{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MPWPQDX4MVAVLY7TJOS5GQREIH","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":"08c197bfffc25d64b3c085def5fc2c0f97bb0620c2fe8eab2504d0b01cb123ed","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-12-31T11:47:36Z","title_canon_sha256":"bf1a5d6f4172879943297bdb1e334c149cba631bfa6fc24f054ad0557f996ba7"},"schema_version":"1.0","source":{"id":"2512.24804","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.24804","created_at":"2026-05-21T01:04:20Z"},{"alias_kind":"arxiv_version","alias_value":"2512.24804v3","created_at":"2026-05-21T01:04:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.24804","created_at":"2026-05-21T01:04:20Z"},{"alias_kind":"pith_short_12","alias_value":"MPWPQDX4MVAV","created_at":"2026-05-21T01:04:20Z"},{"alias_kind":"pith_short_16","alias_value":"MPWPQDX4MVAVLY7T","created_at":"2026-05-21T01:04:20Z"},{"alias_kind":"pith_short_8","alias_value":"MPWPQDX4","created_at":"2026-05-21T01:04:20Z"}],"graph_snapshots":[{"event_id":"sha256:43720389e3fd1a513b7a98e3e8cf95044df59de529e5935a4518a1ac67818962","target":"graph","created_at":"2026-05-21T01:04:20Z","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/2512.24804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An extension of the Standard Model with $\\Gamma_2\\simeq S_3$ modular flavor symmetry is presented. We consider the construction of the lepton sector, augmented by two right-handed neutrino states, in the vicinity of the fixed points $\\tau = i\\infty $, $\\tau = i$ and $\\tau \\!=\\!\\omega \\!=\\!-\\frac{1}{2}\\!+\\!i\\frac{\\sqrt{3}}{2}$. Due to the residual symmetries at these points, and with the aid of nonholomorphic modular forms (which constitute representations of $S_3$) and by assigning specific transformation properties to the fermion fields, highly economical models (without flavon fields) are co","authors_text":"Zurab Tavartkiladze","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-12-31T11:47:36Z","title":"Minimal Modular Flavor Symmetry and Lepton Textures Near Fixed Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.24804","kind":"arxiv","version":3},"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":"sha256:07347c857aada31db07830c7f639a92e34bab4721c091041c4674c58e35c443b","target":"record","created_at":"2026-05-21T01:04:20Z","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":"08c197bfffc25d64b3c085def5fc2c0f97bb0620c2fe8eab2504d0b01cb123ed","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2025-12-31T11:47:36Z","title_canon_sha256":"bf1a5d6f4172879943297bdb1e334c149cba631bfa6fc24f054ad0557f996ba7"},"schema_version":"1.0","source":{"id":"2512.24804","kind":"arxiv","version":3}},"canonical_sha256":"63ecf80efc654155e3f34ba5d3422441e4599f35d34f7c97381ae4ecc2789926","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63ecf80efc654155e3f34ba5d3422441e4599f35d34f7c97381ae4ecc2789926","first_computed_at":"2026-05-21T01:04:20.192051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:20.192051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fm7fChhaYmoWbK2P1JevP9FTra2YKBLkeFYgGfx2fmvBaezF0leM9W4z1WSDzlPLveJabyYKWEODAqF1Cjm4Cw==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:20.192954Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.24804","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07347c857aada31db07830c7f639a92e34bab4721c091041c4674c58e35c443b","sha256:43720389e3fd1a513b7a98e3e8cf95044df59de529e5935a4518a1ac67818962"],"state_sha256":"6de6e7868b56b13ea94b04a6927cdf9c92220f14ecf778aa9597d10d463c659c"}