{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6U6CVR267ADPV64TOC3O42LQVL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7b729857a1ab27adce79fb6bc5ccb8a785d82b0cdbf53ad176d3c2ff96f02a71","cross_cats_sorted":["hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-10-16T17:50:12Z","title_canon_sha256":"95907cf2dc4db182632d9f01a154104fbb25eaf91a4f5582cda41a54ba3dcbe4"},"schema_version":"1.0","source":{"id":"2310.10626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.10626","created_at":"2026-07-05T08:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2310.10626v2","created_at":"2026-07-05T08:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.10626","created_at":"2026-07-05T08:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"6U6CVR267ADP","created_at":"2026-07-05T08:39:17Z"},{"alias_kind":"pith_short_16","alias_value":"6U6CVR267ADPV64T","created_at":"2026-07-05T08:39:17Z"},{"alias_kind":"pith_short_8","alias_value":"6U6CVR26","created_at":"2026-07-05T08:39:17Z"}],"graph_snapshots":[{"event_id":"sha256:978a84ad22849d0464c8154b83dfaabe5127a151a0065128415efb86e7c81653","target":"graph","created_at":"2026-07-05T08:39:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.10626/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a framework to classify hyperbolic monopoles with continuous symmetries and find a Structure Theorem, greatly simplifying the construction of all those with spherically symmetry. In doing so, we reduce the problem of finding spherically symmetric hyperbolic monopoles to a problem in representation theory. Additionally, we determine constraints on the structure groups of such monopoles. Using these results, we construct novel spherically symmetric $\\mathrm{Sp}(n)$ hyperbolic monopoles.","authors_text":"C. J. Lang","cross_cats":["hep-th","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-10-16T17:50:12Z","title":"Hyperbolic monopoles with continuous symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.10626","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c47c01b67988f73702d6dca849f142ac5ba61ce0837f00d3164c5fe0508bcb82","target":"record","created_at":"2026-07-05T08:39:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7b729857a1ab27adce79fb6bc5ccb8a785d82b0cdbf53ad176d3c2ff96f02a71","cross_cats_sorted":["hep-th","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2023-10-16T17:50:12Z","title_canon_sha256":"95907cf2dc4db182632d9f01a154104fbb25eaf91a4f5582cda41a54ba3dcbe4"},"schema_version":"1.0","source":{"id":"2310.10626","kind":"arxiv","version":2}},"canonical_sha256":"f53c2ac75ef806fafb9370b6ee6970aafb5db325c039ff26b008135ec28f5b46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f53c2ac75ef806fafb9370b6ee6970aafb5db325c039ff26b008135ec28f5b46","first_computed_at":"2026-07-05T08:39:17.958208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:39:17.958208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q9mk6r/BNEwMjJU1eY54vrI2t7KK21hJfPv74v7jK1mTj/HOVPH5yNek1JYQVwfazRaP1b37WPNzyzXGjqUXDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:39:17.958688Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.10626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c47c01b67988f73702d6dca849f142ac5ba61ce0837f00d3164c5fe0508bcb82","sha256:978a84ad22849d0464c8154b83dfaabe5127a151a0065128415efb86e7c81653"],"state_sha256":"9ac07497a9bd797d6267eefd9f5a23fe3ba44d7636b502e9cd93ae90b2e0cf48"}