{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CYWCE3N452P7CVWQNPZFFONXSC","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":"1fed650d3d37b12b05de9587a1b46a466a4ad642e272ab72f99e327290ddcd26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-21T14:23:23Z","title_canon_sha256":"2da5a7caf63410fb78915ecbd262e522edf2e130902c4b7ffe652c141bb0dbc4"},"schema_version":"1.0","source":{"id":"1612.07133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07133","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07133v1","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07133","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"pith_short_12","alias_value":"CYWCE3N452P7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CYWCE3N452P7CVWQ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CYWCE3N4","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:bf87b1be09ed2d53c3da730f5dadc65417c6b3be4ae9e34db56bb82cefb0da1a","target":"graph","created_at":"2026-05-18T00:54:14Z","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":"When $Sp(2n,\\mathbb{C})$ acts on the flag variety of $SL(2n,\\mathbb{C})$, the orbits are in bijection with fixed point free involutions in the symmetric group $S_{2n}$. In this case, the associated Kazhdan-Lusztig-Vogan polynomials $P_{v,u}$ can be indexed by pairs of fixed point free involutions $v\\geq u$, where $\\geq$ denotes the Bruhat order on $S_{2n}$. We prove that these polynomials are combinatorial invariants in the sense that if $f: [u, w_0 ] \\rightarrow [u , w_0]$ is a poset isomorphism of upper intervals in the Bruhat order on fixed point free involutions, then $P_{v,u} = P_{f(v),u}","authors_text":"Axel Hultman, Nancy Abdallah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-21T14:23:23Z","title":"Combinatorial Invariance of Kazhdan-Lusztig-Vogan Polyomials for Fixed Point Free Involutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07133","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":"sha256:69ea6d208ad4bbee034b41d04ca7fe9744c29fc1a8dbed8aed511e0f5d5b7b53","target":"record","created_at":"2026-05-18T00:54:14Z","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":"1fed650d3d37b12b05de9587a1b46a466a4ad642e272ab72f99e327290ddcd26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-21T14:23:23Z","title_canon_sha256":"2da5a7caf63410fb78915ecbd262e522edf2e130902c4b7ffe652c141bb0dbc4"},"schema_version":"1.0","source":{"id":"1612.07133","kind":"arxiv","version":1}},"canonical_sha256":"162c226dbcee9ff156d06bf252b9b790bf6e41850a05ecb5e3c8447498bcc752","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"162c226dbcee9ff156d06bf252b9b790bf6e41850a05ecb5e3c8447498bcc752","first_computed_at":"2026-05-18T00:54:14.601423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:14.601423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5X2rJKzhk0bf3sUTUOPQjx+dzKduLq4PU6Ld3Ay12IlKUZyLtupvNzMlJ4tfOSCf90Q9QCJxgcLxy55zd7+6Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:14.601877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69ea6d208ad4bbee034b41d04ca7fe9744c29fc1a8dbed8aed511e0f5d5b7b53","sha256:bf87b1be09ed2d53c3da730f5dadc65417c6b3be4ae9e34db56bb82cefb0da1a"],"state_sha256":"43ac1dd961f6d330d9d38869fee4e016b295db1d6bfe527bcdd3069ee70e21d6"}