{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:CTVG3B7Y7XYHABND5IBU6PRCCB","short_pith_number":"pith:CTVG3B7Y","canonical_record":{"source":{"id":"2311.06929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-12T19:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"2db034280d292642c8c62c4b6b88b6af95181b84f8973018bf5a3f804c5d4808","abstract_canon_sha256":"8a396301bc62581b09df97419f3edd455211e2fcb5c6003a0cedbe4b167f8f70"},"schema_version":"1.0"},"canonical_sha256":"14ea6d87f8fdf07005a3ea034f3e22104c283ef496feb0182e8da7a5e215816f","source":{"kind":"arxiv","id":"2311.06929","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.06929","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"arxiv_version","alias_value":"2311.06929v1","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06929","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"pith_short_12","alias_value":"CTVG3B7Y7XYH","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"pith_short_16","alias_value":"CTVG3B7Y7XYHABND","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"pith_short_8","alias_value":"CTVG3B7Y","created_at":"2026-07-05T07:12:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:CTVG3B7Y7XYHABND5IBU6PRCCB","target":"record","payload":{"canonical_record":{"source":{"id":"2311.06929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-12T19:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"2db034280d292642c8c62c4b6b88b6af95181b84f8973018bf5a3f804c5d4808","abstract_canon_sha256":"8a396301bc62581b09df97419f3edd455211e2fcb5c6003a0cedbe4b167f8f70"},"schema_version":"1.0"},"canonical_sha256":"14ea6d87f8fdf07005a3ea034f3e22104c283ef496feb0182e8da7a5e215816f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:12:05.555423Z","signature_b64":"eqIJ1A2ZNWXL80adq6vt9FCjiZUSFob0ZC14MFDu45bxdvhpIzzkV//Wrp7CM7zjMDsL2NbXhqWVov5bePvACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14ea6d87f8fdf07005a3ea034f3e22104c283ef496feb0182e8da7a5e215816f","last_reissued_at":"2026-07-05T07:12:05.554515Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:12:05.554515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.06929","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:12:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxBh6OiBXJOpw1kLlV5TCBvdCX/z3tRhK08IcGrXpBd/TO1P+5MZhpdxmfrYOGuGZEjIduXKRfGdWTEhI5g5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T14:41:59.451980Z"},"content_sha256":"43908c4063f5a94a6d78e48f37903e3ffc9aa1135994146bad175b36212c200a","schema_version":"1.0","event_id":"sha256:43908c4063f5a94a6d78e48f37903e3ffc9aa1135994146bad175b36212c200a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:CTVG3B7Y7XYHABND5IBU6PRCCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The combinatorics behind the leading Kazhdan-Lusztig coefficients of braid matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alice L.L. Gao, Arthur L.B. Yang, Nicholas Proudfoot, Zhong-Xue Zhang","submitted_at":"2023-11-12T19:04:02Z","abstract_excerpt":"Ferroni and Larson gave a combinatorial interpretation of the braid Kazhdan-Lusztig polynomials in terms of series-parallel matroids. As a consequence, they confirmed an explicit formula for the leading Kazhdan-Lusztig coefficients of braid matroids with odd rank, as conjectured by Elias, Proudfoot, and Wakefield. Based on Ferroni and Larson's work, we further explore the combinatorics behind the leading Kazhdan-Lusztig coefficients of braid matroids. The main results of this paper include an explicit formula for the leading Kazhdan-Lusztig coefficients of braid matroids with even rank, a simp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06929","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.06929/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:12:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K04X/2wFSz1OcTvISHBZj6LZm9fU8xzjOI2A6vvmGtgIl0Hh4dnzCyzuHxhB9TZSU2k0M+7ZUGsRg3T+wtjEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T14:41:59.452704Z"},"content_sha256":"783ba94646d605b59056a15a7cf0e986f378a1196bbc8a1ce299e72362ecbf43","schema_version":"1.0","event_id":"sha256:783ba94646d605b59056a15a7cf0e986f378a1196bbc8a1ce299e72362ecbf43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CTVG3B7Y7XYHABND5IBU6PRCCB/bundle.json","state_url":"https://pith.science/pith/CTVG3B7Y7XYHABND5IBU6PRCCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CTVG3B7Y7XYHABND5IBU6PRCCB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-22T14:41:59Z","links":{"resolver":"https://pith.science/pith/CTVG3B7Y7XYHABND5IBU6PRCCB","bundle":"https://pith.science/pith/CTVG3B7Y7XYHABND5IBU6PRCCB/bundle.json","state":"https://pith.science/pith/CTVG3B7Y7XYHABND5IBU6PRCCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CTVG3B7Y7XYHABND5IBU6PRCCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:CTVG3B7Y7XYHABND5IBU6PRCCB","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":"8a396301bc62581b09df97419f3edd455211e2fcb5c6003a0cedbe4b167f8f70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-12T19:04:02Z","title_canon_sha256":"2db034280d292642c8c62c4b6b88b6af95181b84f8973018bf5a3f804c5d4808"},"schema_version":"1.0","source":{"id":"2311.06929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.06929","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"arxiv_version","alias_value":"2311.06929v1","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.06929","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"pith_short_12","alias_value":"CTVG3B7Y7XYH","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"pith_short_16","alias_value":"CTVG3B7Y7XYHABND","created_at":"2026-07-05T07:12:05Z"},{"alias_kind":"pith_short_8","alias_value":"CTVG3B7Y","created_at":"2026-07-05T07:12:05Z"}],"graph_snapshots":[{"event_id":"sha256:783ba94646d605b59056a15a7cf0e986f378a1196bbc8a1ce299e72362ecbf43","target":"graph","created_at":"2026-07-05T07:12:05Z","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/2311.06929/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ferroni and Larson gave a combinatorial interpretation of the braid Kazhdan-Lusztig polynomials in terms of series-parallel matroids. As a consequence, they confirmed an explicit formula for the leading Kazhdan-Lusztig coefficients of braid matroids with odd rank, as conjectured by Elias, Proudfoot, and Wakefield. Based on Ferroni and Larson's work, we further explore the combinatorics behind the leading Kazhdan-Lusztig coefficients of braid matroids. The main results of this paper include an explicit formula for the leading Kazhdan-Lusztig coefficients of braid matroids with even rank, a simp","authors_text":"Alice L.L. Gao, Arthur L.B. Yang, Nicholas Proudfoot, Zhong-Xue Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-12T19:04:02Z","title":"The combinatorics behind the leading Kazhdan-Lusztig coefficients of braid matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.06929","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":"sha256:43908c4063f5a94a6d78e48f37903e3ffc9aa1135994146bad175b36212c200a","target":"record","created_at":"2026-07-05T07:12:05Z","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":"8a396301bc62581b09df97419f3edd455211e2fcb5c6003a0cedbe4b167f8f70","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-11-12T19:04:02Z","title_canon_sha256":"2db034280d292642c8c62c4b6b88b6af95181b84f8973018bf5a3f804c5d4808"},"schema_version":"1.0","source":{"id":"2311.06929","kind":"arxiv","version":1}},"canonical_sha256":"14ea6d87f8fdf07005a3ea034f3e22104c283ef496feb0182e8da7a5e215816f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14ea6d87f8fdf07005a3ea034f3e22104c283ef496feb0182e8da7a5e215816f","first_computed_at":"2026-07-05T07:12:05.554515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:12:05.554515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eqIJ1A2ZNWXL80adq6vt9FCjiZUSFob0ZC14MFDu45bxdvhpIzzkV//Wrp7CM7zjMDsL2NbXhqWVov5bePvACQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:12:05.555423Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.06929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43908c4063f5a94a6d78e48f37903e3ffc9aa1135994146bad175b36212c200a","sha256:783ba94646d605b59056a15a7cf0e986f378a1196bbc8a1ce299e72362ecbf43"],"state_sha256":"d3901be73699d58b2c1de5b8733ac46b0a5d5aaedf3dcb202523ca6c3e9a8523"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCpzgMSv9E4XhNTCYhesOZCb4rULcQtjWqJMd1QRCrr5zlR82s5mrq6ESjtwVJCkdrjevTrtAsvKM9ofaBYbDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T14:41:59.457954Z","bundle_sha256":"16edd9c0b5bac4f084d6244e6684e8700fdb6457951d368b9374b9780398ecac"}}