{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:H5WW7ZOX3VKDZMXOLNH2MC3RMK","short_pith_number":"pith:H5WW7ZOX","schema_version":"1.0","canonical_sha256":"3f6d6fe5d7dd543cb2ee5b4fa60b7162b4ae709cdf16e832b2f781ba8538f6a9","source":{"kind":"arxiv","id":"2212.11915","version":1},"attestation_state":"computed","paper":{"title":"Geometric Bounds on the 1-Form Gauge Sector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Paul-Konstantin Oehlmann, Seung-Joo Lee","submitted_at":"2022-12-22T17:55:38Z","abstract_excerpt":"We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\\mathbb{Z}_m$ and in particular demands each cyclic factor to obey $m\\leq 6$. Our bounds correspond to the universal geometric constraints on the torsion subgroup of the Mordell-Weil group of elliptic Calabi-Yau three-folds. For any F-theory vacua with at least one tensor multiplet, we derive the constraints from the $\\mathbb{P}^1$ fibration structure of the base two-fold and identify thei"},"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":"2212.11915","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2022-12-22T17:55:38Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"804007532c1d0109cc3c6c65569153ea464a6c1bc52848cd782395ceed0b0606","abstract_canon_sha256":"078c36fcc66d482ad6b0666eafe66005d307d19786b1699e4728b11e52c108af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:27:44.681494Z","signature_b64":"RreWRskB9E8Vm8F0eUnB0kot2FamYB0YTLCKO6q9UEMTjE4A72orgLHMZ+WqAa1itjBIkiIP0dXOJwKt5Uz6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f6d6fe5d7dd543cb2ee5b4fa60b7162b4ae709cdf16e832b2f781ba8538f6a9","last_reissued_at":"2026-07-05T05:27:44.681083Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:27:44.681083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Bounds on the 1-Form Gauge Sector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Paul-Konstantin Oehlmann, Seung-Joo Lee","submitted_at":"2022-12-22T17:55:38Z","abstract_excerpt":"We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\\mathbb{Z}_m$ and in particular demands each cyclic factor to obey $m\\leq 6$. Our bounds correspond to the universal geometric constraints on the torsion subgroup of the Mordell-Weil group of elliptic Calabi-Yau three-folds. For any F-theory vacua with at least one tensor multiplet, we derive the constraints from the $\\mathbb{P}^1$ fibration structure of the base two-fold and identify thei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11915","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/2212.11915/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":"2212.11915","created_at":"2026-07-05T05:27:44.681146+00:00"},{"alias_kind":"arxiv_version","alias_value":"2212.11915v1","created_at":"2026-07-05T05:27:44.681146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11915","created_at":"2026-07-05T05:27:44.681146+00:00"},{"alias_kind":"pith_short_12","alias_value":"H5WW7ZOX3VKD","created_at":"2026-07-05T05:27:44.681146+00:00"},{"alias_kind":"pith_short_16","alias_value":"H5WW7ZOX3VKDZMXO","created_at":"2026-07-05T05:27:44.681146+00:00"},{"alias_kind":"pith_short_8","alias_value":"H5WW7ZOX","created_at":"2026-07-05T05:27:44.681146+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/H5WW7ZOX3VKDZMXOLNH2MC3RMK","json":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK.json","graph_json":"https://pith.science/api/pith-number/H5WW7ZOX3VKDZMXOLNH2MC3RMK/graph.json","events_json":"https://pith.science/api/pith-number/H5WW7ZOX3VKDZMXOLNH2MC3RMK/events.json","paper":"https://pith.science/paper/H5WW7ZOX"},"agent_actions":{"view_html":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK","download_json":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK.json","view_paper":"https://pith.science/paper/H5WW7ZOX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2212.11915&json=true","fetch_graph":"https://pith.science/api/pith-number/H5WW7ZOX3VKDZMXOLNH2MC3RMK/graph.json","fetch_events":"https://pith.science/api/pith-number/H5WW7ZOX3VKDZMXOLNH2MC3RMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/action/storage_attestation","attest_author":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/action/author_attestation","sign_citation":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/action/citation_signature","submit_replication":"https://pith.science/pith/H5WW7ZOX3VKDZMXOLNH2MC3RMK/action/replication_record"}},"created_at":"2026-07-05T05:27:44.681146+00:00","updated_at":"2026-07-05T05:27:44.681146+00:00"}