{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NFXOEULCXWN7FY7YXGW3HAOGM3","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":"393d547cb6dd828c38df7117d51c54051099c56781cf1c3b93ef928ec9e80b04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-01T23:39:05Z","title_canon_sha256":"8e2601e590aa0b44ad0d5c567a0bd68a9ce25e540ff2d5c893d7b2635582ebf0"},"schema_version":"1.0","source":{"id":"1412.0736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0736","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0736v1","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0736","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"NFXOEULCXWN7","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NFXOEULCXWN7FY7Y","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NFXOEULC","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:fc71fe816fabc70f8b24bc62562e2273eed26278b601f2b9af23709e9bb98e17","target":"graph","created_at":"2026-05-18T02:32:21Z","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"},"paper":{"abstract_excerpt":"We introduce a new distance, a Lipschitz-Prokhorov distance $d_{LP}$, on the set $\\mathcal {PM}$ of isomorphism classes of pairs $(X, P)$ where $X$ is a compact metric space and $P$ is the law of a continuous stochastic process on $X$. We show that $(\\mathcal {PM}, d_{LP})$ is a complete metric space. For Markov processes on Riemannian manifolds, we study relative compactness and convergence.","authors_text":"Kohei Suzuki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-01T23:39:05Z","title":"Convergence of continuous stochastic processes on compact metric spaces converging in the Lipschitz distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0736","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":"sha256:5a6b4d0b943ca8aee970ddcb2ff13665f56bc7d6d5b7fff2e18b8b0f70ecc09f","target":"record","created_at":"2026-05-18T02:32:21Z","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":"393d547cb6dd828c38df7117d51c54051099c56781cf1c3b93ef928ec9e80b04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-01T23:39:05Z","title_canon_sha256":"8e2601e590aa0b44ad0d5c567a0bd68a9ce25e540ff2d5c893d7b2635582ebf0"},"schema_version":"1.0","source":{"id":"1412.0736","kind":"arxiv","version":1}},"canonical_sha256":"696ee25162bd9bf2e3f8b9adb381c666c462216a9e734c4494bcbd0ed4ac0204","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"696ee25162bd9bf2e3f8b9adb381c666c462216a9e734c4494bcbd0ed4ac0204","first_computed_at":"2026-05-18T02:32:21.295172Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:21.295172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XHtokj1UlahgTCWTE5wRpdWgGmKsS9xqudcMkL8kS2+KykXlcf6GZnFqu5xQOhyFQXDSWVperIJ5rn+4sMClAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:21.295557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a6b4d0b943ca8aee970ddcb2ff13665f56bc7d6d5b7fff2e18b8b0f70ecc09f","sha256:fc71fe816fabc70f8b24bc62562e2273eed26278b601f2b9af23709e9bb98e17"],"state_sha256":"f9c4f1a277507cca54f9e44f7e81034dc8bab92f765174bbed8fb943485c66c8"}