{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WPQMVRIPZJ2KYU7JHHA3F5BT6H","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":"82d344d7cd6b91b542f9efd47f422dd198de46a7908a1a0d80723b04a85fc16a","cross_cats_sorted":["math.PR","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-23T19:12:03Z","title_canon_sha256":"cde9c9ae7e5b4b51bd12eb8a1fda2023533e4ef6a4cd94494f40bde8a7a47fbb"},"schema_version":"1.0","source":{"id":"2605.24705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24705","created_at":"2026-05-26T01:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24705v1","created_at":"2026-05-26T01:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24705","created_at":"2026-05-26T01:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"WPQMVRIPZJ2K","created_at":"2026-05-26T01:03:54Z"},{"alias_kind":"pith_short_16","alias_value":"WPQMVRIPZJ2KYU7J","created_at":"2026-05-26T01:03:54Z"},{"alias_kind":"pith_short_8","alias_value":"WPQMVRIP","created_at":"2026-05-26T01:03:54Z"}],"graph_snapshots":[{"event_id":"sha256:3c2ba7814f61f3f74f7151999e918f2c6eaa56de282a806f61f977bb0ca7a782","target":"graph","created_at":"2026-05-26T01:03:54Z","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/2605.24705/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Caffarelli's contraction theorem states that the Brenier optimal transport map from the standard Gaussian measure to a more log-concave probability measure is 1-Lipschitz. Owing to its many applications in analysis, probability, and geometry, the problem of extending this theorem to curved spaces has appeared repeatedly in the literature, going back to Villani [V09]. More recently, Milman [Mil18] formulated precise conjectures in this direction. In this work, we construct counterexamples to these conjectures.","authors_text":"Shrey Aryan","cross_cats":["math.PR","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-23T19:12:03Z","title":"Spectral Obstructions to Contracting Transport Maps on Curved Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24705","kind":"arxiv","version":1},"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":"sha256:97721ea7e1afd2e62ce1c797cdd14316759d1831a813649844916a4e8d0124da","target":"record","created_at":"2026-05-26T01:03:54Z","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":"82d344d7cd6b91b542f9efd47f422dd198de46a7908a1a0d80723b04a85fc16a","cross_cats_sorted":["math.PR","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-23T19:12:03Z","title_canon_sha256":"cde9c9ae7e5b4b51bd12eb8a1fda2023533e4ef6a4cd94494f40bde8a7a47fbb"},"schema_version":"1.0","source":{"id":"2605.24705","kind":"arxiv","version":1}},"canonical_sha256":"b3e0cac50fca74ac53e939c1b2f433f1d28dbc94c06663c0de88f14cfd3bfb98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3e0cac50fca74ac53e939c1b2f433f1d28dbc94c06663c0de88f14cfd3bfb98","first_computed_at":"2026-05-26T01:03:54.428563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:54.428563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5iiqYdAFkvdig3yexZQYjRrpqKKn+1xSWQxGWwf463Hgf/508egVqmpgmENW6h2TF27mB2EUkDLTrKA07sGKAA==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:54.429611Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97721ea7e1afd2e62ce1c797cdd14316759d1831a813649844916a4e8d0124da","sha256:3c2ba7814f61f3f74f7151999e918f2c6eaa56de282a806f61f977bb0ca7a782"],"state_sha256":"898c28c23b0e75b24c254c002ff9fedc3a52f6b78a9f764512b183d8c6308127"}