{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JJS3AHGOFM2624WP4AXBDZ3ANN","short_pith_number":"pith:JJS3AHGO","schema_version":"1.0","canonical_sha256":"4a65b01cce2b35ed72cfe02e11e7606b44a3b3559b3c99b1e5a407810991239c","source":{"kind":"arxiv","id":"1706.08749","version":2},"attestation_state":"computed","paper":{"title":"Are neutrino masses modular forms?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Ferruccio Feruglio","submitted_at":"2017-06-27T09:26:24Z","abstract_excerpt":"We explore a new class of supersymmetric models for lepton masses and mixing angles where the role of flavour symmetry is played by modular invariance. The building blocks are modular forms of level N and matter supermultiplets, both transforming in representations of a finite discrete group Gamma_N. In the simplest version of these models, Yukawa couplings are just modular forms and the only source of flavour symmetry breaking is the vacuum expectation value of a single complex field, the modulus. In the special case where modular forms are constant functions the whole construction collapses "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1706.08749","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2017-06-27T09:26:24Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"23bc7873abeec3d7053c238762ffd54bcf39f5020f1b6467cfd92c438638ed5e","abstract_canon_sha256":"f4891c3d33bfb7e8cea924a9a2623ca6e28834b49f498fd0b0c68a072cb391b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:04.628266Z","signature_b64":"yFSEXWaAqZRDfK5hKAiptzJmTN3d4SNgt5QQyXQ0ehHP6sh5CnUhUvvdZmDkqj++B9tgISgkbNQhVJuaPqN2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a65b01cce2b35ed72cfe02e11e7606b44a3b3559b3c99b1e5a407810991239c","last_reissued_at":"2026-05-18T00:34:04.627532Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:04.627532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Are neutrino masses modular forms?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Ferruccio Feruglio","submitted_at":"2017-06-27T09:26:24Z","abstract_excerpt":"We explore a new class of supersymmetric models for lepton masses and mixing angles where the role of flavour symmetry is played by modular invariance. The building blocks are modular forms of level N and matter supermultiplets, both transforming in representations of a finite discrete group Gamma_N. In the simplest version of these models, Yukawa couplings are just modular forms and the only source of flavour symmetry breaking is the vacuum expectation value of a single complex field, the modulus. In the special case where modular forms are constant functions the whole construction collapses "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08749","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1706.08749","created_at":"2026-05-18T00:34:04.627656+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.08749v2","created_at":"2026-05-18T00:34:04.627656+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08749","created_at":"2026-05-18T00:34:04.627656+00:00"},{"alias_kind":"pith_short_12","alias_value":"JJS3AHGOFM26","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JJS3AHGOFM2624WP","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JJS3AHGO","created_at":"2026-05-18T12:31:24.725408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":16,"internal_anchor_count":10,"sample":[{"citing_arxiv_id":"2606.25027","citing_title":"Fermion mass relations in one-parameter modular models","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2606.24277","citing_title":"Non-holomorphic $S^{\\prime}_{4}$ modular symmetry for leptons and leptogenesis","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2607.00528","citing_title":"Finite modular Coleman-Weinberg inflation","ref_index":1,"is_internal_anchor":true},{"citing_arxiv_id":"2605.28141","citing_title":"More about modular symmetries and non-invertible properties in magnetized compactifications","ref_index":16,"is_internal_anchor":true},{"citing_arxiv_id":"2605.23202","citing_title":"Zee models with a non-invertible $Z_M$ symmetry","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2411.07476","citing_title":"A rich structure of renormalization group flows for Higgs-like models in 4 dimensions","ref_index":74,"is_internal_anchor":true},{"citing_arxiv_id":"2503.21432","citing_title":"Exploring the flavor structure of leptons via diffusion models","ref_index":9,"is_internal_anchor":true},{"citing_arxiv_id":"2512.24804","citing_title":"Minimal Modular Flavor Symmetry and Lepton Textures Near Fixed Points","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2509.10373","citing_title":"The Seesaw Evaded Modular Dirac Framework","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2603.15455","citing_title":"Why Quarks and Leptons Demand Different Symmetries: A Systematic $Z_3$ Froggatt-Nielsen Analysis","ref_index":16,"is_internal_anchor":true},{"citing_arxiv_id":"2605.11097","citing_title":"Two-loop neutrino mass model with modular $S_4$ symmetry","ref_index":53,"is_internal_anchor":false},{"citing_arxiv_id":"2604.21979","citing_title":"Quark hierarchies and CP violation from the Siegel modular group","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2604.18070","citing_title":"A Type-I Seesaw Framework with Non-Holomorphic Modular Symmetry","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2604.06635","citing_title":"Massive modes on magnetized blow-up manifold of $T^2/\\mathbb{Z}_N$","ref_index":65,"is_internal_anchor":false},{"citing_arxiv_id":"2604.04585","citing_title":"Predictions of Modular Symmetry Fixed Points on Neutrino Masses, Mixing, and Leptogenesis","ref_index":12,"is_internal_anchor":false},{"citing_arxiv_id":"2604.05548","citing_title":"Cosmological collider signals of modular spontaneous CP breaking","ref_index":5,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN","json":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN.json","graph_json":"https://pith.science/api/pith-number/JJS3AHGOFM2624WP4AXBDZ3ANN/graph.json","events_json":"https://pith.science/api/pith-number/JJS3AHGOFM2624WP4AXBDZ3ANN/events.json","paper":"https://pith.science/paper/JJS3AHGO"},"agent_actions":{"view_html":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN","download_json":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN.json","view_paper":"https://pith.science/paper/JJS3AHGO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.08749&json=true","fetch_graph":"https://pith.science/api/pith-number/JJS3AHGOFM2624WP4AXBDZ3ANN/graph.json","fetch_events":"https://pith.science/api/pith-number/JJS3AHGOFM2624WP4AXBDZ3ANN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN/action/storage_attestation","attest_author":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN/action/author_attestation","sign_citation":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN/action/citation_signature","submit_replication":"https://pith.science/pith/JJS3AHGOFM2624WP4AXBDZ3ANN/action/replication_record"}},"created_at":"2026-05-18T00:34:04.627656+00:00","updated_at":"2026-05-18T00:34:04.627656+00:00"}