{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7UBO3HIMAA2A4IIL3AIE6UO6W4","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":"ced40711261a3dabc6e5417578453f0050299437886c1ab56d5ddca0c5c30cc8","cross_cats_sorted":["math.CT","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-24T17:22:09Z","title_canon_sha256":"b87ef229b84fafee87a99cb554b3c47689155a4138d12f19cfb579f51628fc0b"},"schema_version":"1.0","source":{"id":"1810.10503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10503","created_at":"2026-05-18T00:02:22Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10503v1","created_at":"2026-05-18T00:02:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10503","created_at":"2026-05-18T00:02:22Z"},{"alias_kind":"pith_short_12","alias_value":"7UBO3HIMAA2A","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7UBO3HIMAA2A4IIL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7UBO3HIM","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:9a239f49d07244dca3bc1383c1a121659daf6942a3b1a88ab1ad8683b9066c7b","target":"graph","created_at":"2026-05-18T00:02:22Z","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 set up foundations of representation theory over $S$, the sphere spectrum, which is the `initial ring' of stable homotopy theory. In particular, we treat $S$-Lie algebras and their representations, characters, $gl_n(S)$-Verma modules and their duals, Harish-Chandra pairs and Zuckermann functors. As an application, we construct a Khovanov $sl_k$-stable homotopy type with a large prime hypothesis, which is a new link invariant, using a stable homotopy analogue of the method of J.Sussan.","authors_text":"Igor Kriz, Petr Somberg, Po Hu","cross_cats":["math.CT","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-24T17:22:09Z","title":"Derived representation theory of Lie algebras and stable homotopy categorification of $sl_k$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10503","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":"sha256:9c6bea5ccae394b0e1ff1f5f53ea80951ccf34446ac976d9627e81d23606de3b","target":"record","created_at":"2026-05-18T00:02:22Z","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":"ced40711261a3dabc6e5417578453f0050299437886c1ab56d5ddca0c5c30cc8","cross_cats_sorted":["math.CT","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-10-24T17:22:09Z","title_canon_sha256":"b87ef229b84fafee87a99cb554b3c47689155a4138d12f19cfb579f51628fc0b"},"schema_version":"1.0","source":{"id":"1810.10503","kind":"arxiv","version":1}},"canonical_sha256":"fd02ed9d0c00340e210bd8104f51deb70f2d3bcf9c47f7054b92b223b266cb2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd02ed9d0c00340e210bd8104f51deb70f2d3bcf9c47f7054b92b223b266cb2a","first_computed_at":"2026-05-18T00:02:22.904049Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:22.904049Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mPh5J/ktxghk2Qyp12T82B4W2V+bfH6LsZ0pyBqcSITA5e32ZkECpXA09MlLswAc/HjuQJeu2EKKHQhypXF0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:22.904697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c6bea5ccae394b0e1ff1f5f53ea80951ccf34446ac976d9627e81d23606de3b","sha256:9a239f49d07244dca3bc1383c1a121659daf6942a3b1a88ab1ad8683b9066c7b"],"state_sha256":"6a0b215abc4a6274ef8c1866de69bfb4b585644c9f0f34a112bd0f7fc407d8d9"}