{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:V4TSTATSACHRW3HEI65ZQ5V3TD","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":"6ad908beefe7e6f6576eb2700c42dc1a3573094052ce569a37173b6712804cf7","cross_cats_sorted":["q-fin.MF"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-11-18T09:30:02Z","title_canon_sha256":"f7240dd110ed80f8ef2074c43dd2ae39b07f7baa7bfd03c792d8ed7357c5fbe5"},"schema_version":"1.0","source":{"id":"2411.11408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.11408","created_at":"2026-07-05T09:36:55Z"},{"alias_kind":"arxiv_version","alias_value":"2411.11408v1","created_at":"2026-07-05T09:36:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.11408","created_at":"2026-07-05T09:36:55Z"},{"alias_kind":"pith_short_12","alias_value":"V4TSTATSACHR","created_at":"2026-07-05T09:36:55Z"},{"alias_kind":"pith_short_16","alias_value":"V4TSTATSACHRW3HE","created_at":"2026-07-05T09:36:55Z"},{"alias_kind":"pith_short_8","alias_value":"V4TSTATS","created_at":"2026-07-05T09:36:55Z"}],"graph_snapshots":[{"event_id":"sha256:3cbe9857d6cdc5188fe9ae9c7ad17c0d65f45840e0dc435c540d0d81a91a60b9","target":"graph","created_at":"2026-07-05T09:36:55Z","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/2411.11408/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In continuous time, the laws of martingales tend to be singular to each other. Notably, N. Gantert introduced the concept of specific relative entropy between real-valued continuous martingales, defined as a scaling limit of finite-dimensional relative entropies, and showed that this quantity is non-trivial despite the aforementioned mutual singularity of martingale laws.\n  Our main mathematical contribution is to extend this object, originally restricted to one-dimensional martingales, to multiple dimensions. Among other results, we establish that Gantert's inequality, bounding the specific r","authors_text":"Edoardo Kimani Bellotto, Julio Backhoff","cross_cats":["q-fin.MF"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-11-18T09:30:02Z","title":"Multidimensional specific relative entropy between continuous martingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.11408","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:f76825118646378a1dc1e9b6f2d910591ba3620ffcfd6e5d9d93d91ae503505b","target":"record","created_at":"2026-07-05T09:36:55Z","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":"6ad908beefe7e6f6576eb2700c42dc1a3573094052ce569a37173b6712804cf7","cross_cats_sorted":["q-fin.MF"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-11-18T09:30:02Z","title_canon_sha256":"f7240dd110ed80f8ef2074c43dd2ae39b07f7baa7bfd03c792d8ed7357c5fbe5"},"schema_version":"1.0","source":{"id":"2411.11408","kind":"arxiv","version":1}},"canonical_sha256":"af27298272008f1b6ce447bb9876bb98cd9e7d8ec0d926a750ccebfaa371a648","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af27298272008f1b6ce447bb9876bb98cd9e7d8ec0d926a750ccebfaa371a648","first_computed_at":"2026-07-05T09:36:55.928037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:36:55.928037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wMssZepdSUoGnGLrmmO56jMVzzGUeYQY7YiWxqknIWEIAdeGHXJbz9h/ZQWK3i2d1dE95bQXaON6p6i3Vp6FCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:36:55.928611Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.11408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f76825118646378a1dc1e9b6f2d910591ba3620ffcfd6e5d9d93d91ae503505b","sha256:3cbe9857d6cdc5188fe9ae9c7ad17c0d65f45840e0dc435c540d0d81a91a60b9"],"state_sha256":"11ea20bdfa54c6af4943f90927ed423446583ba2441035a5786ad61b7cac0fa4"}