{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YK4T466TRCKVP4S3ONPUWBSIED","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":"de33d554efb634cfcbc6d31c8ce3c826738b5cf2308af1a36d06c65b0ca67e44","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-08T01:13:29Z","title_canon_sha256":"fd5b4c276fbde578a2d9e9541dc806fca775b3e10e925969f3fe62e5ebb4b943"},"schema_version":"1.0","source":{"id":"1711.02784","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02784","created_at":"2026-05-18T00:31:01Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02784v1","created_at":"2026-05-18T00:31:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02784","created_at":"2026-05-18T00:31:01Z"},{"alias_kind":"pith_short_12","alias_value":"YK4T466TRCKV","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YK4T466TRCKVP4S3","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YK4T466T","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d950c63ed2d3a3a796734041f016681f9b9cd46c42dc541a64f033b384a25bdf","target":"graph","created_at":"2026-05-18T00:31:01Z","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":"Given an initial (resp., terminal) probability measure $\\mu$ (resp., $\\nu$) on $\\mathbb{R}^d$, we characterize those optimal stopping times $\\tau$ that maximize or minimize the functional $\\mathbb{E} |B_0 - B_\\tau|^{\\alpha}$, $\\alpha > 0$, where $(B_t)_t$ is Brownian motion with initial law $B_0\\sim \\mu$ and with final distribution --once stopped at $\\tau$-- equal to $B_\\tau\\sim \\nu$.\n  The existence of such stopping times is guaranteed by Skorohod-type embeddings of probability measures in \"subharmoic order\" into Brownian motion. This problem is equivalent to an optimal mass transport problem","authors_text":"Nassif Ghoussoub, Tongseok Lim, Young-Heon Kim","cross_cats":["math.OC","q-fin.MF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-08T01:13:29Z","title":"Optimal Brownian Stopping between radially symmetric marginals in general dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02784","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":"sha256:6941f5b55698e27b62d10d6573d150971c14a483b81db6e3c55583c5c800b833","target":"record","created_at":"2026-05-18T00:31:01Z","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":"de33d554efb634cfcbc6d31c8ce3c826738b5cf2308af1a36d06c65b0ca67e44","cross_cats_sorted":["math.OC","q-fin.MF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-08T01:13:29Z","title_canon_sha256":"fd5b4c276fbde578a2d9e9541dc806fca775b3e10e925969f3fe62e5ebb4b943"},"schema_version":"1.0","source":{"id":"1711.02784","kind":"arxiv","version":1}},"canonical_sha256":"c2b93e7bd3889557f25b735f4b064820ecb3a63e6da70c662b48d97ff4e6cfec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2b93e7bd3889557f25b735f4b064820ecb3a63e6da70c662b48d97ff4e6cfec","first_computed_at":"2026-05-18T00:31:01.776719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:01.776719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TRu8ZaOMbNy/qtNJhA5RoOfFmvQDkt5GznPfgmQwIU5VqW3mpNsylKfwaqphjHkDWVM7oOZ6b5i/nAniqysyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:01.777422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02784","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6941f5b55698e27b62d10d6573d150971c14a483b81db6e3c55583c5c800b833","sha256:d950c63ed2d3a3a796734041f016681f9b9cd46c42dc541a64f033b384a25bdf"],"state_sha256":"e7fb2fa8f6af5ef87906bb0479b27d89c7d269bc6aa2a236f6ed12b2a2a35a49"}