{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5PKPFFTWO74WPDVAPSF42RQMXK","short_pith_number":"pith:5PKPFFTW","canonical_record":{"source":{"id":"1705.01773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-04T10:08:06Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"03dc076f81b2ca3587740c52492c159d87f32e2e2c2fc4d11a7cc3b75b100d17","abstract_canon_sha256":"ae11605b772f2987b461b44bdebe9e0ef86d51b53fa10d218a00cdcb67ba2e3e"},"schema_version":"1.0"},"canonical_sha256":"ebd4f2967677f9678ea07c8bcd460cba99e5a98490522353ffe5f91f25fc2580","source":{"kind":"arxiv","id":"1705.01773","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01773","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01773v1","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01773","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"5PKPFFTWO74W","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5PKPFFTWO74WPDVA","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5PKPFFTW","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5PKPFFTWO74WPDVAPSF42RQMXK","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01773","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-04T10:08:06Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"03dc076f81b2ca3587740c52492c159d87f32e2e2c2fc4d11a7cc3b75b100d17","abstract_canon_sha256":"ae11605b772f2987b461b44bdebe9e0ef86d51b53fa10d218a00cdcb67ba2e3e"},"schema_version":"1.0"},"canonical_sha256":"ebd4f2967677f9678ea07c8bcd460cba99e5a98490522353ffe5f91f25fc2580","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:02.330428Z","signature_b64":"oCd+oPy0spidE6em+I01H7u5FkvdaqKAH1hqHux4nqiclceaCI8gj1gcIilFpNguty4zNF/4Fk1ryY4Iy/QcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebd4f2967677f9678ea07c8bcd460cba99e5a98490522353ffe5f91f25fc2580","last_reissued_at":"2026-05-18T00:45:02.330070Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:02.330070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01773","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":"2026-05-18T00:45:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GVrPvttUtbevm99RnVe9qEliElDNR62GcgJQbowQKLxJMsbk3GJsk50SbX3paBDdX1DuVMiT37o4Ne4z4Dn1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:12:28.137439Z"},"content_sha256":"9f86199c71a6307683384586f404797560e3845ffd84c7abf54eda0a2a60e59a","schema_version":"1.0","event_id":"sha256:9f86199c71a6307683384586f404797560e3845ffd84c7abf54eda0a2a60e59a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5PKPFFTWO74WPDVAPSF42RQMXK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uncountable realtime probabilistic classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"cs.CC","authors_text":"Abuzer Yakary{\\i}lmaz, Maksims Dimitrijevs","submitted_at":"2017-05-04T10:08:06Z","abstract_excerpt":"We investigate the minimum cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On binary case, we follow the same result for double logarithmic space, which is tight. When replacing the worktape with some limited memories, we can follow uncountable results on unary languages for two counters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01773","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":"2026-05-18T00:45:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YTHDlqjlGW0zN6SPfqJRpMUvfnXe3UKqJaT+RRJ1HtNIC3yk+3AfXeIMWvaWyDNxdSjRxXRBVQn6HzULYYk0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:12:28.138039Z"},"content_sha256":"a5e28a368624f94ef3071f1fe229ee3033c860ea215f887ea414009997317a2b","schema_version":"1.0","event_id":"sha256:a5e28a368624f94ef3071f1fe229ee3033c860ea215f887ea414009997317a2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PKPFFTWO74WPDVAPSF42RQMXK/bundle.json","state_url":"https://pith.science/pith/5PKPFFTWO74WPDVAPSF42RQMXK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PKPFFTWO74WPDVAPSF42RQMXK/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":"2026-06-26T16:12:28Z","links":{"resolver":"https://pith.science/pith/5PKPFFTWO74WPDVAPSF42RQMXK","bundle":"https://pith.science/pith/5PKPFFTWO74WPDVAPSF42RQMXK/bundle.json","state":"https://pith.science/pith/5PKPFFTWO74WPDVAPSF42RQMXK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PKPFFTWO74WPDVAPSF42RQMXK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5PKPFFTWO74WPDVAPSF42RQMXK","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":"ae11605b772f2987b461b44bdebe9e0ef86d51b53fa10d218a00cdcb67ba2e3e","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-04T10:08:06Z","title_canon_sha256":"03dc076f81b2ca3587740c52492c159d87f32e2e2c2fc4d11a7cc3b75b100d17"},"schema_version":"1.0","source":{"id":"1705.01773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01773","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01773v1","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01773","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"5PKPFFTWO74W","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5PKPFFTWO74WPDVA","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5PKPFFTW","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:a5e28a368624f94ef3071f1fe229ee3033c860ea215f887ea414009997317a2b","target":"graph","created_at":"2026-05-18T00:45:02Z","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"},"paper":{"abstract_excerpt":"We investigate the minimum cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On binary case, we follow the same result for double logarithmic space, which is tight. When replacing the worktape with some limited memories, we can follow uncountable results on unary languages for two counters.","authors_text":"Abuzer Yakary{\\i}lmaz, Maksims Dimitrijevs","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-04T10:08:06Z","title":"Uncountable realtime probabilistic classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01773","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":"sha256:9f86199c71a6307683384586f404797560e3845ffd84c7abf54eda0a2a60e59a","target":"record","created_at":"2026-05-18T00:45:02Z","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":"ae11605b772f2987b461b44bdebe9e0ef86d51b53fa10d218a00cdcb67ba2e3e","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-04T10:08:06Z","title_canon_sha256":"03dc076f81b2ca3587740c52492c159d87f32e2e2c2fc4d11a7cc3b75b100d17"},"schema_version":"1.0","source":{"id":"1705.01773","kind":"arxiv","version":1}},"canonical_sha256":"ebd4f2967677f9678ea07c8bcd460cba99e5a98490522353ffe5f91f25fc2580","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebd4f2967677f9678ea07c8bcd460cba99e5a98490522353ffe5f91f25fc2580","first_computed_at":"2026-05-18T00:45:02.330070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:02.330070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oCd+oPy0spidE6em+I01H7u5FkvdaqKAH1hqHux4nqiclceaCI8gj1gcIilFpNguty4zNF/4Fk1ryY4Iy/QcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:02.330428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f86199c71a6307683384586f404797560e3845ffd84c7abf54eda0a2a60e59a","sha256:a5e28a368624f94ef3071f1fe229ee3033c860ea215f887ea414009997317a2b"],"state_sha256":"24a6a4d7e12e17c3325018211fbade1d520dab19fbc1788cf31327170547a945"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h6TrxlnGdFtEvW1qoFcwsp/vH3nHPXbSuMLHNdcastOj7M4K5OqBH5BTjQwQCLnm4QIrOs+OG55PM6HnyMGHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:12:28.140148Z","bundle_sha256":"1fcd1d677a60fe80b0f49356d7baae0b23c87611fb77f64bd2d6f178f3e34d3d"}}