{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OHUOW3PEM6RBALQ3PQMMNR3W3O","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":"b4887a46e52d93deff5bb5222c0c5f3cfbcc0540a1bbe0ff7453467402840c70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-03-15T17:47:29Z","title_canon_sha256":"f76950c4537798ef62257d2c8b5dc4e7c0b8e0f0befa7d4a8cba89795ca04db9"},"schema_version":"1.0","source":{"id":"2103.08580","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.08580","created_at":"2026-07-05T02:33:30Z"},{"alias_kind":"arxiv_version","alias_value":"2103.08580v4","created_at":"2026-07-05T02:33:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.08580","created_at":"2026-07-05T02:33:30Z"},{"alias_kind":"pith_short_12","alias_value":"OHUOW3PEM6RB","created_at":"2026-07-05T02:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"OHUOW3PEM6RBALQ3","created_at":"2026-07-05T02:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"OHUOW3PE","created_at":"2026-07-05T02:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:9c0c571ebc59a5fa857aee93253bbe09b7019359eb801c741bbd4e0a02ba45e6","target":"graph","created_at":"2026-07-05T02:33:30Z","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/2103.08580/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Following the work of Gao and Xie in [2], we state some properties of the inverse Kazhdan-Lusztig polynomial of a matroid. We also give partial answers to a conjecture that states that regular connected matroids are non-degenerate. We link the degeneracy of a matroid to the inverse Kazhdan-Lusztig polynomial and we show that the Conjecture holds for modular matroids, by proving that degenerate modular matroids are not regular.","authors_text":"Lorenzo Vecchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-03-15T17:47:29Z","title":"On matroid modularity and the coefficients of the inverse Kazhdan-Lusztig polynomial of a matroid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.08580","kind":"arxiv","version":4},"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:ead7732a87459eca881f57ecace0dad6e87decc8fd5f6ac1837f5ae42d5d30a1","target":"record","created_at":"2026-07-05T02:33:30Z","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":"b4887a46e52d93deff5bb5222c0c5f3cfbcc0540a1bbe0ff7453467402840c70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2021-03-15T17:47:29Z","title_canon_sha256":"f76950c4537798ef62257d2c8b5dc4e7c0b8e0f0befa7d4a8cba89795ca04db9"},"schema_version":"1.0","source":{"id":"2103.08580","kind":"arxiv","version":4}},"canonical_sha256":"71e8eb6de467a2102e1b7c18c6c776dbbb0e66bbf9512124d24eb452b96d83a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71e8eb6de467a2102e1b7c18c6c776dbbb0e66bbf9512124d24eb452b96d83a6","first_computed_at":"2026-07-05T02:33:30.824325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:33:30.824325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oknhQMH80/bzzipkTCLJ8pKwkT1aMoD5KnhTa4t+b4filg0sC8LPPUqB9K5cb8g5U+RayiLAS4S2k6lRB0l4DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:33:30.824810Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.08580","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ead7732a87459eca881f57ecace0dad6e87decc8fd5f6ac1837f5ae42d5d30a1","sha256:9c0c571ebc59a5fa857aee93253bbe09b7019359eb801c741bbd4e0a02ba45e6"],"state_sha256":"1ec7dc204b5948c69c504acf264e41ef9d0f0a5afe5ea771c7a9c10c9a29b69d"}