{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5U2WUOU5UP5BXJ6WRKBHVCWUPT","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":"786f707e47ab935dbfcfa9072cd3ae451f6beda206e5c2fc718905c6c14ecb86","cross_cats_sorted":["hep-th","math.AT","math.CT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-05-07T19:39:42Z","title_canon_sha256":"66c1efa934676ff029861d98401d0e9def068e323a3d39f1630ec2dfe138ae12"},"schema_version":"1.0","source":{"id":"2505.04761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.04761","created_at":"2026-07-05T11:00:13Z"},{"alias_kind":"arxiv_version","alias_value":"2505.04761v1","created_at":"2026-07-05T11:00:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.04761","created_at":"2026-07-05T11:00:13Z"},{"alias_kind":"pith_short_12","alias_value":"5U2WUOU5UP5B","created_at":"2026-07-05T11:00:13Z"},{"alias_kind":"pith_short_16","alias_value":"5U2WUOU5UP5BXJ6W","created_at":"2026-07-05T11:00:13Z"},{"alias_kind":"pith_short_8","alias_value":"5U2WUOU5","created_at":"2026-07-05T11:00:13Z"}],"graph_snapshots":[{"event_id":"sha256:d02f32a9b13e5d77a1c75394188393f7be5570a4000aa31b7dc647fd79378711","target":"graph","created_at":"2026-07-05T11:00:13Z","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/2505.04761/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or $\\operatorname{Pin}^{\\pm}$-structures, in terms of structured versions of higher dagger categories. This recovers all previously known results, including the description of oriented topological defects in 2-dimensional quantum field theories by pivotal bicategories. Assuming the stratified cobordism hypothesis, we prove our proposal for topological defects with stable tangential st","authors_text":"Lukas M\\\"uller","cross_cats":["hep-th","math.AT","math.CT","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-05-07T19:39:42Z","title":"On the Higher Categorical Structure of Topological Defects in Quantum Field Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04761","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":"sha256:0ba130327b1c6b1a278186ec089184b2c8199e431c39995daa51f87dbe6eecc5","target":"record","created_at":"2026-07-05T11:00:13Z","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":"786f707e47ab935dbfcfa9072cd3ae451f6beda206e5c2fc718905c6c14ecb86","cross_cats_sorted":["hep-th","math.AT","math.CT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2025-05-07T19:39:42Z","title_canon_sha256":"66c1efa934676ff029861d98401d0e9def068e323a3d39f1630ec2dfe138ae12"},"schema_version":"1.0","source":{"id":"2505.04761","kind":"arxiv","version":1}},"canonical_sha256":"ed356a3a9da3fa1ba7d68a827a8ad47ce572b72147394b769c2adfdc4297509b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed356a3a9da3fa1ba7d68a827a8ad47ce572b72147394b769c2adfdc4297509b","first_computed_at":"2026-07-05T11:00:13.318058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:00:13.318058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eu0o7zSDIrZyZ7SXM2eTFi2tidStWSBe6k7lq1j/mSkM51CK/GcUdM4tenDDsYgArpGK2VzMZx/t3Z4rdoUEDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:00:13.318564Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.04761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ba130327b1c6b1a278186ec089184b2c8199e431c39995daa51f87dbe6eecc5","sha256:d02f32a9b13e5d77a1c75394188393f7be5570a4000aa31b7dc647fd79378711"],"state_sha256":"0c6e677f264288ced1d56fe527db6789d6f91248045e57a77f54288ecee22936"}