first_computed_at":"2026-05-17T23:48:04.417388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:04.417388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pK24uAww1akxrw3+5yW/rYzCWysgT1wHSUF4YJ+m79nXvHNcOBYEpRY4iTM+TgWn2mhU2hzL2Z43N4DLxPtNBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:04.417835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03162","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb15e074556c83e4eb6a1f4c63f28f68bd6e02309cfd857f5f51a206d88cb6fd","sha256:7a2b7fd49520b953df4320c5f7e68c05ad095e5df7bec67b2c706f0ac489151c"],"state_sha256":"c3a0d144160a96776706c820576d0c02ccef9748bf08c23ee6de15404bf92617"}