{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CXM24AEDOCQX7G6BW6FBW6QUU5","short_pith_number":"pith:CXM24AED","canonical_record":{"source":{"id":"1406.3378","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-12T21:33:48Z","cross_cats_sorted":[],"title_canon_sha256":"159571d81e80c69391f65c9a6339c9934fe058c8301c43b68d6b239e2709f57c","abstract_canon_sha256":"570079376271de7ab6d260f56d4215eecd9e96678a956351613d7c82a9830036"},"schema_version":"1.0"},"canonical_sha256":"15d9ae008370a17f9bc1b78a1b7a14a774bada00a6eb9ba1d2c10e3cadf4ff35","source":{"kind":"arxiv","id":"1406.3378","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3378","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3378v2","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3378","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"pith_short_12","alias_value":"CXM24AEDOCQX","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CXM24AEDOCQX7G6B","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CXM24AED","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CXM24AEDOCQX7G6BW6FBW6QUU5","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3378","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-12T21:33:48Z","cross_cats_sorted":[],"title_canon_sha256":"159571d81e80c69391f65c9a6339c9934fe058c8301c43b68d6b239e2709f57c","abstract_canon_sha256":"570079376271de7ab6d260f56d4215eecd9e96678a956351613d7c82a9830036"},"schema_version":"1.0"},"canonical_sha256":"15d9ae008370a17f9bc1b78a1b7a14a774bada00a6eb9ba1d2c10e3cadf4ff35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:02.322300Z","signature_b64":"L/2+rPw9L4QvBYKpmD67Rlt8VOtZd74N27ua9voJK2THryuDosx0HaJAebN9FhYaPE4gsnB4TTERCaVJhd0nCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15d9ae008370a17f9bc1b78a1b7a14a774bada00a6eb9ba1d2c10e3cadf4ff35","last_reissued_at":"2026-05-18T02:49:02.321887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:02.321887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3378","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":"2026-05-18T02:49:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lWo0kp9gJ8khETp/NcnxCx4Mrt9O+5EJXmIjBOjNhKnKKJ1/WuM5Qmd5GZe8bLxxKFWgz0S/fYec0ds/7MzcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:55:35.760086Z"},"content_sha256":"cf8e80f6bd9b1c0171bb3158625b39807c75154049f5489a99cb19284c245877","schema_version":"1.0","event_id":"sha256:cf8e80f6bd9b1c0171bb3158625b39807c75154049f5489a99cb19284c245877"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CXM24AEDOCQX7G6BW6FBW6QUU5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Probabilistic Recursion Theory and Implicit Computational Complexity (Long Version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Sara Zuppiroli, Ugo Dal Lago","submitted_at":"2014-06-12T21:33:48Z","abstract_excerpt":"We show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene's partial recursive functions. The obtained algebra, following Leivant, can be restricted so as to capture the notion of polytime sampleable distributions, a key concept in average-case complexity and cryptography."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3378","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":"2026-05-18T02:49:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gQmHUh12+FlzWSbAOST8V7yB5JlMJm3pDnFV48mqulyRO3aWI1NN8Mp4B1Ow0PpombnXmr7pvMg3gCvpRjo5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:55:35.760434Z"},"content_sha256":"9d261bd339c3e5e8237a37cb9281a4509a5aa6b701f54e1232adbec91b3f9c2e","schema_version":"1.0","event_id":"sha256:9d261bd339c3e5e8237a37cb9281a4509a5aa6b701f54e1232adbec91b3f9c2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXM24AEDOCQX7G6BW6FBW6QUU5/bundle.json","state_url":"https://pith.science/pith/CXM24AEDOCQX7G6BW6FBW6QUU5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXM24AEDOCQX7G6BW6FBW6QUU5/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":"2026-06-05T12:55:35Z","links":{"resolver":"https://pith.science/pith/CXM24AEDOCQX7G6BW6FBW6QUU5","bundle":"https://pith.science/pith/CXM24AEDOCQX7G6BW6FBW6QUU5/bundle.json","state":"https://pith.science/pith/CXM24AEDOCQX7G6BW6FBW6QUU5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXM24AEDOCQX7G6BW6FBW6QUU5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CXM24AEDOCQX7G6BW6FBW6QUU5","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":"570079376271de7ab6d260f56d4215eecd9e96678a956351613d7c82a9830036","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-12T21:33:48Z","title_canon_sha256":"159571d81e80c69391f65c9a6339c9934fe058c8301c43b68d6b239e2709f57c"},"schema_version":"1.0","source":{"id":"1406.3378","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3378","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3378v2","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3378","created_at":"2026-05-18T02:49:02Z"},{"alias_kind":"pith_short_12","alias_value":"CXM24AEDOCQX","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CXM24AEDOCQX7G6B","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CXM24AED","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:9d261bd339c3e5e8237a37cb9281a4509a5aa6b701f54e1232adbec91b3f9c2e","target":"graph","created_at":"2026-05-18T02:49:02Z","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 show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene's partial recursive functions. The obtained algebra, following Leivant, can be restricted so as to capture the notion of polytime sampleable distributions, a key concept in average-case complexity and cryptography.","authors_text":"Sara Zuppiroli, Ugo Dal Lago","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-12T21:33:48Z","title":"Probabilistic Recursion Theory and Implicit Computational Complexity (Long Version)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3378","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:cf8e80f6bd9b1c0171bb3158625b39807c75154049f5489a99cb19284c245877","target":"record","created_at":"2026-05-18T02:49:02Z","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":"570079376271de7ab6d260f56d4215eecd9e96678a956351613d7c82a9830036","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-12T21:33:48Z","title_canon_sha256":"159571d81e80c69391f65c9a6339c9934fe058c8301c43b68d6b239e2709f57c"},"schema_version":"1.0","source":{"id":"1406.3378","kind":"arxiv","version":2}},"canonical_sha256":"15d9ae008370a17f9bc1b78a1b7a14a774bada00a6eb9ba1d2c10e3cadf4ff35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15d9ae008370a17f9bc1b78a1b7a14a774bada00a6eb9ba1d2c10e3cadf4ff35","first_computed_at":"2026-05-18T02:49:02.321887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:02.321887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L/2+rPw9L4QvBYKpmD67Rlt8VOtZd74N27ua9voJK2THryuDosx0HaJAebN9FhYaPE4gsnB4TTERCaVJhd0nCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:02.322300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3378","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf8e80f6bd9b1c0171bb3158625b39807c75154049f5489a99cb19284c245877","sha256:9d261bd339c3e5e8237a37cb9281a4509a5aa6b701f54e1232adbec91b3f9c2e"],"state_sha256":"25df25b8f63aaadc408d6af64c409f9d297cce022232c82f9129575573fe8f91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y2YoVdo9c3A0KrY+0sR3WStlEqs1T1FsAU3GDujD/kb67zcEJD6EBPFW3MSuPzMAWdM1YWQyCQ0PaaLqAIRBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:55:35.762320Z","bundle_sha256":"22728502ee385ea8dd5c8dee78798c2990d550b9010d99880d0853715433bb5d"}}