{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5PB5PKKON43VPJAJUPZTNUBMKZ","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":"1af3bcdc3b8d65266faa8292725bd02afdbf9d80945b52523899cd0a4a680402","cross_cats_sorted":["math.GT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-09T17:21:17Z","title_canon_sha256":"0e736b6a9601e10670075d573169fb3dadf7ec280743082a54ff503a854d5c1d"},"schema_version":"1.0","source":{"id":"2606.11122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.11122","created_at":"2026-06-10T01:11:12Z"},{"alias_kind":"arxiv_version","alias_value":"2606.11122v1","created_at":"2026-06-10T01:11:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.11122","created_at":"2026-06-10T01:11:12Z"},{"alias_kind":"pith_short_12","alias_value":"5PB5PKKON43V","created_at":"2026-06-10T01:11:12Z"},{"alias_kind":"pith_short_16","alias_value":"5PB5PKKON43VPJAJ","created_at":"2026-06-10T01:11:12Z"},{"alias_kind":"pith_short_8","alias_value":"5PB5PKKO","created_at":"2026-06-10T01:11:12Z"}],"graph_snapshots":[{"event_id":"sha256:208571697e9ba4ae6cee20a605688f0019ccead22decbcdc4873716b12917dea","target":"graph","created_at":"2026-06-10T01:11:12Z","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/2606.11122/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a model-independent axiomatic framework for the derived skein theory of oriented 3-manifolds with coefficients in a ribbon tensor category, especially focusing on the case where the input category is the category of finite-dimensional representations of a quantum group with quantum parameter not a root of unity. The axioms are designed so that the 0th homology recovers the ordinary skein module and gluing is governed by a bar construction. We establish several relationships between the derived skein theory and the ordinary skein theory. We show that this framework yields computable ","authors_text":"Chun-Yu Bai","cross_cats":["math.GT","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-09T17:21:17Z","title":"Derived skein module"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11122","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:a609b837f8bff7e2cdbb09d18eb8cec00df41025a95889206e2e9e4ba98755ba","target":"record","created_at":"2026-06-10T01:11:12Z","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":"1af3bcdc3b8d65266faa8292725bd02afdbf9d80945b52523899cd0a4a680402","cross_cats_sorted":["math.GT","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2026-06-09T17:21:17Z","title_canon_sha256":"0e736b6a9601e10670075d573169fb3dadf7ec280743082a54ff503a854d5c1d"},"schema_version":"1.0","source":{"id":"2606.11122","kind":"arxiv","version":1}},"canonical_sha256":"ebc3d7a94e6f3757a409a3f336d02c564065483f53685ba53121590a5fd849b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebc3d7a94e6f3757a409a3f336d02c564065483f53685ba53121590a5fd849b2","first_computed_at":"2026-06-10T01:11:12.258165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:11:12.258165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TNAr3ZtB8xhGDpfH9TneYVZApHOD9rKlQM64gCWoeqEUycjgIn4mwYwA8bdi2vCHUzHMDQ5UyEm6EBEgbp0rDA==","signature_status":"signed_v1","signed_at":"2026-06-10T01:11:12.258920Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.11122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a609b837f8bff7e2cdbb09d18eb8cec00df41025a95889206e2e9e4ba98755ba","sha256:208571697e9ba4ae6cee20a605688f0019ccead22decbcdc4873716b12917dea"],"state_sha256":"052ede3c2f2d122b6b4071aa9375c0a1e9c833a76966b72210b4a37567480193"}