{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:G3ABQ4EHBLSYNNRGSH4QBEG4C4","short_pith_number":"pith:G3ABQ4EH","schema_version":"1.0","canonical_sha256":"36c01870870ae586b62691f90090dc17052effa20cf1b0c57844b0e7832da63b","source":{"kind":"arxiv","id":"hep-th/0501224","version":1},"attestation_state":"computed","paper":{"title":"Grand Unification with Higher Rank Product Groups","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Erik Kramer","submitted_at":"2005-01-27T21:40:45Z","abstract_excerpt":"Various ideas support the notion that the GUT gauge group might be a semi-simple direct-product group such as $SU(5) \\times SU(5)$. The doublet-triplet splitting problem can be solved with a direct product group. String theory suggests that the GUT scale is a modulus. Requiring this rules out a single SU(5) gauge group. A model with $SU(5) \\times SU(5)$ gauge symmetry and the GUT scale as a modulus has been shown to exist. It is shown that extending these ideas to $SO(10) \\times SO(10)$ cannot be done with the above requirement without unwanted massless modes at lower energy scales that spoil "},"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":"hep-th/0501224","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2005-01-27T21:40:45Z","cross_cats_sorted":[],"title_canon_sha256":"9ed62e3cab6f6370a1116ea9b600d2222ab88fd3da8063c7d44456ccce22ee0a","abstract_canon_sha256":"c190faccea72685074042774fd1995ff6cc30f10df8a75e7273394f8e760570f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:32:21.691765Z","signature_b64":"jm0AhxKJc9SaYHNSCLlTImOLAXuKYwN29UgHtzdtnleMf2LZ9iCudDLUEHCWbD/WsAqV3kdmCoDTjnCF1Tb9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36c01870870ae586b62691f90090dc17052effa20cf1b0c57844b0e7832da63b","last_reissued_at":"2026-07-04T14:32:21.691368Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:32:21.691368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Grand Unification with Higher Rank Product Groups","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Erik Kramer","submitted_at":"2005-01-27T21:40:45Z","abstract_excerpt":"Various ideas support the notion that the GUT gauge group might be a semi-simple direct-product group such as $SU(5) \\times SU(5)$. The doublet-triplet splitting problem can be solved with a direct product group. String theory suggests that the GUT scale is a modulus. Requiring this rules out a single SU(5) gauge group. A model with $SU(5) \\times SU(5)$ gauge symmetry and the GUT scale as a modulus has been shown to exist. It is shown that extending these ideas to $SO(10) \\times SO(10)$ cannot be done with the above requirement without unwanted massless modes at lower energy scales that spoil "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0501224","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/0501224/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"hep-th/0501224","created_at":"2026-07-04T14:32:21.691425+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0501224v1","created_at":"2026-07-04T14:32:21.691425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0501224","created_at":"2026-07-04T14:32:21.691425+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3ABQ4EHBLSY","created_at":"2026-07-04T14:32:21.691425+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3ABQ4EHBLSYNNRG","created_at":"2026-07-04T14:32:21.691425+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3ABQ4EH","created_at":"2026-07-04T14:32:21.691425+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/G3ABQ4EHBLSYNNRGSH4QBEG4C4","json":"https://pith.science/pith/G3ABQ4EHBLSYNNRGSH4QBEG4C4.json","graph_json":"https://pith.science/api/pith-number/G3ABQ4EHBLSYNNRGSH4QBEG4C4/graph.json","events_json":"https://pith.science/api/pith-number/G3ABQ4EHBLSYNNRGSH4QBEG4C4/events.json","paper":"https://pith.science/paper/G3ABQ4EH"},"agent_actions":{"view_html":"https://pith.science/pith/G3ABQ4EHBLSYNNRGSH4QBEG4C4","download_json":"https://pith.science/pith/G3ABQ4EHBLSYNNRGSH4QBEG4C4.json","view_paper":"https://pith.science/paper/G3ABQ4EH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-th/0501224&json=true","fetch_graph":"https://pith.science/api/pith-number/G3ABQ4EHBLSYNNRGSH4QBEG4C4/graph.json","fetch_events":"https://pith.science/api/pith-number/G3ABQ4EHBLSYNNRGSH4QBEG4C4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3ABQ4EHBLSYNNRGSH4QBEG4C4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3ABQ4EHBLSYNNRGSH4QBEG4C4/action/storage_attestation","attest_author":"https://pith.science/pith/G3ABQ4EHBLSYNNRGSH4QBEG4C4/action/author_attestation","sign_citation":"https://pith.science/pith/G3ABQ4EHBLSYNNRGSH4QBEG4C4/action/citation_signature","submit_replication":"https://pith.science/pith/G3ABQ4EHBLSYNNRGSH4QBEG4C4/action/replication_record"}},"created_at":"2026-07-04T14:32:21.691425+00:00","updated_at":"2026-07-04T14:32:21.691425+00:00"}