{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:C7ZAXCDA5GI5CYDGINVXSVHMCX","short_pith_number":"pith:C7ZAXCDA","schema_version":"1.0","canonical_sha256":"17f20b8860e991d16066436b7954ec15d2e507249a022e1e02ebdcc0f15e3d55","source":{"kind":"arxiv","id":"0809.0330","version":2},"attestation_state":"computed","paper":{"title":"On orbifolds and free fermion constructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"hep-th","authors_text":"Katrin Wendland, Ron Donagi","submitted_at":"2008-09-02T19:56:16Z","abstract_excerpt":"This work develops the correspondence between orbifolds and free fermion models. A complete classification is obtained for orbifolds X/G with X the product of three elliptic curves and G an abelian extension of a group (Z_2)^2 of twists acting on X. Each such quotient X/G is shown to give a geometric interpretation to an appropriate free fermion model, including the geometric NAHE+ model. However, the semi-realistic NAHE free fermion model is proved to be non-geometric: its Hodge numbers are not reproduced by any orbifold X/G. In particular cases it is shown that X/G can agree with some Borcea"},"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":"0809.0330","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2008-09-02T19:56:16Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"25f657a89bfc5ecc2a09654181617c265dfab636baffee2c2a337a40c6e57002","abstract_canon_sha256":"10271daab2437eed7b7c7621aafc922aaa04c5352451252272cc77829d007fa6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:15.015081Z","signature_b64":"BPL4UZc38x8+7Z0znCwB2nw3hLueQBTuZMy7/7idbzTOhMwkpFNO0HolBDVCyKPFfRMHIO74FST440e2WMfkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17f20b8860e991d16066436b7954ec15d2e507249a022e1e02ebdcc0f15e3d55","last_reissued_at":"2026-05-18T02:35:15.014528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:15.014528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On orbifolds and free fermion constructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"hep-th","authors_text":"Katrin Wendland, Ron Donagi","submitted_at":"2008-09-02T19:56:16Z","abstract_excerpt":"This work develops the correspondence between orbifolds and free fermion models. A complete classification is obtained for orbifolds X/G with X the product of three elliptic curves and G an abelian extension of a group (Z_2)^2 of twists acting on X. Each such quotient X/G is shown to give a geometric interpretation to an appropriate free fermion model, including the geometric NAHE+ model. However, the semi-realistic NAHE free fermion model is proved to be non-geometric: its Hodge numbers are not reproduced by any orbifold X/G. In particular cases it is shown that X/G can agree with some Borcea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0330","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":"0809.0330","created_at":"2026-05-18T02:35:15.014624+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.0330v2","created_at":"2026-05-18T02:35:15.014624+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0330","created_at":"2026-05-18T02:35:15.014624+00:00"},{"alias_kind":"pith_short_12","alias_value":"C7ZAXCDA5GI5","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"C7ZAXCDA5GI5CYDG","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"C7ZAXCDA","created_at":"2026-05-18T12:25:57.157939+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/C7ZAXCDA5GI5CYDGINVXSVHMCX","json":"https://pith.science/pith/C7ZAXCDA5GI5CYDGINVXSVHMCX.json","graph_json":"https://pith.science/api/pith-number/C7ZAXCDA5GI5CYDGINVXSVHMCX/graph.json","events_json":"https://pith.science/api/pith-number/C7ZAXCDA5GI5CYDGINVXSVHMCX/events.json","paper":"https://pith.science/paper/C7ZAXCDA"},"agent_actions":{"view_html":"https://pith.science/pith/C7ZAXCDA5GI5CYDGINVXSVHMCX","download_json":"https://pith.science/pith/C7ZAXCDA5GI5CYDGINVXSVHMCX.json","view_paper":"https://pith.science/paper/C7ZAXCDA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.0330&json=true","fetch_graph":"https://pith.science/api/pith-number/C7ZAXCDA5GI5CYDGINVXSVHMCX/graph.json","fetch_events":"https://pith.science/api/pith-number/C7ZAXCDA5GI5CYDGINVXSVHMCX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C7ZAXCDA5GI5CYDGINVXSVHMCX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C7ZAXCDA5GI5CYDGINVXSVHMCX/action/storage_attestation","attest_author":"https://pith.science/pith/C7ZAXCDA5GI5CYDGINVXSVHMCX/action/author_attestation","sign_citation":"https://pith.science/pith/C7ZAXCDA5GI5CYDGINVXSVHMCX/action/citation_signature","submit_replication":"https://pith.science/pith/C7ZAXCDA5GI5CYDGINVXSVHMCX/action/replication_record"}},"created_at":"2026-05-18T02:35:15.014624+00:00","updated_at":"2026-05-18T02:35:15.014624+00:00"}