{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ECY2JAEYXVPHJMIAUNUEBKLIU3","short_pith_number":"pith:ECY2JAEY","canonical_record":{"source":{"id":"2606.13453","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T15:11:54Z","cross_cats_sorted":["math.MP","stat.ML"],"title_canon_sha256":"5f431745015e98b40e1a4860b084d3783fe986be4292c2a12ca9936663c30781","abstract_canon_sha256":"1181fdf4c555242166fbad9af857361d8d15eb700e7564b2e397a683a40ccaaf"},"schema_version":"1.0"},"canonical_sha256":"20b1a48098bd5e74b100a36840a968a6f4b0cd16eaa7d408b5235ffe4736740b","source":{"kind":"arxiv","id":"2606.13453","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13453","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13453v1","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13453","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"pith_short_12","alias_value":"ECY2JAEYXVPH","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"pith_short_16","alias_value":"ECY2JAEYXVPHJMIA","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"pith_short_8","alias_value":"ECY2JAEY","created_at":"2026-06-12T01:10:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ECY2JAEYXVPHJMIAUNUEBKLIU3","target":"record","payload":{"canonical_record":{"source":{"id":"2606.13453","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T15:11:54Z","cross_cats_sorted":["math.MP","stat.ML"],"title_canon_sha256":"5f431745015e98b40e1a4860b084d3783fe986be4292c2a12ca9936663c30781","abstract_canon_sha256":"1181fdf4c555242166fbad9af857361d8d15eb700e7564b2e397a683a40ccaaf"},"schema_version":"1.0"},"canonical_sha256":"20b1a48098bd5e74b100a36840a968a6f4b0cd16eaa7d408b5235ffe4736740b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:10:03.329750Z","signature_b64":"viQamgLHNihzXTpv/sEWa+fUkeOJeHvF9EbhtV0pZUXFQfPE83XyhQh+3qvMT97qaW3bQ6G0RXiCuGeunHnRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20b1a48098bd5e74b100a36840a968a6f4b0cd16eaa7d408b5235ffe4736740b","last_reissued_at":"2026-06-12T01:10:03.328882Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:10:03.328882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.13453","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-12T01:10:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6zC4NCwf0w/TAjguAL6i0xdzID6IXvlA48irAKTX5f3DGyGpajM4hI7Cqu6rsAjH3Oo4Lae62MVY+DisIpXzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:41:36.777060Z"},"content_sha256":"0c449249696e359f07e2ef6c145c55cf3683ca9e7fec9d946fc846adbd616f50","schema_version":"1.0","event_id":"sha256:0c449249696e359f07e2ef6c145c55cf3683ca9e7fec9d946fc846adbd616f50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ECY2JAEYXVPHJMIAUNUEBKLIU3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rapid mixing for Gibbs measures in Riemannian manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","stat.ML"],"primary_cat":"math-ph","authors_text":"\\'Angela Capel, Angelo Lucia, David P\\'erez-Garc\\'ia, Marco Castrill\\'on-L\\'opez, Pablo P\\'aez-Velasco, Sofyan Iblisdir","submitted_at":"2026-06-11T15:11:54Z","abstract_excerpt":"Langevin dynamics on Riemannian manifolds is analyzed. Conditions ensuring the existence of a suitable logarithmic Sobolev inequality (rapid mixing to the Gibbs measure) are identified. These conditions involve the curvature of the manifold, the inverse temperature, escaping directions from saddle points, and exclude barren plateaus and spurious local minima. We show that when these conditions are met, mixing times polynomial in the dimension of the manifold are achievable. This result is obtained through a relation between Langevin processes in the domain and in the image of a Riemannian subm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13453","kind":"arxiv","version":1},"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/2606.13453/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-12T01:10:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QynNuJKXr1zByzXVqmkc8cD9LP/beF7iVHB3O/OFS9Yeaa7aG/maRz7UOsRURm/L94VtVmfuVcwIwNQF1HSEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T19:41:36.777435Z"},"content_sha256":"18d300fd85b553a21c423ce489b93fc60510b04df2cf7bc963945f81442621c0","schema_version":"1.0","event_id":"sha256:18d300fd85b553a21c423ce489b93fc60510b04df2cf7bc963945f81442621c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ECY2JAEYXVPHJMIAUNUEBKLIU3/bundle.json","state_url":"https://pith.science/pith/ECY2JAEYXVPHJMIAUNUEBKLIU3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ECY2JAEYXVPHJMIAUNUEBKLIU3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T19:41:36Z","links":{"resolver":"https://pith.science/pith/ECY2JAEYXVPHJMIAUNUEBKLIU3","bundle":"https://pith.science/pith/ECY2JAEYXVPHJMIAUNUEBKLIU3/bundle.json","state":"https://pith.science/pith/ECY2JAEYXVPHJMIAUNUEBKLIU3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ECY2JAEYXVPHJMIAUNUEBKLIU3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ECY2JAEYXVPHJMIAUNUEBKLIU3","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":"1181fdf4c555242166fbad9af857361d8d15eb700e7564b2e397a683a40ccaaf","cross_cats_sorted":["math.MP","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T15:11:54Z","title_canon_sha256":"5f431745015e98b40e1a4860b084d3783fe986be4292c2a12ca9936663c30781"},"schema_version":"1.0","source":{"id":"2606.13453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.13453","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.13453v1","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.13453","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"pith_short_12","alias_value":"ECY2JAEYXVPH","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"pith_short_16","alias_value":"ECY2JAEYXVPHJMIA","created_at":"2026-06-12T01:10:03Z"},{"alias_kind":"pith_short_8","alias_value":"ECY2JAEY","created_at":"2026-06-12T01:10:03Z"}],"graph_snapshots":[{"event_id":"sha256:18d300fd85b553a21c423ce489b93fc60510b04df2cf7bc963945f81442621c0","target":"graph","created_at":"2026-06-12T01:10:03Z","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/2606.13453/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Langevin dynamics on Riemannian manifolds is analyzed. Conditions ensuring the existence of a suitable logarithmic Sobolev inequality (rapid mixing to the Gibbs measure) are identified. These conditions involve the curvature of the manifold, the inverse temperature, escaping directions from saddle points, and exclude barren plateaus and spurious local minima. We show that when these conditions are met, mixing times polynomial in the dimension of the manifold are achievable. This result is obtained through a relation between Langevin processes in the domain and in the image of a Riemannian subm","authors_text":"\\'Angela Capel, Angelo Lucia, David P\\'erez-Garc\\'ia, Marco Castrill\\'on-L\\'opez, Pablo P\\'aez-Velasco, Sofyan Iblisdir","cross_cats":["math.MP","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T15:11:54Z","title":"Rapid mixing for Gibbs measures in Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.13453","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":"sha256:0c449249696e359f07e2ef6c145c55cf3683ca9e7fec9d946fc846adbd616f50","target":"record","created_at":"2026-06-12T01:10:03Z","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":"1181fdf4c555242166fbad9af857361d8d15eb700e7564b2e397a683a40ccaaf","cross_cats_sorted":["math.MP","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-06-11T15:11:54Z","title_canon_sha256":"5f431745015e98b40e1a4860b084d3783fe986be4292c2a12ca9936663c30781"},"schema_version":"1.0","source":{"id":"2606.13453","kind":"arxiv","version":1}},"canonical_sha256":"20b1a48098bd5e74b100a36840a968a6f4b0cd16eaa7d408b5235ffe4736740b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20b1a48098bd5e74b100a36840a968a6f4b0cd16eaa7d408b5235ffe4736740b","first_computed_at":"2026-06-12T01:10:03.328882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:10:03.328882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"viQamgLHNihzXTpv/sEWa+fUkeOJeHvF9EbhtV0pZUXFQfPE83XyhQh+3qvMT97qaW3bQ6G0RXiCuGeunHnRCw==","signature_status":"signed_v1","signed_at":"2026-06-12T01:10:03.329750Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.13453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c449249696e359f07e2ef6c145c55cf3683ca9e7fec9d946fc846adbd616f50","sha256:18d300fd85b553a21c423ce489b93fc60510b04df2cf7bc963945f81442621c0"],"state_sha256":"aba850d23a659fa41dcec9be6dd37a955d65776e0070f3fafbbeb00a5374081e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xarvN4wHp/EKTroup6CFnmp9uQPCQbD8OE/H3aMUHb6iAvIEDJRyL9CMGYMNudqzcD6MSW6mOTmgj0Nicc9DCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T19:41:36.779334Z","bundle_sha256":"d1382f05a0d86b187767664755a0cf6f804ee366e2621beb804b55ded18af2f1"}}