{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IJXC3YQDXB67SOEZJTLQPJOLO4","short_pith_number":"pith:IJXC3YQD","canonical_record":{"source":{"id":"1505.04714","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.HO","submitted_at":"2015-05-18T16:42:32Z","cross_cats_sorted":[],"title_canon_sha256":"2e30fb9e78fe94c11c53595f76846343e82e342e237e3c12c20a23c823caa3a8","abstract_canon_sha256":"179177cc814b4494e631a77c09fb8ebc96c034d07550b387474804ab5feb9bf6"},"schema_version":"1.0"},"canonical_sha256":"426e2de203b87df938994cd707a5cb7711f32acf715dda1c9832af776d9651c2","source":{"kind":"arxiv","id":"1505.04714","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04714","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04714v2","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04714","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"IJXC3YQDXB67","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IJXC3YQDXB67SOEZ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IJXC3YQD","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IJXC3YQDXB67SOEZJTLQPJOLO4","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04714","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.HO","submitted_at":"2015-05-18T16:42:32Z","cross_cats_sorted":[],"title_canon_sha256":"2e30fb9e78fe94c11c53595f76846343e82e342e237e3c12c20a23c823caa3a8","abstract_canon_sha256":"179177cc814b4494e631a77c09fb8ebc96c034d07550b387474804ab5feb9bf6"},"schema_version":"1.0"},"canonical_sha256":"426e2de203b87df938994cd707a5cb7711f32acf715dda1c9832af776d9651c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:32.233192Z","signature_b64":"6IlBruTFmaVMNhkIAQpllAvGBUw/wqJ882yyrPABjWper2npNiT4vGsSCQS2A4vERVd2SOX1l0dIXK8ZcRclDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"426e2de203b87df938994cd707a5cb7711f32acf715dda1c9832af776d9651c2","last_reissued_at":"2026-05-18T02:03:32.232549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:32.232549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04714","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":"2026-05-18T02:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aceqoea0r6fJP0wZAWyQ5boaIDcTrpR2yb/2cr1OKQEFXhjqSmzOun8/+RheE5QIEuJWwJjs+UxyQW3aXEhyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:36:29.897283Z"},"content_sha256":"b140047e7f6a7a8429871a8df7f852a249b218683dd987cd37f508cb3da5af90","schema_version":"1.0","event_id":"sha256:b140047e7f6a7a8429871a8df7f852a249b218683dd987cd37f508cb3da5af90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IJXC3YQDXB67SOEZJTLQPJOLO4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alan M. Turing: The Applications of Probability to Cryptography","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Ian Taylor","submitted_at":"2015-05-18T16:42:32Z","abstract_excerpt":"This is a typeset version of Alan Turing's Second World War research paper \\textit{The Applications of Probability to Cryptography}. A companion paper \\textit{Paper on Statistics of Repetitions} is also available in typeset form from arXiv at arXiv:1505.04715. The original papers give a text along with figures and tables. They provide a fascinating insight into the preparation of the manuscripts, as well as the style of writing at a time when typographical errors were corrected by hand, and mathematical expression handwritten into spaces left in the text. Working with the papers in their origi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04714","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":"2026-05-18T02:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDylBWFgSdWE4AagS7EXQbJN9B88n/0JdI62eNuwnzJctDPfS2xn8ZcuK5IUVr6g2boR2eg6hH3wge/SSwhsDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:36:29.897896Z"},"content_sha256":"242e368271894caa8bc974670a2c36e9121310f21d384fcc1bf6d5d7ae3793bd","schema_version":"1.0","event_id":"sha256:242e368271894caa8bc974670a2c36e9121310f21d384fcc1bf6d5d7ae3793bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IJXC3YQDXB67SOEZJTLQPJOLO4/bundle.json","state_url":"https://pith.science/pith/IJXC3YQDXB67SOEZJTLQPJOLO4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IJXC3YQDXB67SOEZJTLQPJOLO4/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":"2026-05-21T21:36:29Z","links":{"resolver":"https://pith.science/pith/IJXC3YQDXB67SOEZJTLQPJOLO4","bundle":"https://pith.science/pith/IJXC3YQDXB67SOEZJTLQPJOLO4/bundle.json","state":"https://pith.science/pith/IJXC3YQDXB67SOEZJTLQPJOLO4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IJXC3YQDXB67SOEZJTLQPJOLO4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IJXC3YQDXB67SOEZJTLQPJOLO4","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":"179177cc814b4494e631a77c09fb8ebc96c034d07550b387474804ab5feb9bf6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.HO","submitted_at":"2015-05-18T16:42:32Z","title_canon_sha256":"2e30fb9e78fe94c11c53595f76846343e82e342e237e3c12c20a23c823caa3a8"},"schema_version":"1.0","source":{"id":"1505.04714","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04714","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04714v2","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04714","created_at":"2026-05-18T02:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"IJXC3YQDXB67","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IJXC3YQDXB67SOEZ","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IJXC3YQD","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:242e368271894caa8bc974670a2c36e9121310f21d384fcc1bf6d5d7ae3793bd","target":"graph","created_at":"2026-05-18T02:03:32Z","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":"This is a typeset version of Alan Turing's Second World War research paper \\textit{The Applications of Probability to Cryptography}. A companion paper \\textit{Paper on Statistics of Repetitions} is also available in typeset form from arXiv at arXiv:1505.04715. The original papers give a text along with figures and tables. They provide a fascinating insight into the preparation of the manuscripts, as well as the style of writing at a time when typographical errors were corrected by hand, and mathematical expression handwritten into spaces left in the text. Working with the papers in their origi","authors_text":"Ian Taylor","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.HO","submitted_at":"2015-05-18T16:42:32Z","title":"Alan M. Turing: The Applications of Probability to Cryptography"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04714","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:b140047e7f6a7a8429871a8df7f852a249b218683dd987cd37f508cb3da5af90","target":"record","created_at":"2026-05-18T02:03:32Z","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":"179177cc814b4494e631a77c09fb8ebc96c034d07550b387474804ab5feb9bf6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.HO","submitted_at":"2015-05-18T16:42:32Z","title_canon_sha256":"2e30fb9e78fe94c11c53595f76846343e82e342e237e3c12c20a23c823caa3a8"},"schema_version":"1.0","source":{"id":"1505.04714","kind":"arxiv","version":2}},"canonical_sha256":"426e2de203b87df938994cd707a5cb7711f32acf715dda1c9832af776d9651c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"426e2de203b87df938994cd707a5cb7711f32acf715dda1c9832af776d9651c2","first_computed_at":"2026-05-18T02:03:32.232549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:32.232549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6IlBruTFmaVMNhkIAQpllAvGBUw/wqJ882yyrPABjWper2npNiT4vGsSCQS2A4vERVd2SOX1l0dIXK8ZcRclDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:32.233192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04714","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b140047e7f6a7a8429871a8df7f852a249b218683dd987cd37f508cb3da5af90","sha256:242e368271894caa8bc974670a2c36e9121310f21d384fcc1bf6d5d7ae3793bd"],"state_sha256":"f9306a6cee77a3d92476b84e591dce61e9fa654522fcf0900b7f1f9525222469"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bCSBUXDrM00PcmQR9Rl96NVS9ZpMT69ING6bjCC4GX3riR6fY97KGCYJr9jMaA2FJQ8q3Q+XOCOp0a1u7PpwBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T21:36:29.899957Z","bundle_sha256":"d49075c1304063db5ee6babd0d2e015e1c062ff389e6575075baeaeca4f09ecc"}}