{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DO752Y6HQ7HC4ZYBN4KT7JBIKP","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":"1ef979097ca5ec5c9ad605ca349702e37e7b9be5b12165a3ad9bc7574baa125d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-11-18T22:59:25Z","title_canon_sha256":"6fb538a4aa89b3965f498f9613af8b7981310bc1f1e5d5ac6b72e483f10d11e3"},"schema_version":"1.0","source":{"id":"2111.09966","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.09966","created_at":"2026-07-05T04:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"2111.09966v2","created_at":"2026-07-05T04:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.09966","created_at":"2026-07-05T04:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"DO752Y6HQ7HC","created_at":"2026-07-05T04:51:05Z"},{"alias_kind":"pith_short_16","alias_value":"DO752Y6HQ7HC4ZYB","created_at":"2026-07-05T04:51:05Z"},{"alias_kind":"pith_short_8","alias_value":"DO752Y6H","created_at":"2026-07-05T04:51:05Z"}],"graph_snapshots":[{"event_id":"sha256:a8345fe856ff669357fb0fa572e42d38c2605bfcd3f8f33233a8f32af6d6a47a","target":"graph","created_at":"2026-07-05T04:51:05Z","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/2111.09966/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a map relating the gauge symmetry groups of heterotic strings on $T^4$ to other components of the moduli space with rank reduction. This generalizes the results for $T^2$ and $T^3$ which mirror the singularity freezing mechanism of K3 surfaces in F and M-theory, respectively. The novel feature in six dimensions is that the map explicitly involves the topology of the gauge groups, in particular acting only on non-simply-connected ones. This relation is equivalent to that of connected components of the moduli space of flat $G$-bundles over $T^2$ with $G$ non-simply-connected. These res","authors_text":"Bernardo Fraiman, H\\'ector Parra De Freitas","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-11-18T22:59:25Z","title":"Freezing of Gauge Symmetries in the Heterotic String on $T^4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09966","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":"sha256:0236696fba5e19ad9359b7fad0f92072de0f66ce9081350983a29c7363c1edf7","target":"record","created_at":"2026-07-05T04:51:05Z","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":"1ef979097ca5ec5c9ad605ca349702e37e7b9be5b12165a3ad9bc7574baa125d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-11-18T22:59:25Z","title_canon_sha256":"6fb538a4aa89b3965f498f9613af8b7981310bc1f1e5d5ac6b72e483f10d11e3"},"schema_version":"1.0","source":{"id":"2111.09966","kind":"arxiv","version":2}},"canonical_sha256":"1bbfdd63c787ce2e67016f153fa42853ff331753b4dee6666f6cfdb62aec4043","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bbfdd63c787ce2e67016f153fa42853ff331753b4dee6666f6cfdb62aec4043","first_computed_at":"2026-07-05T04:51:05.584775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:51:05.584775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f/ncUpHU4k58BlUWHu0MtUEnK3GIJ3Ha+d4I+oPxdsr+8tKrs4+hl0P5t774ttOkM40tsTrDOWP1Br4iyBiiBw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:51:05.585149Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.09966","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0236696fba5e19ad9359b7fad0f92072de0f66ce9081350983a29c7363c1edf7","sha256:a8345fe856ff669357fb0fa572e42d38c2605bfcd3f8f33233a8f32af6d6a47a"],"state_sha256":"2a38e04c73a85739fa62e668fc2910635b44a2b1cf5eba49aac5143ec6c339c8"}