{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:URJ25DLTJZ75HFDFCBROMJX5BL","short_pith_number":"pith:URJ25DLT","schema_version":"1.0","canonical_sha256":"a453ae8d734e7fd394651062e626fd0aff2bedc3787dc0ef1081938a34ee1755","source":{"kind":"arxiv","id":"2208.04885","version":2},"attestation_state":"computed","paper":{"title":"Unstable minimal surfaces in symmetric spaces of non-compact type","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Nathaniel Sagman, Peter Smillie","submitted_at":"2022-08-09T16:27:32Z","abstract_excerpt":"We prove that if $\\Sigma$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation $\\rho:\\pi_1(\\Sigma)\\to G$ and a $\\rho$-equivariant unstable minimal map from the universal cover of $\\Sigma$ to $N$. This follows from a new lower bound on the index of high energy minimal maps into an arbitrary symmetric space of non-compact type. Taking $G=\\mathrm{PSL}(n,\\mathbb{R})$, $n\\geq 4$, this disproves the Labourie conjecture."},"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":"2208.04885","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2022-08-09T16:27:32Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"d6effc2a6748a6949c5ac1eaa9af641cfbea4cc199c7dd7af76cbb7c21eb2499","abstract_canon_sha256":"f38946a0923641c930080f400076df8662fc868a33345e0cf575628b5fa4a2e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:21.945497Z","signature_b64":"SsA5ow70WC4E0sLzJP8wi3R+xu+jbhI6p58+6Qf1TLK8oooF6QwJO3P+ws7y3nCN4v4wuEYaI63fNqZGcHaxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a453ae8d734e7fd394651062e626fd0aff2bedc3787dc0ef1081938a34ee1755","last_reissued_at":"2026-07-05T10:07:21.945148Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:21.945148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unstable minimal surfaces in symmetric spaces of non-compact type","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DG","authors_text":"Nathaniel Sagman, Peter Smillie","submitted_at":"2022-08-09T16:27:32Z","abstract_excerpt":"We prove that if $\\Sigma$ is a closed surface of genus at least 3 and $G$ is a split real semisimple Lie group of rank at least $3$ acting faithfully by isometries on a symmetric space $N$, then there exists a Hitchin representation $\\rho:\\pi_1(\\Sigma)\\to G$ and a $\\rho$-equivariant unstable minimal map from the universal cover of $\\Sigma$ to $N$. This follows from a new lower bound on the index of high energy minimal maps into an arbitrary symmetric space of non-compact type. Taking $G=\\mathrm{PSL}(n,\\mathbb{R})$, $n\\geq 4$, this disproves the Labourie conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.04885","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.04885/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":"2208.04885","created_at":"2026-07-05T10:07:21.945204+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.04885v2","created_at":"2026-07-05T10:07:21.945204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.04885","created_at":"2026-07-05T10:07:21.945204+00:00"},{"alias_kind":"pith_short_12","alias_value":"URJ25DLTJZ75","created_at":"2026-07-05T10:07:21.945204+00:00"},{"alias_kind":"pith_short_16","alias_value":"URJ25DLTJZ75HFDF","created_at":"2026-07-05T10:07:21.945204+00:00"},{"alias_kind":"pith_short_8","alias_value":"URJ25DLT","created_at":"2026-07-05T10:07:21.945204+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.11746","citing_title":"Complex harmonic maps and rank 2 higher Teichm\\\"uller theory","ref_index":66,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL","json":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL.json","graph_json":"https://pith.science/api/pith-number/URJ25DLTJZ75HFDFCBROMJX5BL/graph.json","events_json":"https://pith.science/api/pith-number/URJ25DLTJZ75HFDFCBROMJX5BL/events.json","paper":"https://pith.science/paper/URJ25DLT"},"agent_actions":{"view_html":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL","download_json":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL.json","view_paper":"https://pith.science/paper/URJ25DLT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.04885&json=true","fetch_graph":"https://pith.science/api/pith-number/URJ25DLTJZ75HFDFCBROMJX5BL/graph.json","fetch_events":"https://pith.science/api/pith-number/URJ25DLTJZ75HFDFCBROMJX5BL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL/action/storage_attestation","attest_author":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL/action/author_attestation","sign_citation":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL/action/citation_signature","submit_replication":"https://pith.science/pith/URJ25DLTJZ75HFDFCBROMJX5BL/action/replication_record"}},"created_at":"2026-07-05T10:07:21.945204+00:00","updated_at":"2026-07-05T10:07:21.945204+00:00"}