{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JSNWZOODVHWP7FP5BOCKEYMR2S","short_pith_number":"pith:JSNWZOOD","canonical_record":{"source":{"id":"1307.3951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-15T14:06:14Z","cross_cats_sorted":[],"title_canon_sha256":"e8774f81ab1c5edf17246add1a4841780e5326a9e3730fe5e69bcfe7fcbf5452","abstract_canon_sha256":"1b3ba7021ce01e2cf8db01ed25aa57dfd3558134de46330f036f8343597d8bf3"},"schema_version":"1.0"},"canonical_sha256":"4c9b6cb9c3a9ecff95fd0b84a26191d488c330e76728fb1772bd1f07dc10b3de","source":{"kind":"arxiv","id":"1307.3951","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3951","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3951v1","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3951","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"JSNWZOODVHWP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JSNWZOODVHWP7FP5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JSNWZOOD","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JSNWZOODVHWP7FP5BOCKEYMR2S","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-15T14:06:14Z","cross_cats_sorted":[],"title_canon_sha256":"e8774f81ab1c5edf17246add1a4841780e5326a9e3730fe5e69bcfe7fcbf5452","abstract_canon_sha256":"1b3ba7021ce01e2cf8db01ed25aa57dfd3558134de46330f036f8343597d8bf3"},"schema_version":"1.0"},"canonical_sha256":"4c9b6cb9c3a9ecff95fd0b84a26191d488c330e76728fb1772bd1f07dc10b3de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:35.465577Z","signature_b64":"PVrdSNeLqtc4VJdHZTEB6vVRbz7zxltBdl6AzxwrktCUsK6kaywiXNo8Rsf0u+aZowE6Q2SwthWsU7XcUMlUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c9b6cb9c3a9ecff95fd0b84a26191d488c330e76728fb1772bd1f07dc10b3de","last_reissued_at":"2026-05-17T23:53:35.464805Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:35.464805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3951","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+aOXuwVgsa8ZFvp0vihtFFcKICVwa9bUKq4BL8xvgwDuN2QeK2PAITH+t7IP4MHupfNOTd/sggyjSjgEDwmWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:27:32.685879Z"},"content_sha256":"0359ee1fa9deff8e60c9c0db3a0527b3fef057fabb232c3cee2ab049ce040f0c","schema_version":"1.0","event_id":"sha256:0359ee1fa9deff8e60c9c0db3a0527b3fef057fabb232c3cee2ab049ce040f0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JSNWZOODVHWP7FP5BOCKEYMR2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Determinacy and indeterminacy of games played on complete metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David S. Simmons, Lior Fishman, Tue Ly","submitted_at":"2013-07-15T14:06:14Z","abstract_excerpt":"Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address determinacy and indeterminacy questions regarding Schmidt's game and its variations, as well as more general games played on complete metric spaces (e.g. fractals). We show that except for certain exceptional cases, these games are undetermined on Bernstein sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3951","kind":"arxiv","version":1},"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":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TiuulrwnQJeM35CQi8UzydKOrXdQRVhCIlD1GaW8QU5Tfl626AshfD3qd1flDFnIadevBIUnM9jpI2duz6IgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:27:32.686402Z"},"content_sha256":"82cd911a32539d1565aed0c914252bdca9755dc117dabc0645660ee84c0a4f8c","schema_version":"1.0","event_id":"sha256:82cd911a32539d1565aed0c914252bdca9755dc117dabc0645660ee84c0a4f8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JSNWZOODVHWP7FP5BOCKEYMR2S/bundle.json","state_url":"https://pith.science/pith/JSNWZOODVHWP7FP5BOCKEYMR2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JSNWZOODVHWP7FP5BOCKEYMR2S/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":"2026-06-05T00:27:32Z","links":{"resolver":"https://pith.science/pith/JSNWZOODVHWP7FP5BOCKEYMR2S","bundle":"https://pith.science/pith/JSNWZOODVHWP7FP5BOCKEYMR2S/bundle.json","state":"https://pith.science/pith/JSNWZOODVHWP7FP5BOCKEYMR2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JSNWZOODVHWP7FP5BOCKEYMR2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JSNWZOODVHWP7FP5BOCKEYMR2S","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":"1b3ba7021ce01e2cf8db01ed25aa57dfd3558134de46330f036f8343597d8bf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-15T14:06:14Z","title_canon_sha256":"e8774f81ab1c5edf17246add1a4841780e5326a9e3730fe5e69bcfe7fcbf5452"},"schema_version":"1.0","source":{"id":"1307.3951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3951","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3951v1","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3951","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"JSNWZOODVHWP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JSNWZOODVHWP7FP5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JSNWZOOD","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:82cd911a32539d1565aed0c914252bdca9755dc117dabc0645660ee84c0a4f8c","target":"graph","created_at":"2026-05-17T23:53:35Z","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":"Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address determinacy and indeterminacy questions regarding Schmidt's game and its variations, as well as more general games played on complete metric spaces (e.g. fractals). We show that except for certain exceptional cases, these games are undetermined on Bernstein sets.","authors_text":"David S. Simmons, Lior Fishman, Tue Ly","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-15T14:06:14Z","title":"Determinacy and indeterminacy of games played on complete metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3951","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":"sha256:0359ee1fa9deff8e60c9c0db3a0527b3fef057fabb232c3cee2ab049ce040f0c","target":"record","created_at":"2026-05-17T23:53:35Z","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":"1b3ba7021ce01e2cf8db01ed25aa57dfd3558134de46330f036f8343597d8bf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-15T14:06:14Z","title_canon_sha256":"e8774f81ab1c5edf17246add1a4841780e5326a9e3730fe5e69bcfe7fcbf5452"},"schema_version":"1.0","source":{"id":"1307.3951","kind":"arxiv","version":1}},"canonical_sha256":"4c9b6cb9c3a9ecff95fd0b84a26191d488c330e76728fb1772bd1f07dc10b3de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c9b6cb9c3a9ecff95fd0b84a26191d488c330e76728fb1772bd1f07dc10b3de","first_computed_at":"2026-05-17T23:53:35.464805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:35.464805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PVrdSNeLqtc4VJdHZTEB6vVRbz7zxltBdl6AzxwrktCUsK6kaywiXNo8Rsf0u+aZowE6Q2SwthWsU7XcUMlUAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:35.465577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0359ee1fa9deff8e60c9c0db3a0527b3fef057fabb232c3cee2ab049ce040f0c","sha256:82cd911a32539d1565aed0c914252bdca9755dc117dabc0645660ee84c0a4f8c"],"state_sha256":"d9ddd0584ea89bfc457202cf99a967f74ad25ad2ffe4522e1f4dcfcd215474b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XdOwH1VDroWjRxuxo8+bXmbpXew+5DG6xkVCOqVoPYU44cPoPUmJA4+Ku4PmGQ8Ix8z8ourFoOs90M1jWbFrBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:27:32.689286Z","bundle_sha256":"fb87a37e5e9e2446cc12680fdbbc7a8dc582d5e4d0f65fc1bf01397ee7c2eb09"}}