{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IHHKKW5SNMJ6SN5CAKG3APAB56","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":"989f26bea752191cff36f76eb6fd0cc697c00e0b13061bf891d4ee59b4ce366d","cross_cats_sorted":["hep-th","math-ph","math.AC","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-14T00:38:24Z","title_canon_sha256":"4282938f0608520d52773c15a65a8e1ce44a82002e35493b3c9bf865b1171ed7"},"schema_version":"1.0","source":{"id":"1311.3354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3354","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3354v1","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3354","created_at":"2026-05-18T01:26:49Z"},{"alias_kind":"pith_short_12","alias_value":"IHHKKW5SNMJ6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IHHKKW5SNMJ6SN5C","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IHHKKW5S","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:1f67c956a9c4432ba3df5f48ae32aed189d92723df78dbdcceb3a978d5c64f2f","target":"graph","created_at":"2026-05-18T01:26:49Z","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"},"paper":{"abstract_excerpt":"To a graded finite-rank matrix factorisation of the difference of two homogeneous potentials one can assign two numbers, the left and right quantum dimension. The existence of such a matrix factorisation with non-zero quantum dimensions defines an equivalence relation between potentials, giving rise to non-obvious equivalences of categories.\n  Restricted to ADE singularities, the resulting equivalence classes of potentials are those of type {A_{d-1}} for d odd, {A_{d-1},D_{d/2+1}} for d even but not in {12,18,30}, and {A_{11}, D_7, E_6}, {A_{17}, D_{10}, E_7} and {A_{29}, D_{16}, E_8}. This is","authors_text":"Ana Ros Camacho, Ingo Runkel, Nils Carqueville","cross_cats":["hep-th","math-ph","math.AC","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-14T00:38:24Z","title":"Orbifold equivalent potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3354","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":"sha256:4e1e4e69a5a91fdc7d73f9be840718b50afb95f62e3d0fe5e83954f25e019fb3","target":"record","created_at":"2026-05-18T01:26:49Z","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":"989f26bea752191cff36f76eb6fd0cc697c00e0b13061bf891d4ee59b4ce366d","cross_cats_sorted":["hep-th","math-ph","math.AC","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-11-14T00:38:24Z","title_canon_sha256":"4282938f0608520d52773c15a65a8e1ce44a82002e35493b3c9bf865b1171ed7"},"schema_version":"1.0","source":{"id":"1311.3354","kind":"arxiv","version":1}},"canonical_sha256":"41cea55bb26b13e937a2028db03c01ef8562ef60e56abf0b84442235359f0686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41cea55bb26b13e937a2028db03c01ef8562ef60e56abf0b84442235359f0686","first_computed_at":"2026-05-18T01:26:49.314379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:49.314379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4yY3/o5akA/3nl52THvbhjGFqN3zCzGzzhebxeqGnhp8jaz1p8QXhqe6hPPmYmP32F5PaUCReFo0dCyEw3qsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:49.315030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e1e4e69a5a91fdc7d73f9be840718b50afb95f62e3d0fe5e83954f25e019fb3","sha256:1f67c956a9c4432ba3df5f48ae32aed189d92723df78dbdcceb3a978d5c64f2f"],"state_sha256":"fb955434612028b0e5600465082fd70026b5e0b43f0ebce18146d61269e8919b"}