{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TNM3I6Q7ZGJIG46XBXDFRMLQ4E","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":"04f68b12bf27b9752e5bb9e75c36832007fc84803d35a52451da0f2290857844","cross_cats_sorted":["astro-ph.CO","hep-ex","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-05-07T04:19:07Z","title_canon_sha256":"f738074c37926bc676465b923ad25feb2099d6e0da0cde9f6a0882fcf481ffc3"},"schema_version":"1.0","source":{"id":"2405.03996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03996","created_at":"2026-07-05T08:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03996v1","created_at":"2026-07-05T08:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03996","created_at":"2026-07-05T08:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"TNM3I6Q7ZGJI","created_at":"2026-07-05T08:16:30Z"},{"alias_kind":"pith_short_16","alias_value":"TNM3I6Q7ZGJIG46X","created_at":"2026-07-05T08:16:30Z"},{"alias_kind":"pith_short_8","alias_value":"TNM3I6Q7","created_at":"2026-07-05T08:16:30Z"}],"graph_snapshots":[{"event_id":"sha256:87d646e45faa3288b4b778fb44dfcb8f11b4d85b2958983a0d7b55d5ff51cf26","target":"graph","created_at":"2026-07-05T08:16:30Z","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/2405.03996/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We point out that the accidental $U(1)_{B-L}$ symmetry can arise from a finite modular symmetry $\\Gamma_N$ in the type-I seesaw. The finite modular symmetry is spontaneously broken in such a way that the residual $\\mathbb{Z}^T_N$ discrete symmetry, associated with the $T$-transformation which shifts the modulus $\\tau \\to \\tau+ 1$, remains unbroken. This discrete $\\mathbb{Z}^T_N$ symmetry mimics $U(1)_{B-L}$, and hence the majoron appears as a pseudo Nambu-Goldstone boson of $U(1)_{B-L}$. Without introducing additional interactions, the modulus $\\tau$ can be stabilized by the Coleman-Weinberg (","authors_text":"Junichiro Kawamura, Tae Hyun Jung","cross_cats":["astro-ph.CO","hep-ex","hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-05-07T04:19:07Z","title":"Finite modular majoron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03996","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":"sha256:7a26e8fdd14542c63edbc67e3da682e05ba2f546588bd985e377d366171e74bb","target":"record","created_at":"2026-07-05T08:16:30Z","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":"04f68b12bf27b9752e5bb9e75c36832007fc84803d35a52451da0f2290857844","cross_cats_sorted":["astro-ph.CO","hep-ex","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-05-07T04:19:07Z","title_canon_sha256":"f738074c37926bc676465b923ad25feb2099d6e0da0cde9f6a0882fcf481ffc3"},"schema_version":"1.0","source":{"id":"2405.03996","kind":"arxiv","version":1}},"canonical_sha256":"9b59b47a1fc9928373d70dc658b170e1143f7685906683847df393d3b3b3fb94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b59b47a1fc9928373d70dc658b170e1143f7685906683847df393d3b3b3fb94","first_computed_at":"2026-07-05T08:16:30.253090Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:16:30.253090Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m6xdqxs02KHERX2pcv1XMqMfidZ0kmOT7W81Q2bbVE8/rW55mNs6IQ4BRdtj0tYwOpQsyH0E9peseitT1/kWBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:16:30.253536Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.03996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a26e8fdd14542c63edbc67e3da682e05ba2f546588bd985e377d366171e74bb","sha256:87d646e45faa3288b4b778fb44dfcb8f11b4d85b2958983a0d7b55d5ff51cf26"],"state_sha256":"3057fd2bd35aaee8f5c17c0888afd304c949039097a3d63f106b4976d118362c"}