{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CKIL56GKC3D3A3QVS6IPSFJCEG","short_pith_number":"pith:CKIL56GK","canonical_record":{"source":{"id":"2502.04208","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-06T16:48:47Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"06c2e89c4fd2a7250e45507c9a7bd43b676d7f4505824feb9e077e9090d62250","abstract_canon_sha256":"5305c18f56f951131b40b49543511ebcf91618228b0e846ec91755243ab8b031"},"schema_version":"1.0"},"canonical_sha256":"1290bef8ca16c7b06e159790f9152221810fce1fd3acb0c277c0fff4894d7ec7","source":{"kind":"arxiv","id":"2502.04208","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.04208","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"2502.04208v2","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04208","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"CKIL56GKC3D3","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"pith_short_16","alias_value":"CKIL56GKC3D3A3QV","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"pith_short_8","alias_value":"CKIL56GK","created_at":"2026-07-05T10:10:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CKIL56GKC3D3A3QVS6IPSFJCEG","target":"record","payload":{"canonical_record":{"source":{"id":"2502.04208","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-06T16:48:47Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"06c2e89c4fd2a7250e45507c9a7bd43b676d7f4505824feb9e077e9090d62250","abstract_canon_sha256":"5305c18f56f951131b40b49543511ebcf91618228b0e846ec91755243ab8b031"},"schema_version":"1.0"},"canonical_sha256":"1290bef8ca16c7b06e159790f9152221810fce1fd3acb0c277c0fff4894d7ec7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:49.728864Z","signature_b64":"o7rgN1SwZP9+ZBplVcCcRSueJSD+b+YSQ9CpH1UlevzMOzSli5z6oB7/nHzhJ/ZAc4oLzyy3SsAUR18zNe+jDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1290bef8ca16c7b06e159790f9152221810fce1fd3acb0c277c0fff4894d7ec7","last_reissued_at":"2026-07-05T10:10:49.728442Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:49.728442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.04208","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:10:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UBanWGEWSe3Y7st7d/Wou+TTWNn0esMCD9IdRuaP4pnfyiUiVYVkABeP/z4kndRRiqWtHDQM3KxYeiglBivnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:31:21.274027Z"},"content_sha256":"882fa9650cf319bdb46379f6dce872e4020f6c39b4fe6d61c3add1385dd4ba93","schema_version":"1.0","event_id":"sha256:882fa9650cf319bdb46379f6dce872e4020f6c39b4fe6d61c3add1385dd4ba93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CKIL56GKC3D3A3QVS6IPSFJCEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Supermartingales for One-Sided Tests: Sufficient Monotone Likelihood Ratios are Sufficient","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Peter D. Gr\\\"unwald, Wouter M. Koolen","submitted_at":"2025-02-06T16:48:47Z","abstract_excerpt":"The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of falsely rejecting the null. For one-sided sequential tests, which reject when the t-statistic is too positive, a natural question is whether they also control false rejection when the true mean is negative. We prove that this is the case using monotone likelihood ratios and sufficient statistics. We develop applications to the scale-invariant t-test, the loca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04208","kind":"arxiv","version":2},"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/2502.04208/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":"2026-07-05T10:10:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WMRxQKojbEF5ZmNz6NGZa5vcfZi4X9OqsBGS1lCJ7iAsukl39+GU2h7GqF23MsSq8E4zhQSrhftdHjG6vqZsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:31:21.274621Z"},"content_sha256":"9f1e3321907bfddbf3374061f022484870392117582863254e9974bb2e00761e","schema_version":"1.0","event_id":"sha256:9f1e3321907bfddbf3374061f022484870392117582863254e9974bb2e00761e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKIL56GKC3D3A3QVS6IPSFJCEG/bundle.json","state_url":"https://pith.science/pith/CKIL56GKC3D3A3QVS6IPSFJCEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKIL56GKC3D3A3QVS6IPSFJCEG/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":"2026-08-10T20:31:21Z","links":{"resolver":"https://pith.science/pith/CKIL56GKC3D3A3QVS6IPSFJCEG","bundle":"https://pith.science/pith/CKIL56GKC3D3A3QVS6IPSFJCEG/bundle.json","state":"https://pith.science/pith/CKIL56GKC3D3A3QVS6IPSFJCEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKIL56GKC3D3A3QVS6IPSFJCEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CKIL56GKC3D3A3QVS6IPSFJCEG","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":"5305c18f56f951131b40b49543511ebcf91618228b0e846ec91755243ab8b031","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-06T16:48:47Z","title_canon_sha256":"06c2e89c4fd2a7250e45507c9a7bd43b676d7f4505824feb9e077e9090d62250"},"schema_version":"1.0","source":{"id":"2502.04208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.04208","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"2502.04208v2","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.04208","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"CKIL56GKC3D3","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"pith_short_16","alias_value":"CKIL56GKC3D3A3QV","created_at":"2026-07-05T10:10:49Z"},{"alias_kind":"pith_short_8","alias_value":"CKIL56GK","created_at":"2026-07-05T10:10:49Z"}],"graph_snapshots":[{"event_id":"sha256:9f1e3321907bfddbf3374061f022484870392117582863254e9974bb2e00761e","target":"graph","created_at":"2026-07-05T10:10:49Z","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/2502.04208/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of falsely rejecting the null. For one-sided sequential tests, which reject when the t-statistic is too positive, a natural question is whether they also control false rejection when the true mean is negative. We prove that this is the case using monotone likelihood ratios and sufficient statistics. We develop applications to the scale-invariant t-test, the loca","authors_text":"Peter D. Gr\\\"unwald, Wouter M. Koolen","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-06T16:48:47Z","title":"Supermartingales for One-Sided Tests: Sufficient Monotone Likelihood Ratios are Sufficient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.04208","kind":"arxiv","version":2},"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":"sha256:882fa9650cf319bdb46379f6dce872e4020f6c39b4fe6d61c3add1385dd4ba93","target":"record","created_at":"2026-07-05T10:10:49Z","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":"5305c18f56f951131b40b49543511ebcf91618228b0e846ec91755243ab8b031","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-02-06T16:48:47Z","title_canon_sha256":"06c2e89c4fd2a7250e45507c9a7bd43b676d7f4505824feb9e077e9090d62250"},"schema_version":"1.0","source":{"id":"2502.04208","kind":"arxiv","version":2}},"canonical_sha256":"1290bef8ca16c7b06e159790f9152221810fce1fd3acb0c277c0fff4894d7ec7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1290bef8ca16c7b06e159790f9152221810fce1fd3acb0c277c0fff4894d7ec7","first_computed_at":"2026-07-05T10:10:49.728442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:10:49.728442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o7rgN1SwZP9+ZBplVcCcRSueJSD+b+YSQ9CpH1UlevzMOzSli5z6oB7/nHzhJ/ZAc4oLzyy3SsAUR18zNe+jDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:10:49.728864Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.04208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:882fa9650cf319bdb46379f6dce872e4020f6c39b4fe6d61c3add1385dd4ba93","sha256:9f1e3321907bfddbf3374061f022484870392117582863254e9974bb2e00761e"],"state_sha256":"71d4c70861491f8e080979b1a0fb55728b9bbb6642617669ba0f6e59207e5b13"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4+TPQFM90+fQBr0uPwU8l9a8VPwny3tl/0d6DGacsUh3/hveYFrpuSIu6VdLJF5jb9J51ugVhnPGt9y76F8DBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T20:31:21.280295Z","bundle_sha256":"76ef3377e1f267f7bb43e35439641f032d9b37ff92671c0ad4c883ceeaad6f41"}}