{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6JDOWSFGR4755YPUUSGGTUTBK5","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":"8c30d77c209b44e8678af1bb512f51bee7ea53dc21ed45d0a3d3f4dbebe1ee7d","cross_cats_sorted":["math.GT","math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-11-14T16:41:49Z","title_canon_sha256":"1d3114e630a55891e6133bcf46b5df5dc992f5b7b7ab50a61771938561c73773"},"schema_version":"1.0","source":{"id":"2511.11469","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.11469","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"arxiv_version","alias_value":"2511.11469v3","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.11469","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"pith_short_12","alias_value":"6JDOWSFGR475","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"pith_short_16","alias_value":"6JDOWSFGR4755YPU","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"pith_short_8","alias_value":"6JDOWSFG","created_at":"2026-06-23T03:13:51Z"}],"graph_snapshots":[{"event_id":"sha256:520cb0d926aeb1eb039d74349127ccd91b136a42c6a4f36c0c840c745096536b","target":"graph","created_at":"2026-06-23T03:13:51Z","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/2511.11469/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a sufficient criterion, which we call stability, for a coarse Lipschitz map $f$ from a complete manifold $X$ with Ricci curvature bounded below to a proper Hadamard space $Y$ to be within bounded distance of a harmonic map. We prove uniqueness of the harmonic map under additional assumptions on $X$ and $Y$.\n  Using this criterion, we prove a significant generalization of the Schoen-Li-Wang conjecture on quasi-isometric embeddings between rank 1 symmetric spaces. In particular, under a natural generalization of the quasi-isometric condition, we remove the assumption that the target has ","authors_text":"J. Maxwell Riestenberg, Peter Smillie","cross_cats":["math.GT","math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-11-14T16:41:49Z","title":"Harmonic maps to Hadamard spaces and a universal higher Teichm\\\"{u}ller space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.11469","kind":"arxiv","version":3},"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:b7066b653d2ae14848ec70721220b23467c545e0b376f477767bd272c9877e01","target":"record","created_at":"2026-06-23T03:13:51Z","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":"8c30d77c209b44e8678af1bb512f51bee7ea53dc21ed45d0a3d3f4dbebe1ee7d","cross_cats_sorted":["math.GT","math.MG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-11-14T16:41:49Z","title_canon_sha256":"1d3114e630a55891e6133bcf46b5df5dc992f5b7b7ab50a61771938561c73773"},"schema_version":"1.0","source":{"id":"2511.11469","kind":"arxiv","version":3}},"canonical_sha256":"f246eb48a68f3fdee1f4a48c69d2615755ca62d9d38b29fb088ff65d526057c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f246eb48a68f3fdee1f4a48c69d2615755ca62d9d38b29fb088ff65d526057c3","first_computed_at":"2026-06-23T03:13:51.302358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:51.302358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9xVpjNSTcL2aFs1ofVPyBrI6KtneNN1Ksh6McHTaJXvjVdLU98i5JWXs7hxzf3eHQi5ymj1sLoPzxOtExIp+Ag==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:51.302767Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.11469","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7066b653d2ae14848ec70721220b23467c545e0b376f477767bd272c9877e01","sha256:520cb0d926aeb1eb039d74349127ccd91b136a42c6a4f36c0c840c745096536b"],"state_sha256":"6c7fd002f353da2829d1f5233d7b8a3ae23b62adc5c265aae438fa5c4e7314ce"}