{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:L7OIMU6EDD3BH2C7M3S2AKH3T7","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":"bc7d48b3c013ad392b6b5b63a9a72099f683efba64611f212c2d91c641c04a48","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-28T13:56:40Z","title_canon_sha256":"ba8c5791244c2b32545e170a49094e727db67842f6b69c93d1819538bf6d9161"},"schema_version":"1.0","source":{"id":"2309.16447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.16447","created_at":"2026-07-05T06:55:17Z"},{"alias_kind":"arxiv_version","alias_value":"2309.16447v1","created_at":"2026-07-05T06:55:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.16447","created_at":"2026-07-05T06:55:17Z"},{"alias_kind":"pith_short_12","alias_value":"L7OIMU6EDD3B","created_at":"2026-07-05T06:55:17Z"},{"alias_kind":"pith_short_16","alias_value":"L7OIMU6EDD3BH2C7","created_at":"2026-07-05T06:55:17Z"},{"alias_kind":"pith_short_8","alias_value":"L7OIMU6E","created_at":"2026-07-05T06:55:17Z"}],"graph_snapshots":[{"event_id":"sha256:b8203f92915f24c24a0fdf36277d69303a2bee1cedfab61798de33aa10134d4a","target":"graph","created_at":"2026-07-05T06:55:17Z","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/2309.16447/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the modular symmetry in magnetized $T^{2g}$ torus and orbifold models. The $T^{2g}$ torus has the modular symmetry $\\Gamma_{g}=Sp(2g,\\mathbb{Z})$. Magnetic flux background breaks the modular symmetry to a certain normalizer $N_{g}(H)$. We classify remaining modular symmetries by magnetic flux matrix types. Furthermore, we study the modular symmetry for wave functions on the magnetized $T^{2g}$ and certain orbifolds. It is found that wave functions on magnetized $T^{2g}$ as well as its orbifolds behave as the Siegel modular forms of weight $1/2$ and $\\widetilde{N}_{g}(H,h)$, which is t","authors_text":"Hikaru Uchida, Kaito Nasu, Shohei Takada, Shota Kikuchi, Tatsuo Kobayashi","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-28T13:56:40Z","title":"Modular symmetry in magnetized $T^{2g}$ torus and orbifold models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.16447","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":"sha256:2e38e2e85f526f98341d7102ac19cf35aeeb480c2f70487079e7fbb87fc0ba48","target":"record","created_at":"2026-07-05T06:55:17Z","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":"bc7d48b3c013ad392b6b5b63a9a72099f683efba64611f212c2d91c641c04a48","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-09-28T13:56:40Z","title_canon_sha256":"ba8c5791244c2b32545e170a49094e727db67842f6b69c93d1819538bf6d9161"},"schema_version":"1.0","source":{"id":"2309.16447","kind":"arxiv","version":1}},"canonical_sha256":"5fdc8653c418f613e85f66e5a028fb9fca50b042e42f51299d1c22328fd3b9f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fdc8653c418f613e85f66e5a028fb9fca50b042e42f51299d1c22328fd3b9f4","first_computed_at":"2026-07-05T06:55:17.081596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:55:17.081596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zdfz+HcEq6IbqPLySfF9e8WVUojqXngf6UwdF+7X5udDpGlPQryC/hbsH0mz8iyzWIQRSxktNJZPxz9zBkvkBw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:55:17.082049Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.16447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e38e2e85f526f98341d7102ac19cf35aeeb480c2f70487079e7fbb87fc0ba48","sha256:b8203f92915f24c24a0fdf36277d69303a2bee1cedfab61798de33aa10134d4a"],"state_sha256":"4d1fb8cfdcf33bff2fd669475c0c1a0619f1419e2ae171f88dd22593500cfb8b"}