{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OWBUI4M323JLWQ7YZSYMOCRFWO","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":"977096592d67be611f9213ea7f4add7a62a4aef4b5666a181c26308df42ed0d6","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-12-31T00:25:38Z","title_canon_sha256":"e447108be118901cd47585f0da97a6e2bc99a8419201ab962d5dd662b572ed08"},"schema_version":"1.0","source":{"id":"2501.00197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.00197","created_at":"2026-07-05T09:55:40Z"},{"alias_kind":"arxiv_version","alias_value":"2501.00197v1","created_at":"2026-07-05T09:55:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.00197","created_at":"2026-07-05T09:55:40Z"},{"alias_kind":"pith_short_12","alias_value":"OWBUI4M323JL","created_at":"2026-07-05T09:55:40Z"},{"alias_kind":"pith_short_16","alias_value":"OWBUI4M323JLWQ7Y","created_at":"2026-07-05T09:55:40Z"},{"alias_kind":"pith_short_8","alias_value":"OWBUI4M3","created_at":"2026-07-05T09:55:40Z"}],"graph_snapshots":[{"event_id":"sha256:054171784e78b9322d43b707711932793b111e116f5bdc4eb4071797eb55e0bc","target":"graph","created_at":"2026-07-05T09:55:40Z","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/2501.00197/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a variety $Y_{n,k}$, which we call the \\textit{affine $\\Delta$-Springer fiber}, generalizing the affine Springer fiber studied by Hikita, whose Borel-Moore homology has an $S_n$ action and a bigrading that corresponds to the Delta Conjecture symmetric function $\\mathrm{rev}_q\\,\\omega \\Delta'_{e_{k-1}}e_n$ under the Frobenius character map. We similarly provide a geometric interpretation for the Rational Shuffle Theorem in the integer slope case $(km,k)$. The variety $Y_{n,k}$ has a map to the affine Grassmannian whose fibers are the $\\Delta$-Springer fibers introduced by Levinson,","authors_text":"Eugene Gorsky, Maria Gillespie, Sean T. Griffin","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-12-31T00:25:38Z","title":"A geometric interpretation of the Delta Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.00197","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":"sha256:46a59de0887f3b56a9eecce7e1dc2d45ca63cd7c5e7d9e23620976cde5199fd5","target":"record","created_at":"2026-07-05T09:55:40Z","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":"977096592d67be611f9213ea7f4add7a62a4aef4b5666a181c26308df42ed0d6","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-12-31T00:25:38Z","title_canon_sha256":"e447108be118901cd47585f0da97a6e2bc99a8419201ab962d5dd662b572ed08"},"schema_version":"1.0","source":{"id":"2501.00197","kind":"arxiv","version":1}},"canonical_sha256":"758344719bd6d2bb43f8ccb0c70a25b3936779f55b1740c20cc086dc1cf7eb79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"758344719bd6d2bb43f8ccb0c70a25b3936779f55b1740c20cc086dc1cf7eb79","first_computed_at":"2026-07-05T09:55:40.556840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:55:40.556840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EVFysORPoFllga5mp/ctloEdfTUA8PXFYn+FN3JEngR2Pi3f2IX/437CqbkJYHr7667mgzKrqpHXQRU3YR8UBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:55:40.557391Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.00197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46a59de0887f3b56a9eecce7e1dc2d45ca63cd7c5e7d9e23620976cde5199fd5","sha256:054171784e78b9322d43b707711932793b111e116f5bdc4eb4071797eb55e0bc"],"state_sha256":"d27c6fbfb53678d0ee254d64ecd8f14d58971331ba477c2d8c77a42d388d0323"}