{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UWMJAXVJBAH5WLIHSPSYMCLRRQ","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":"8c84907e25ab70144c19a662401147b028dc62a077363329560990e18fd15e58","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-24T18:58:39Z","title_canon_sha256":"636f67fe78afec7313d96498a11e3dcd363420a24b9baf250a1315719efac9e1"},"schema_version":"1.0","source":{"id":"1403.6083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6083","created_at":"2026-05-18T02:55:46Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6083v1","created_at":"2026-05-18T02:55:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6083","created_at":"2026-05-18T02:55:46Z"},{"alias_kind":"pith_short_12","alias_value":"UWMJAXVJBAH5","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UWMJAXVJBAH5WLIH","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UWMJAXVJ","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:8b9b1424bbcac295610237a3d6a3d95317b6759b53d088ef9f137b39b5bf9f37","target":"graph","created_at":"2026-05-18T02:55:46Z","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"},"paper":{"abstract_excerpt":"In arXiv:1308.3152, the author proved that the Khovanov-Rozansky homology $\\mathcal{H}_N$ with potential $ax^{N+1}$ is an invariant for transverse links in the standard contact $3$-sphere. In the current paper, we study the $\\mathbb{Z}_2 \\oplus \\mathbb{Z}^{\\oplus 3}$-graded $\\mathbb{Q}[a]$-module structure of $\\mathcal{H}_N$, which leads to better understanding of the effect of stabilization on $\\mathcal{H}_N$. As an application, we compute $\\mathcal{H}_N$ for all transverse unknots.","authors_text":"Hao Wu","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-24T18:58:39Z","title":"On the Transverse Khovanov-Rozansky Homologies: Graded Module Structure and Stabilization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6083","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":"sha256:6aa87e048d1addf5ae46f36985a315239913389ffce775f83012aad2a9b85347","target":"record","created_at":"2026-05-18T02:55:46Z","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":"8c84907e25ab70144c19a662401147b028dc62a077363329560990e18fd15e58","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-03-24T18:58:39Z","title_canon_sha256":"636f67fe78afec7313d96498a11e3dcd363420a24b9baf250a1315719efac9e1"},"schema_version":"1.0","source":{"id":"1403.6083","kind":"arxiv","version":1}},"canonical_sha256":"a598905ea9080fdb2d0793e58609718c0c1e56dea42320a7bba45d5311fe55db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a598905ea9080fdb2d0793e58609718c0c1e56dea42320a7bba45d5311fe55db","first_computed_at":"2026-05-18T02:55:46.932369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:46.932369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a65Gyc6k3NWoxFCtesD545kPatmKdw46GlSWjgb9tN9DfxQZW1JR8F/x+hp1UnTCWrsVRSWvkfh9vMj0bmyNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:46.933102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6aa87e048d1addf5ae46f36985a315239913389ffce775f83012aad2a9b85347","sha256:8b9b1424bbcac295610237a3d6a3d95317b6759b53d088ef9f137b39b5bf9f37"],"state_sha256":"55c7a2baac4c848864f1557cda982bd1ca94fada632bdfecb98d0816362d448c"}