{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ARPH4I3LFCG3L57ULRINWYXSO6","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":"6368935fe612c0558d00a7d84fe2f8aa05e8c2d57caf0361485a51268b88104e","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-22T07:21:59Z","title_canon_sha256":"60165fe268dbf3b048e9465bb234db3839a8c435d304f78aa7f805ec94a8825a"},"schema_version":"1.0","source":{"id":"2607.19839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19839","created_at":"2026-07-23T01:24:02Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19839v1","created_at":"2026-07-23T01:24:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19839","created_at":"2026-07-23T01:24:02Z"},{"alias_kind":"pith_short_12","alias_value":"ARPH4I3LFCG3","created_at":"2026-07-23T01:24:02Z"},{"alias_kind":"pith_short_16","alias_value":"ARPH4I3LFCG3L57U","created_at":"2026-07-23T01:24:02Z"},{"alias_kind":"pith_short_8","alias_value":"ARPH4I3L","created_at":"2026-07-23T01:24:02Z"}],"graph_snapshots":[{"event_id":"sha256:3ac96b35af6931f33416d3d8d9489cb997007619d4f933e93dcb375a8bd78026","target":"graph","created_at":"2026-07-23T01:24:02Z","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/2607.19839/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Martingale posteriors quantify uncertainty by forward-imputing observations from one-step-ahead predictive distributions, but implementations stop after finitely many imputations. For the empirical P\\'olya-urn posterior of a quantile the law of the stopped state is derived. The quantile of the stopped urn measure keeps the familiar martingale tail-sum variance fraction; the deployed stochastic-approximation tracker with frozen gain $c$ does not. Its variance carries an explicit factor $G_a$ with $a=cf_0(q_\\tau)$, which may fall below or exceed the tail fraction, and a density-adapted gain rest","authors_text":"Nam Anh Le","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-22T07:21:59Z","title":"Finite-horizon quantile martingale posteriors: raw-urn laws and matrix-gain regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19839","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":"sha256:959bbd04a833a7cfd8660bd68fe2387547a728d756507e4ced2afab185efac75","target":"record","created_at":"2026-07-23T01:24:02Z","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":"6368935fe612c0558d00a7d84fe2f8aa05e8c2d57caf0361485a51268b88104e","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-22T07:21:59Z","title_canon_sha256":"60165fe268dbf3b048e9465bb234db3839a8c435d304f78aa7f805ec94a8825a"},"schema_version":"1.0","source":{"id":"2607.19839","kind":"arxiv","version":1}},"canonical_sha256":"045e7e236b288db5f7f45c50db62f27782caa11639a7d1a8934c634881f379ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"045e7e236b288db5f7f45c50db62f27782caa11639a7d1a8934c634881f379ef","first_computed_at":"2026-07-23T01:24:02.939655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-23T01:24:02.939655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UwshMc6Z+3yNo5IWoIdmujt1ZB8/+6lcDrK66G3vvoRJU5sJVzpMlrC6FmrxLHGQEX7W0qwQyC9UECIyMd51Dg==","signature_status":"signed_v1","signed_at":"2026-07-23T01:24:02.940535Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.19839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:959bbd04a833a7cfd8660bd68fe2387547a728d756507e4ced2afab185efac75","sha256:3ac96b35af6931f33416d3d8d9489cb997007619d4f933e93dcb375a8bd78026"],"state_sha256":"e35f51f091b4d74c4149cbd25c7412d5cb494d2a1b940826aeb7be8226124b8f"}