{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EOXQOBCMC5OEOYKSSNYYKOKZZM","short_pith_number":"pith:EOXQOBCM","schema_version":"1.0","canonical_sha256":"23af07044c175c4761529371853959cb13bc9d269e4c63cb7b4cbd182efc9df9","source":{"kind":"arxiv","id":"2604.14288","version":2},"attestation_state":"computed","paper":{"title":"Exact Toda Black Holes of Rank-2 Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Suitable dilaton couplings let the field equations for two-charge black holes reduce exactly to one-dimensional Toda equations of every rank-2 Lie group, producing explicit solutions in arbitrary dimensions.","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"H. Lu, Peng-Yu Wu, Weicheng Zhao, Ze-Hua Wu","submitted_at":"2026-04-15T18:00:03Z","abstract_excerpt":"We consider Einstein gravity coupled to two Maxwell fields and one dilatonic scalar, and construct spherically-symmetric and static black holes that are charged under both Maxwell fields in general $D$ dimensions. We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. We devise a brute-force approach to obtain the most general but remarkably elegant solutions to the Toda equations. This allows us to construct exact black holes associated with all the rank-2 Lie groups. We study their thermodynamics and veri"},"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":"2604.14288","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-15T18:00:03Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"402e35129bbdc24afd26cda421fa0ca05cf034852b362948794899267b9d6d85","abstract_canon_sha256":"be05c8726c658206fc9821c99887a18069d7dc5a013e82af95b521f62c89c2a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:53.136891Z","signature_b64":"XQ1hhr3GxNimzUuVIgLfvL5fSDHhZkHTLQphXMHwbJhCwgZLrIlsQIYwPwX7kKk2raSfI6x3oNJtKIATWDJ/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23af07044c175c4761529371853959cb13bc9d269e4c63cb7b4cbd182efc9df9","last_reissued_at":"2026-06-02T02:04:53.136493Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:53.136493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact Toda Black Holes of Rank-2 Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Suitable dilaton couplings let the field equations for two-charge black holes reduce exactly to one-dimensional Toda equations of every rank-2 Lie group, producing explicit solutions in arbitrary dimensions.","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"H. Lu, Peng-Yu Wu, Weicheng Zhao, Ze-Hua Wu","submitted_at":"2026-04-15T18:00:03Z","abstract_excerpt":"We consider Einstein gravity coupled to two Maxwell fields and one dilatonic scalar, and construct spherically-symmetric and static black holes that are charged under both Maxwell fields in general $D$ dimensions. We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. We devise a brute-force approach to obtain the most general but remarkably elegant solutions to the Toda equations. This allows us to construct exact black holes associated with all the rank-2 Lie groups. We study their thermodynamics and veri"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. This allows us to construct exact black holes associated with all the rank-2 Lie groups. The B2 and G2 Toda black holes are new.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that suitable dilaton couplings exist such that the full system of Einstein-Maxwell-dilaton equations reduces exactly to Toda equations of rank-2 Lie groups without extra constraints or loss of generality.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact spherically symmetric static black hole solutions are constructed for all rank-2 Lie groups by reducing Einstein-Maxwell-dilaton equations to Toda systems, with new B2 and G2 solutions, and thermodynamics derived without explicit metrics.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Suitable dilaton couplings let the field equations for two-charge black holes reduce exactly to one-dimensional Toda equations of every rank-2 Lie group, producing explicit solutions in arbitrary dimensions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a343450c9787ddcac3d936886c0b58c891f7765fffab7e7c69dddf48ef193aa9"},"source":{"id":"2604.14288","kind":"arxiv","version":2},"verdict":{"id":"377af23c-21d9-42c7-b03a-372d6cc82772","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T12:29:39.452116Z","strongest_claim":"We find that for suitable dilaton couplings, the equations of motion can be cast into one-dimensional Toda equations of all rank-2 Lie groups. This allows us to construct exact black holes associated with all the rank-2 Lie groups. The B2 and G2 Toda black holes are new.","one_line_summary":"Exact spherically symmetric static black hole solutions are constructed for all rank-2 Lie groups by reducing Einstein-Maxwell-dilaton equations to Toda systems, with new B2 and G2 solutions, and thermodynamics derived without explicit metrics.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that suitable dilaton couplings exist such that the full system of Einstein-Maxwell-dilaton equations reduces exactly to Toda equations of rank-2 Lie groups without extra constraints or loss of generality.","pith_extraction_headline":"Suitable dilaton couplings let the field equations for two-charge black holes reduce exactly to one-dimensional Toda equations of every rank-2 Lie group, producing explicit solutions in arbitrary dimensions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.14288/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":"2604.14288","created_at":"2026-06-02T02:04:53.136550+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.14288v2","created_at":"2026-06-02T02:04:53.136550+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.14288","created_at":"2026-06-02T02:04:53.136550+00:00"},{"alias_kind":"pith_short_12","alias_value":"EOXQOBCMC5OE","created_at":"2026-06-02T02:04:53.136550+00:00"},{"alias_kind":"pith_short_16","alias_value":"EOXQOBCMC5OEOYKS","created_at":"2026-06-02T02:04:53.136550+00:00"},{"alias_kind":"pith_short_8","alias_value":"EOXQOBCM","created_at":"2026-06-02T02:04:53.136550+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/EOXQOBCMC5OEOYKSSNYYKOKZZM","json":"https://pith.science/pith/EOXQOBCMC5OEOYKSSNYYKOKZZM.json","graph_json":"https://pith.science/api/pith-number/EOXQOBCMC5OEOYKSSNYYKOKZZM/graph.json","events_json":"https://pith.science/api/pith-number/EOXQOBCMC5OEOYKSSNYYKOKZZM/events.json","paper":"https://pith.science/paper/EOXQOBCM"},"agent_actions":{"view_html":"https://pith.science/pith/EOXQOBCMC5OEOYKSSNYYKOKZZM","download_json":"https://pith.science/pith/EOXQOBCMC5OEOYKSSNYYKOKZZM.json","view_paper":"https://pith.science/paper/EOXQOBCM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.14288&json=true","fetch_graph":"https://pith.science/api/pith-number/EOXQOBCMC5OEOYKSSNYYKOKZZM/graph.json","fetch_events":"https://pith.science/api/pith-number/EOXQOBCMC5OEOYKSSNYYKOKZZM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EOXQOBCMC5OEOYKSSNYYKOKZZM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EOXQOBCMC5OEOYKSSNYYKOKZZM/action/storage_attestation","attest_author":"https://pith.science/pith/EOXQOBCMC5OEOYKSSNYYKOKZZM/action/author_attestation","sign_citation":"https://pith.science/pith/EOXQOBCMC5OEOYKSSNYYKOKZZM/action/citation_signature","submit_replication":"https://pith.science/pith/EOXQOBCMC5OEOYKSSNYYKOKZZM/action/replication_record"}},"created_at":"2026-06-02T02:04:53.136550+00:00","updated_at":"2026-06-02T02:04:53.136550+00:00"}