{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6AX3AXUA7VTIGG5CGELBV3ZRCE","short_pith_number":"pith:6AX3AXUA","schema_version":"1.0","canonical_sha256":"f02fb05e80fd66831ba231161aef31113dcbb59dff11bb610cf9c07accc92892","source":{"kind":"arxiv","id":"1704.08251","version":1},"attestation_state":"computed","paper":{"title":"The Geometry of F$_4$-Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Mboyo Esole, Monica Jinwoo Kang, Patrick Jefferson","submitted_at":"2017-04-26T18:00:00Z","abstract_excerpt":"We study the geometry of elliptic fibrations satisfying the conditions of Step 8 of Tate's algorithm. We call such geometries F$_4$-models, as the dual graph of their special fiber is the twisted affine Dynkin diagram $\\widetilde{\\text{F}}_4^t$. These geometries are used in string theory to model gauge theories with the exceptional Lie group F$_4$ on a smooth divisor $S$ of the base. Starting with a singular Weierstrass model of an F$_4$-model, we present a crepant resolution of its singularities. We study the fiber structure of this smooth elliptic fibration and identify the fibral divisors u"},"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":"1704.08251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-04-26T18:00:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ff0ec1641306552ca7a8b47e41d0b7a2fbc90da1b67b94e43d44d0804c59857c","abstract_canon_sha256":"3512a3671e6d953dcb3f0a81b966fe5b0085e1fa880c4086914b0117c5d033b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:29.791492Z","signature_b64":"rd1nYHFzCqmSNzOfuOhSeBiBwePHOtW+0LNXZcI9RxnOvb3HhGWkH4fzoF5FgNoIzcP2qP966TKWMyS9oYFuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f02fb05e80fd66831ba231161aef31113dcbb59dff11bb610cf9c07accc92892","last_reissued_at":"2026-05-18T00:45:29.790958Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:29.790958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Geometry of F$_4$-Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Mboyo Esole, Monica Jinwoo Kang, Patrick Jefferson","submitted_at":"2017-04-26T18:00:00Z","abstract_excerpt":"We study the geometry of elliptic fibrations satisfying the conditions of Step 8 of Tate's algorithm. We call such geometries F$_4$-models, as the dual graph of their special fiber is the twisted affine Dynkin diagram $\\widetilde{\\text{F}}_4^t$. These geometries are used in string theory to model gauge theories with the exceptional Lie group F$_4$ on a smooth divisor $S$ of the base. Starting with a singular Weierstrass model of an F$_4$-model, we present a crepant resolution of its singularities. We study the fiber structure of this smooth elliptic fibration and identify the fibral divisors u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08251","kind":"arxiv","version":1},"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":"1704.08251","created_at":"2026-05-18T00:45:29.791026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.08251v1","created_at":"2026-05-18T00:45:29.791026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08251","created_at":"2026-05-18T00:45:29.791026+00:00"},{"alias_kind":"pith_short_12","alias_value":"6AX3AXUA7VTI","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6AX3AXUA7VTIGG5C","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6AX3AXUA","created_at":"2026-05-18T12:31:03.183658+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE","json":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE.json","graph_json":"https://pith.science/api/pith-number/6AX3AXUA7VTIGG5CGELBV3ZRCE/graph.json","events_json":"https://pith.science/api/pith-number/6AX3AXUA7VTIGG5CGELBV3ZRCE/events.json","paper":"https://pith.science/paper/6AX3AXUA"},"agent_actions":{"view_html":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE","download_json":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE.json","view_paper":"https://pith.science/paper/6AX3AXUA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.08251&json=true","fetch_graph":"https://pith.science/api/pith-number/6AX3AXUA7VTIGG5CGELBV3ZRCE/graph.json","fetch_events":"https://pith.science/api/pith-number/6AX3AXUA7VTIGG5CGELBV3ZRCE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE/action/storage_attestation","attest_author":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE/action/author_attestation","sign_citation":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE/action/citation_signature","submit_replication":"https://pith.science/pith/6AX3AXUA7VTIGG5CGELBV3ZRCE/action/replication_record"}},"created_at":"2026-05-18T00:45:29.791026+00:00","updated_at":"2026-05-18T00:45:29.791026+00:00"}