{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:L5TYUVMSLH6SHXLT3QEYSALHLL","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":"aec493d9071dbe542dafc56f3402c98ab4957d9d7677cfb17f7f8316ad4d685f","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-21T12:32:55Z","title_canon_sha256":"1a98bfd0eacdc15ff788800186320c5074882cc3337e6c49e602c2b3a363903b"},"schema_version":"1.0","source":{"id":"2605.22405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22405","created_at":"2026-05-22T01:04:41Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22405v1","created_at":"2026-05-22T01:04:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22405","created_at":"2026-05-22T01:04:41Z"},{"alias_kind":"pith_short_12","alias_value":"L5TYUVMSLH6S","created_at":"2026-05-22T01:04:41Z"},{"alias_kind":"pith_short_16","alias_value":"L5TYUVMSLH6SHXLT","created_at":"2026-05-22T01:04:41Z"},{"alias_kind":"pith_short_8","alias_value":"L5TYUVMS","created_at":"2026-05-22T01:04:41Z"}],"graph_snapshots":[{"event_id":"sha256:41053f7df13c4abac7e52b263f1a64a6810eb6267026741a6cc2115a5acb26ee","target":"graph","created_at":"2026-05-22T01:04:41Z","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/2605.22405/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a scalar invariant of flat principal 2-bundles over 3-manifolds, with structure 2-group $\\mathcal{G}$, from an involutory Hopf algebra graded by $\\mathcal{G}$. Expressing $\\mathcal{G}$ in terms of a crossed module $\\chi$ and using the classification of such 2-bundles via the classifying space $B\\chi$, this amounts to constructing a homotopy invariant of maps from 3-manifolds to $B\\chi$. The construction of the invariant relies on a combinatorial description of such maps by $\\chi$-colored Heegaard diagrams. When the corresponding map to $B\\chi$ is nullhomotopic or, equivalently, wh","authors_text":"Alexis Virelizier, Kursat Sozer","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-21T12:32:55Z","title":"Quantum invariants of flat 2-bundles over 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22405","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":"sha256:14450820ecdd757428542b71ff738ff339cd6e2235c738a9be07de208e40d408","target":"record","created_at":"2026-05-22T01:04:41Z","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":"aec493d9071dbe542dafc56f3402c98ab4957d9d7677cfb17f7f8316ad4d685f","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-21T12:32:55Z","title_canon_sha256":"1a98bfd0eacdc15ff788800186320c5074882cc3337e6c49e602c2b3a363903b"},"schema_version":"1.0","source":{"id":"2605.22405","kind":"arxiv","version":1}},"canonical_sha256":"5f678a559259fd23dd73dc098901675aed94d45415792b98834e9fbe51ab4c7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f678a559259fd23dd73dc098901675aed94d45415792b98834e9fbe51ab4c7a","first_computed_at":"2026-05-22T01:04:41.930303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:41.930303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c3uIm9ZxaaFdSLJCU1e0mNWcgrr7dZR2H0d01Dn82a+p8920kFtbKQAmV3mfWFm/IahiC2AYnm7kFUJDTljVAA==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:41.931271Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14450820ecdd757428542b71ff738ff339cd6e2235c738a9be07de208e40d408","sha256:41053f7df13c4abac7e52b263f1a64a6810eb6267026741a6cc2115a5acb26ee"],"state_sha256":"a5ab3ed10d6ab223a8f5c7cb2d9d5901d08a984cbf27138a4868288fd04c28f4"}