{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:OES7UUL2CRVC3HZNNCFUGT2N3D","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":"00f409327a22c993be2a7ad62d901a8c26b143acc5f8356e388a59f44e30d4ca","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.RT","submitted_at":"2006-05-03T19:30:33Z","title_canon_sha256":"02cc576371705503d48118e571999b2a6ed6264bca6757c68a37df84961b7a0e"},"schema_version":"1.0","source":{"id":"math/0605103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605103","created_at":"2026-07-04T14:55:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605103v1","created_at":"2026-07-04T14:55:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605103","created_at":"2026-07-04T14:55:02Z"},{"alias_kind":"pith_short_12","alias_value":"OES7UUL2CRVC","created_at":"2026-07-04T14:55:02Z"},{"alias_kind":"pith_short_16","alias_value":"OES7UUL2CRVC3HZN","created_at":"2026-07-04T14:55:02Z"},{"alias_kind":"pith_short_8","alias_value":"OES7UUL2","created_at":"2026-07-04T14:55:02Z"}],"graph_snapshots":[{"event_id":"sha256:b9106a5379aacb9857c3ff5df6bbfb7bb4d0db1f863c3774fefe388071407c94","target":"graph","created_at":"2026-07-04T14:55:02Z","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/math/0605103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study projective functors (i.e. direct summands of compositions of translations through walls) for parabolic versions of $\\cO$ as well as for integral regular blocks outside the critical hyperplanes in the symmetrizable Kac-Moody case. It turns out that in both situations the functors are completely determined by their restriction to the additive category generated by (the limit of) a `full projective tilting' object. We describe how projective functors in the parabolic setup give rise to an invariant of tangle cobordisms and formulate a conjectural direct connection to Khovanov homology. O","authors_text":"Catharina Stroppel","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"math.RT","submitted_at":"2006-05-03T19:30:33Z","title":"TQFT with corners and tilting functors in the Kac-Moody case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605103","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:ffc2ea86d00e9c3a8279cde6c8d6597f97bcc0bdb1ac542e6fcfc09cb7a29491","target":"record","created_at":"2026-07-04T14:55:02Z","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":"00f409327a22c993be2a7ad62d901a8c26b143acc5f8356e388a59f44e30d4ca","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"math.RT","submitted_at":"2006-05-03T19:30:33Z","title_canon_sha256":"02cc576371705503d48118e571999b2a6ed6264bca6757c68a37df84961b7a0e"},"schema_version":"1.0","source":{"id":"math/0605103","kind":"arxiv","version":1}},"canonical_sha256":"7125fa517a146a2d9f2d688b434f4dd8d9ea9c0356500d899b01add596479934","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7125fa517a146a2d9f2d688b434f4dd8d9ea9c0356500d899b01add596479934","first_computed_at":"2026-07-04T14:55:02.053348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:55:02.053348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9BnJjW2DBOlggKkCb0OhQ+ug+T2eq6FCKaz4ADGJvl3OlfNA9bRsJvbR1uAsXIiZ46bdmwM8aE53bL4ZSVVjAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:55:02.053717Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffc2ea86d00e9c3a8279cde6c8d6597f97bcc0bdb1ac542e6fcfc09cb7a29491","sha256:b9106a5379aacb9857c3ff5df6bbfb7bb4d0db1f863c3774fefe388071407c94"],"state_sha256":"1d6089a7b2a33b9283e171ec37249eea2c76e3340711e03b5310b13c9b8c6de3"}