{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IIIPJ3C2MQT5AY2O2XXV7EGEKK","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":"9e4ff81333e69182095343a5f3d9e16a4c9966a683a7c64134e49519165ced58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-26T22:44:30Z","title_canon_sha256":"ffb304816a1090313e833215c08dae3d209cfad1ffd1f674f0909a2ae99e1394"},"schema_version":"1.0","source":{"id":"1508.06679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06679","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06679v2","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06679","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"IIIPJ3C2MQT5","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IIIPJ3C2MQT5AY2O","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IIIPJ3C2","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:9fe5f4a508ad468827df38733beab089f672713d90c24798d7bc60791326e057","target":"graph","created_at":"2026-05-18T00:46:02Z","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":"We revisit the duality between ALE singularities in M-theory and 7-branes on a circle in F-theory. We see that a frozen M-theory singularity maps to a circle compactification involving a rotation of the plane transverse to the 7-brane, showing an interesting correspondence between commuting triples in simply-laced groups and Kodaira's classification of singular elliptic fibrations. Our analysis strongly suggests that the O7+ plane is the only completely frozen F-theory singularity.","authors_text":"Yuji Tachikawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-26T22:44:30Z","title":"Frozen"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06679","kind":"arxiv","version":2},"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:facc6efab7f7cb81044c93058b680b246c4e5fc530891cd9c7c52f8da9791a2e","target":"record","created_at":"2026-05-18T00:46:02Z","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":"9e4ff81333e69182095343a5f3d9e16a4c9966a683a7c64134e49519165ced58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-08-26T22:44:30Z","title_canon_sha256":"ffb304816a1090313e833215c08dae3d209cfad1ffd1f674f0909a2ae99e1394"},"schema_version":"1.0","source":{"id":"1508.06679","kind":"arxiv","version":2}},"canonical_sha256":"4210f4ec5a6427d0634ed5ef5f90c452b8256a1342d251f50d92cf5d94dfdb38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4210f4ec5a6427d0634ed5ef5f90c452b8256a1342d251f50d92cf5d94dfdb38","first_computed_at":"2026-05-18T00:46:02.829873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:02.829873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V6sb1men6AjpY9oYmgy6Ng1FqV9ki3YBqOpZFGzngT5/E7SWYASdOwYL+M8wWCkM+zo+9sZr9OT6HbAdQAJeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:02.830274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:facc6efab7f7cb81044c93058b680b246c4e5fc530891cd9c7c52f8da9791a2e","sha256:9fe5f4a508ad468827df38733beab089f672713d90c24798d7bc60791326e057"],"state_sha256":"19977b24c76a0009974250790c0fe1f3a1bafd315687ab6d30810731d18b9910"}