{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:INSNGFZ5ROMLFODEGRAGSGC6TA","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":"20da1f243d4dc3f6e82616fd20be08b9190019fa2047fce16d7771eead5dbf82","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-06-28T15:16:17Z","title_canon_sha256":"fda938be146e3b60f3d34562c2e2f79b1441d6840b1b18850891d7277c010c1b"},"schema_version":"1.0","source":{"id":"2606.29452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29452","created_at":"2026-06-30T01:18:07Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29452v1","created_at":"2026-06-30T01:18:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29452","created_at":"2026-06-30T01:18:07Z"},{"alias_kind":"pith_short_12","alias_value":"INSNGFZ5ROML","created_at":"2026-06-30T01:18:07Z"},{"alias_kind":"pith_short_16","alias_value":"INSNGFZ5ROMLFODE","created_at":"2026-06-30T01:18:07Z"},{"alias_kind":"pith_short_8","alias_value":"INSNGFZ5","created_at":"2026-06-30T01:18:07Z"}],"graph_snapshots":[{"event_id":"sha256:41108f009acd47f954d77cbcac57b84c6da64f0c4ac2418295be7e15d258be67","target":"graph","created_at":"2026-06-30T01:18:07Z","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/2606.29452/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish handle attachment formulas for the Khovanov skein lasagna module with 1-dimensional inputs over $\\mathbb{Q}$, defined recently by Ren, Wedrich, Willis, Zhang, and the second author. For a $4$-manifold built out of $1$- and $2$-handles, the invariant can be computed in terms of a cabled colimit of Rozansky-Willis homologies, modulo a new relation which we call the lasso relation. We then present some explicit calculations for disk bundles over $S^{2}$, as well as a partial vanishing result for $4$-manifolds of the form $\\Sigma_{g}\\times D^{2}$, $g\\geq 1$.","authors_text":"Ian A. Sullivan, Imogen Montague","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-06-28T15:16:17Z","title":"Handle decompositions and the 1-dimensional inputs skein lasagna module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29452","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":"sha256:8c5247912084e1c76676e449e10417fc4158f11c20821688803a2e8fbde18c49","target":"record","created_at":"2026-06-30T01:18:07Z","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":"20da1f243d4dc3f6e82616fd20be08b9190019fa2047fce16d7771eead5dbf82","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-06-28T15:16:17Z","title_canon_sha256":"fda938be146e3b60f3d34562c2e2f79b1441d6840b1b18850891d7277c010c1b"},"schema_version":"1.0","source":{"id":"2606.29452","kind":"arxiv","version":1}},"canonical_sha256":"4364d3173d8b98b2b864344069185e9819f9ef297d9a8720dcbab149c31483c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4364d3173d8b98b2b864344069185e9819f9ef297d9a8720dcbab149c31483c8","first_computed_at":"2026-06-30T01:18:07.087446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:18:07.087446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zo5BkDy+w4pGSvKJOMtvXpw7V61N8EoBECCnWB+uWCCS0YIuY9GZYLdDFHufd5auZLBTQDFylxPPjIABsR6JAQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:18:07.088138Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c5247912084e1c76676e449e10417fc4158f11c20821688803a2e8fbde18c49","sha256:41108f009acd47f954d77cbcac57b84c6da64f0c4ac2418295be7e15d258be67"],"state_sha256":"97066f30b5fbc452385c1a874da907341ec6e7038e8ad41203e55df8eb0bd289"}