{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HBFMJF2BO6BLQWTPPE7IEIB3VG","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":"c28265238ab793fd416cd02b76844ff306ee39c866391efd45150ecc888a2f43","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-30T20:00:01Z","title_canon_sha256":"ed1c282b2233585e4e5651b7a7e9e8921cae35c416b00ba83f7c5b49d52bdad6"},"schema_version":"1.0","source":{"id":"1410.0003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0003","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0003v1","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0003","created_at":"2026-05-18T02:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"HBFMJF2BO6BL","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HBFMJF2BO6BLQWTP","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HBFMJF2B","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:3c379ebb8d8e6c236a00cd1b13a3adbf3b093096f2f9858b3e048eb0b35ef1a8","target":"graph","created_at":"2026-05-18T02:41:18Z","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"},"paper":{"abstract_excerpt":"We introduce a new model for elliptic fibrations endowed with a Mordell-Weil group of rank one. We call it a Q$_7(\\mathscr{L},\\mathscr{S})$ model.\n  It naturally generalizes several previous models of elliptic fibrations popular in the F-theory literature. The model is also explicitly smooth, thus relevant physical quantities can be computed in terms of topological invariants in straight manner. Since the general fiber is defined by a cubic curve, basic arithmetic operations on the curve can be done using the chord-tangent group law. We will use this model to determine the spectrum of singular","authors_text":"Mboyo Esole, Monica Jinwoo Kang, Shing-Tung Yau","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-30T20:00:01Z","title":"A New Model for Elliptic Fibrations with a Rank One Mordell-Weil Group: I. Singular Fibers and Semi-Stable Degenerations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0003","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:ea0634e619d9fbce2ca168039806f853eac19817b7dfbe25448cf86e1fd89867","target":"record","created_at":"2026-05-18T02:41:18Z","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":"c28265238ab793fd416cd02b76844ff306ee39c866391efd45150ecc888a2f43","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-09-30T20:00:01Z","title_canon_sha256":"ed1c282b2233585e4e5651b7a7e9e8921cae35c416b00ba83f7c5b49d52bdad6"},"schema_version":"1.0","source":{"id":"1410.0003","kind":"arxiv","version":1}},"canonical_sha256":"384ac497417782b85a6f793e82203ba9b1818df0b060aaaa8582e937da08409e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"384ac497417782b85a6f793e82203ba9b1818df0b060aaaa8582e937da08409e","first_computed_at":"2026-05-18T02:41:18.185560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:18.185560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDGZGivEez9RI83RKpe7Qkis9AUKokrUj/M2E0moeq9cK+xngJJ+ssaJGkKIT0yFhL/rD4PpLx/LEEAKyl94BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:18.185966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea0634e619d9fbce2ca168039806f853eac19817b7dfbe25448cf86e1fd89867","sha256:3c379ebb8d8e6c236a00cd1b13a3adbf3b093096f2f9858b3e048eb0b35ef1a8"],"state_sha256":"5175b6b02b6b75d0de6dee829453fa4718990606fef46ea9375a97209040ec3d"}