{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BOWV7KB63ZCKJP747VTBYZDW4A","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":"cba6bd2e8387d9e6f5b2ba2e97c8a42bfaff45d30a3df4dd75cd0958ea41cd07","cross_cats_sorted":["math.GT","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-20T10:38:29Z","title_canon_sha256":"07109b8fdcc82860fda1ee3a02017fe6242c4e4f8695f26674c06ce98bbeb536"},"schema_version":"1.0","source":{"id":"2505.14182","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.14182","created_at":"2026-07-05T11:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"2505.14182v1","created_at":"2026-07-05T11:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.14182","created_at":"2026-07-05T11:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"BOWV7KB63ZCK","created_at":"2026-07-05T11:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"BOWV7KB63ZCKJP74","created_at":"2026-07-05T11:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"BOWV7KB6","created_at":"2026-07-05T11:05:57Z"}],"graph_snapshots":[{"event_id":"sha256:aa14990fdbda8ad4c17072556993389814b4379e91ada475f0894b709d9962d3","target":"graph","created_at":"2026-07-05T11:05:57Z","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/2505.14182/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the structure of reduced triply graded link homology $\\overline{\\mathrm{HHH}}$ in the top/bottom three $T-$degrees for links arising as closures of positive/negative braids. Using a diagrammatic approach to the Hochschild cohomology of Soergel bimodules, we provide explicit computations of $\\overline{\\mathrm{HHH}}$ as $R-$modules in these degrees. Our results reveal that the homology here is often zero, especially in the negative braid case, and display striking uniformity.","authors_text":"Cailan Li","cross_cats":["math.GT","math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-20T10:38:29Z","title":"The Last Three T-degrees in Triply-Graded Link Homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.14182","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":"sha256:5e6b1ab27da0197a94beed38a9341b7275932c860f4d070397a8aac1fbb359c1","target":"record","created_at":"2026-07-05T11:05:57Z","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":"cba6bd2e8387d9e6f5b2ba2e97c8a42bfaff45d30a3df4dd75cd0958ea41cd07","cross_cats_sorted":["math.GT","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-20T10:38:29Z","title_canon_sha256":"07109b8fdcc82860fda1ee3a02017fe6242c4e4f8695f26674c06ce98bbeb536"},"schema_version":"1.0","source":{"id":"2505.14182","kind":"arxiv","version":1}},"canonical_sha256":"0bad5fa83ede44a4bffcfd661c6476e021727fd36091d34a5ab64bd2c5211598","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bad5fa83ede44a4bffcfd661c6476e021727fd36091d34a5ab64bd2c5211598","first_computed_at":"2026-07-05T11:05:57.359431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:57.359431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IS6TzZkPLKP0gyFEujlwdEPZU0yx49cRsfL/7I31OdTDCeCUC6C7NYn/AZBa4C9cX2fukGEP3AFfifOSv+0GDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:57.359980Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.14182","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e6b1ab27da0197a94beed38a9341b7275932c860f4d070397a8aac1fbb359c1","sha256:aa14990fdbda8ad4c17072556993389814b4379e91ada475f0894b709d9962d3"],"state_sha256":"862750cb37c467084eb6fcb33af6769cbfb33f4492640c55f3cd9766e4f3c8b8"}