{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:SJHF46DK77PDM7RCERT3IBZZHJ","short_pith_number":"pith:SJHF46DK","canonical_record":{"source":{"id":"1807.04635","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-10T11:50:39Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"b6327ebfc92cd50df1fb1b48cf0854e0e5d2404a42b9cf5a5c6cc968e168ae85","abstract_canon_sha256":"487ddd01512b6bf41d5f1cf1585783ad2aae95967b17a199b2e2659392de6ce5"},"schema_version":"1.0"},"canonical_sha256":"924e5e786affde367e222467b407393a7651fdd685898af990da6cbb066c8262","source":{"kind":"arxiv","id":"1807.04635","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04635","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04635v2","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04635","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"SJHF46DK77PD","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SJHF46DK77PDM7RC","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SJHF46DK","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:SJHF46DK77PDM7RCERT3IBZZHJ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.04635","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-10T11:50:39Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"b6327ebfc92cd50df1fb1b48cf0854e0e5d2404a42b9cf5a5c6cc968e168ae85","abstract_canon_sha256":"487ddd01512b6bf41d5f1cf1585783ad2aae95967b17a199b2e2659392de6ce5"},"schema_version":"1.0"},"canonical_sha256":"924e5e786affde367e222467b407393a7651fdd685898af990da6cbb066c8262","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:22.556242Z","signature_b64":"OuDJbQ0XnULbBvJlDf8sjnBynUN9QqTeP3c4Nox4fPa/bJEvXq5XFLLnk4dSJehMB+lJJGcLHDboy7VudLUbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"924e5e786affde367e222467b407393a7651fdd685898af990da6cbb066c8262","last_reissued_at":"2026-05-17T23:48:22.555667Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:22.555667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.04635","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":"2026-05-17T23:48:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A6EUVHATk/sh7I/DhnSxU8ObCRMogroBYN3Z4mho0K/oWNPFJkjH/HYvr2wCeiescuR6MbDylfuDhyVxzIE6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:30:21.447844Z"},"content_sha256":"4d1fad92ac5da40f912da09506ecb635ec8813f945baad6fb6ebd76d661b29ac","schema_version":"1.0","event_id":"sha256:4d1fad92ac5da40f912da09506ecb635ec8813f945baad6fb6ebd76d661b29ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:SJHF46DK77PDM7RCERT3IBZZHJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonous betting strategies in warped casinos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.LO","authors_text":"Andrew Lewis-Pye, George Barmpalias, Nan Fang","submitted_at":"2018-07-10T11:50:39Z","abstract_excerpt":"Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful `separable' strategy, in the sense that it does not use the winnings from betting on red in order to bet on black, and vice-versa? We study this question from an algorithmic point of view and observe that every strategy $M$ can be replaced by a separable strategy which is computable from $M$ and successful on any outcome-sequence where $M$ is successful. We then consider the case of mixtures and show: (a) there exists an effective mixture of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04635","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":""},"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":"2026-05-17T23:48:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxnxZwC1TmhF8DS6yMIpXTdOVwZJpLKdmlEaQkLwPe/rMGBDsJoYC9rMd6VW0LizB0yaO0nM5OXoH++g1ZSpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:30:21.448189Z"},"content_sha256":"e0cdb79fd0ac73c25aff0a6cd37063d3d185bc5ecc841e606e4b5ec3493c189b","schema_version":"1.0","event_id":"sha256:e0cdb79fd0ac73c25aff0a6cd37063d3d185bc5ecc841e606e4b5ec3493c189b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJHF46DK77PDM7RCERT3IBZZHJ/bundle.json","state_url":"https://pith.science/pith/SJHF46DK77PDM7RCERT3IBZZHJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJHF46DK77PDM7RCERT3IBZZHJ/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":"2026-05-28T01:30:21Z","links":{"resolver":"https://pith.science/pith/SJHF46DK77PDM7RCERT3IBZZHJ","bundle":"https://pith.science/pith/SJHF46DK77PDM7RCERT3IBZZHJ/bundle.json","state":"https://pith.science/pith/SJHF46DK77PDM7RCERT3IBZZHJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJHF46DK77PDM7RCERT3IBZZHJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SJHF46DK77PDM7RCERT3IBZZHJ","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":"487ddd01512b6bf41d5f1cf1585783ad2aae95967b17a199b2e2659392de6ce5","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-10T11:50:39Z","title_canon_sha256":"b6327ebfc92cd50df1fb1b48cf0854e0e5d2404a42b9cf5a5c6cc968e168ae85"},"schema_version":"1.0","source":{"id":"1807.04635","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.04635","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"1807.04635v2","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.04635","created_at":"2026-05-17T23:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"SJHF46DK77PD","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SJHF46DK77PDM7RC","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SJHF46DK","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:e0cdb79fd0ac73c25aff0a6cd37063d3d185bc5ecc841e606e4b5ec3493c189b","target":"graph","created_at":"2026-05-17T23:48:22Z","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":"Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful `separable' strategy, in the sense that it does not use the winnings from betting on red in order to bet on black, and vice-versa? We study this question from an algorithmic point of view and observe that every strategy $M$ can be replaced by a separable strategy which is computable from $M$ and successful on any outcome-sequence where $M$ is successful. We then consider the case of mixtures and show: (a) there exists an effective mixture of","authors_text":"Andrew Lewis-Pye, George Barmpalias, Nan Fang","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-10T11:50:39Z","title":"Monotonous betting strategies in warped casinos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04635","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":"sha256:4d1fad92ac5da40f912da09506ecb635ec8813f945baad6fb6ebd76d661b29ac","target":"record","created_at":"2026-05-17T23:48:22Z","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":"487ddd01512b6bf41d5f1cf1585783ad2aae95967b17a199b2e2659392de6ce5","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-07-10T11:50:39Z","title_canon_sha256":"b6327ebfc92cd50df1fb1b48cf0854e0e5d2404a42b9cf5a5c6cc968e168ae85"},"schema_version":"1.0","source":{"id":"1807.04635","kind":"arxiv","version":2}},"canonical_sha256":"924e5e786affde367e222467b407393a7651fdd685898af990da6cbb066c8262","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"924e5e786affde367e222467b407393a7651fdd685898af990da6cbb066c8262","first_computed_at":"2026-05-17T23:48:22.555667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:22.555667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OuDJbQ0XnULbBvJlDf8sjnBynUN9QqTeP3c4Nox4fPa/bJEvXq5XFLLnk4dSJehMB+lJJGcLHDboy7VudLUbAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:22.556242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.04635","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d1fad92ac5da40f912da09506ecb635ec8813f945baad6fb6ebd76d661b29ac","sha256:e0cdb79fd0ac73c25aff0a6cd37063d3d185bc5ecc841e606e4b5ec3493c189b"],"state_sha256":"68697d6b29ed16652bccfa751dade660d3f8e2b8d9c916d68d0d36d300bdb4a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSyFxswzrW2xcySgWbQehYUQ0BbA5TT6WGBqNntj5NZHJKpDwl6Yb5tSppnvXv7lBUO+wtBfjdRzuShFIrm+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:30:21.450453Z","bundle_sha256":"7629e200f179aea7a4d6304109f3cc03c75da32fc49f07e6626f3e46ce14c4e0"}}