{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3LW6L3AB4F4DRNBIO6QUEKQLLE","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":"1d6d3655996af036fdeac50f4a0d4108da3e9b772e50b9290c948951a5a868a1","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T10:18:10Z","title_canon_sha256":"3c296c6605b829d5798f2ebf705e8a39468c9848c203d2cf496035fa6a52b4f6"},"schema_version":"1.0","source":{"id":"2605.13304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13304","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13304v1","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13304","created_at":"2026-05-18T02:44:48Z"},{"alias_kind":"pith_short_12","alias_value":"3LW6L3AB4F4D","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"3LW6L3AB4F4DRNBI","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"3LW6L3AB","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:4496cd1245507191b0c372be30d7820126565b481a2571aac93e5d8c6296fcf5","target":"graph","created_at":"2026-05-18T02:44:48Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Our results imply that a conjecture stated in [Bull. London Math. Soc., 57 (2025), no. 8] holds for the class of standard hypercube decompositions."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The results apply specifically to standard hypercube decompositions; the conjecture may fail or require different arguments for non-standard decompositions."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The paper proves that a conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals, advancing the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals in the symmetric group."}],"snapshot_sha256":"afd2f16881febc89da9205542f6b522af051797e4df31e4432b7e915e6346ed9"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study the double shortcuts associated with pairs of standard hypercube decompositions of arbitrary Bruhat intervals in the symmetric group. Our results imply that a conjecture stated in [Bull. London Math. Soc., 57 (2025), no. 8] holds for the class of standard hypercube decompositions. If this conjecture were to hold for all hypercube decompositions, then the Combinatorial Invariance Conjecture for Kazhdan--Lusztig polynomials would follow.","authors_text":"Margherita Zannoni","cross_cats":["math.RT"],"headline":"A conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals in the symmetric group.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T10:18:10Z","title":"Double shortcuts of standard hypercube decompositions"},"references":{"count":17,"internal_anchors":0,"resolved_work":17,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"G.T. Barkley, C. Gaetz,Combinatorial invariance for elementary intervals, Math. Ann.392(2025), 3299–3317","work_id":"6febe6c5-42f4-4dcf-a031-21a2148e10e8","year":2025},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"G.T. Barkley, C. Gaetz, T. Lam,Combinatorial invariance for the coefficient ofqin Kazhdan-Lusztig polynomials, arXiv:2601.07793 [math.CO]","work_id":"0314c597-1246-44ed-ab78-e32b3b41517a","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"A.Björner, F.Brenti,Combinatorics of Coxeter Groups, GraduateTextsinMathematics,231, Springer- Verlag, New York, 2005","work_id":"56750cf5-3f1f-4294-bea5-4b1ed333ab95","year":2005},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"C. Blundell, L. Buesing, A. Davies, P. Veli˘ cković, G. Williamson,Towards combinatorial invariance for Kazhdan-Lusztig polynomials, Represent. Theory26(2022), 1145-1191","work_id":"392ba1e8-1979-4aa7-9f34-53d27ff60440","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"F.Brenti,A combinatorial formula for Kazhdan-Lusztig polynomials, Invent.Math.118(1994), 371-394","work_id":"b12079ec-3616-4e67-baaa-5d934816beb6","year":1994}],"snapshot_sha256":"6e3e22ccfaa012941e2c2d2423cba885eab1ea6f0b2ed36265a4f8288f98d1b7"},"source":{"id":"2605.13304","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T20:22:36.328202Z","id":"a7ebb87a-5679-4eba-8428-d55e7efb9126","model_set":{"reader":"grok-4.3"},"one_line_summary":"The paper proves that a conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals, advancing the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A conjecture on double shortcuts holds for standard hypercube decompositions of Bruhat intervals in the symmetric group.","strongest_claim":"Our results imply that a conjecture stated in [Bull. London Math. Soc., 57 (2025), no. 8] holds for the class of standard hypercube decompositions.","weakest_assumption":"The results apply specifically to standard hypercube decompositions; the conjecture may fail or require different arguments for non-standard decompositions."}},"verdict_id":"a7ebb87a-5679-4eba-8428-d55e7efb9126"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3991c41c425bb54f194397cb5a501a15c91fc27d1b95d2b539718896aba91b89","target":"record","created_at":"2026-05-18T02:44:48Z","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":"1d6d3655996af036fdeac50f4a0d4108da3e9b772e50b9290c948951a5a868a1","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-13T10:18:10Z","title_canon_sha256":"3c296c6605b829d5798f2ebf705e8a39468c9848c203d2cf496035fa6a52b4f6"},"schema_version":"1.0","source":{"id":"2605.13304","kind":"arxiv","version":1}},"canonical_sha256":"daede5ec01e17838b42877a1422a0b59139f6b332fbb13406fe28209e73acb02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daede5ec01e17838b42877a1422a0b59139f6b332fbb13406fe28209e73acb02","first_computed_at":"2026-05-18T02:44:48.986932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:48.986932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gefZZ+U0GcMOhV7Q6iJbXMHopZqaF229ozbxmQWxKzsPDLtg9pnuiya1XSNL13NykrJwim72gODQcSJvQlWADg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:48.987480Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3991c41c425bb54f194397cb5a501a15c91fc27d1b95d2b539718896aba91b89","sha256:4496cd1245507191b0c372be30d7820126565b481a2571aac93e5d8c6296fcf5"],"state_sha256":"978707e99773b4feaab4fa454bff7b64c8c859073d5e0378a45f2f6ea41fd988"}