{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:546UK5Z2YV3UTSSIKX43BXFCLH","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":"f827113d95e318c7c67ec694ed437933a6adc1e20c20c2ee7547a8462fce45c0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-04T18:03:19Z","title_canon_sha256":"8110ac7355bf3cc85fa23633744327335432c2bb4833cc13ae3451874a03cb8e"},"schema_version":"1.0","source":{"id":"2506.04346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04346","created_at":"2026-07-05T11:16:12Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04346v1","created_at":"2026-07-05T11:16:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04346","created_at":"2026-07-05T11:16:12Z"},{"alias_kind":"pith_short_12","alias_value":"546UK5Z2YV3U","created_at":"2026-07-05T11:16:12Z"},{"alias_kind":"pith_short_16","alias_value":"546UK5Z2YV3UTSSI","created_at":"2026-07-05T11:16:12Z"},{"alias_kind":"pith_short_8","alias_value":"546UK5Z2","created_at":"2026-07-05T11:16:12Z"}],"graph_snapshots":[{"event_id":"sha256:14fb300f5ceba166c85e9f03ddded2819700523ebfa31f3b8d7721c52ed09201","target":"graph","created_at":"2026-07-05T11:16:12Z","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/2506.04346/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the structure of topological defects for finite Abelian symmetries in quantum field theories, and argue on physical grounds that they satisfy the definition of a higher fusion category proposed by Johnson-Freyd. Our primary focus is on the requirement of Karoubi completeness, i.e. the factorization conditions on higher condensation defects. We demonstrate this on a tree of such defects, constructed by successive higher gauging, explicitly using Lagrangian techniques in a concrete four-dimensional example, before turning to more general field theories. Along the way we also comment on ","authors_text":"Enoch Leung, Ibrahima Bah, Thomas Waddleton","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-04T18:03:19Z","title":"On the Physics of Higher Condensation Defects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04346","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":"sha256:69ce9620ea42d7e7b325a806ae4fcb77ef051d11587caac67657894561ba3568","target":"record","created_at":"2026-07-05T11:16:12Z","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":"f827113d95e318c7c67ec694ed437933a6adc1e20c20c2ee7547a8462fce45c0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2025-06-04T18:03:19Z","title_canon_sha256":"8110ac7355bf3cc85fa23633744327335432c2bb4833cc13ae3451874a03cb8e"},"schema_version":"1.0","source":{"id":"2506.04346","kind":"arxiv","version":1}},"canonical_sha256":"ef3d45773ac57749ca4855f9b0dca259e64ed8aa48a7dde886101cca4e2c772d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef3d45773ac57749ca4855f9b0dca259e64ed8aa48a7dde886101cca4e2c772d","first_computed_at":"2026-07-05T11:16:12.997408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:12.997408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"csjYAnd4//USoNyggS6rM2MNfjkB8um23ERuvt11QFs7O3JkdwhKWCModR5gFH0t9AhDmCrYbyqF9X6t2D5ECA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:12.997899Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69ce9620ea42d7e7b325a806ae4fcb77ef051d11587caac67657894561ba3568","sha256:14fb300f5ceba166c85e9f03ddded2819700523ebfa31f3b8d7721c52ed09201"],"state_sha256":"a0335f558c47e68a0c7992179fab1dde368cdc0d4891dec37dd44071ba6e7bc8"}