{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:RWGQMJ6JU4QDODAVT7BNY2E3WG","short_pith_number":"pith:RWGQMJ6J","canonical_record":{"source":{"id":"2007.14451","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-07-28T19:43:46Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"333e1fdae4bd8a717e2b93537c12007396704aa79d63e5a32f13a25fd20cf4f1","abstract_canon_sha256":"7982bc90ac43470d16044a5af6b43ac350125954afc09675ddf6c1fcf089a7ca"},"schema_version":"1.0"},"canonical_sha256":"8d8d0627c9a720370c159fc2dc689bb18e1fef46807832970e2f2e806df33d67","source":{"kind":"arxiv","id":"2007.14451","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.14451","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"2007.14451v2","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.14451","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"RWGQMJ6JU4QD","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"pith_short_16","alias_value":"RWGQMJ6JU4QDODAV","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"pith_short_8","alias_value":"RWGQMJ6J","created_at":"2026-07-05T02:25:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:RWGQMJ6JU4QDODAVT7BNY2E3WG","target":"record","payload":{"canonical_record":{"source":{"id":"2007.14451","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-07-28T19:43:46Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"333e1fdae4bd8a717e2b93537c12007396704aa79d63e5a32f13a25fd20cf4f1","abstract_canon_sha256":"7982bc90ac43470d16044a5af6b43ac350125954afc09675ddf6c1fcf089a7ca"},"schema_version":"1.0"},"canonical_sha256":"8d8d0627c9a720370c159fc2dc689bb18e1fef46807832970e2f2e806df33d67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:25:21.174561Z","signature_b64":"8iUfUz/coGLWw7RURp1JrNChyl/iIRg3UQk5MAMZvWBPnMpKHDLZCdqwU7Zb8BgwggbuhxGTWAt8wCpYiFyDAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d8d0627c9a720370c159fc2dc689bb18e1fef46807832970e2f2e806df33d67","last_reissued_at":"2026-07-05T02:25:21.174086Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:25:21.174086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.14451","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":"2026-07-05T02:25:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jM9T0aiX4O1Z/K/P82tzq5A1+z1+Hhz4zanfGjDzCdqPJAUIeeSBjuDS4M+34lrGbjZGl7QI9Ex8g2PZxaV0CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:32:06.820735Z"},"content_sha256":"48b322750b8a9edda4e90297b745d9977ce8812e80d0e71bc5ab50374ae08598","schema_version":"1.0","event_id":"sha256:48b322750b8a9edda4e90297b745d9977ce8812e80d0e71bc5ab50374ae08598"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:RWGQMJ6JU4QDODAVT7BNY2E3WG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Quantum versus Classical Learnability of Discrete Distributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"quant-ph","authors_text":"Dominik Hangleiter, Jean-Pierre Seifert, Jens Eisert, Ryan Sweke","submitted_at":"2020-07-28T19:43:46Z","abstract_excerpt":"Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown discrete probability distribution, output with high probability an efficient algorithm for generating new samples from a good approximation of the original distribution. Our primary result is the explicit construction of a class of discrete probability distributions which, under the decisional Diffie-Hellman assumption, is provably not efficiently PAC learnable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.14451","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.14451/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:25:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"88zlVGGViqpWswUUKrxvEKRH0JWHiwIOQpWH6e4QBKFpbsX4y4DPppgqPTuava2ELn5TIkIl/B/dSvK+7uDICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:32:06.821243Z"},"content_sha256":"28b356a7a449e575dcba123f7793b9d26c78e6b47a8ca2f55c51f91afde8934d","schema_version":"1.0","event_id":"sha256:28b356a7a449e575dcba123f7793b9d26c78e6b47a8ca2f55c51f91afde8934d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWGQMJ6JU4QDODAVT7BNY2E3WG/bundle.json","state_url":"https://pith.science/pith/RWGQMJ6JU4QDODAVT7BNY2E3WG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWGQMJ6JU4QDODAVT7BNY2E3WG/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":"2026-08-06T13:32:06Z","links":{"resolver":"https://pith.science/pith/RWGQMJ6JU4QDODAVT7BNY2E3WG","bundle":"https://pith.science/pith/RWGQMJ6JU4QDODAVT7BNY2E3WG/bundle.json","state":"https://pith.science/pith/RWGQMJ6JU4QDODAVT7BNY2E3WG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWGQMJ6JU4QDODAVT7BNY2E3WG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:RWGQMJ6JU4QDODAVT7BNY2E3WG","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":"7982bc90ac43470d16044a5af6b43ac350125954afc09675ddf6c1fcf089a7ca","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-07-28T19:43:46Z","title_canon_sha256":"333e1fdae4bd8a717e2b93537c12007396704aa79d63e5a32f13a25fd20cf4f1"},"schema_version":"1.0","source":{"id":"2007.14451","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.14451","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"2007.14451v2","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.14451","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"RWGQMJ6JU4QD","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"pith_short_16","alias_value":"RWGQMJ6JU4QDODAV","created_at":"2026-07-05T02:25:21Z"},{"alias_kind":"pith_short_8","alias_value":"RWGQMJ6J","created_at":"2026-07-05T02:25:21Z"}],"graph_snapshots":[{"event_id":"sha256:28b356a7a449e575dcba123f7793b9d26c78e6b47a8ca2f55c51f91afde8934d","target":"graph","created_at":"2026-07-05T02:25:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.14451/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework. More specifically we consider the following task: Given samples from some unknown discrete probability distribution, output with high probability an efficient algorithm for generating new samples from a good approximation of the original distribution. Our primary result is the explicit construction of a class of discrete probability distributions which, under the decisional Diffie-Hellman assumption, is provably not efficiently PAC learnable ","authors_text":"Dominik Hangleiter, Jean-Pierre Seifert, Jens Eisert, Ryan Sweke","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-07-28T19:43:46Z","title":"On the Quantum versus Classical Learnability of Discrete Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.14451","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":"sha256:48b322750b8a9edda4e90297b745d9977ce8812e80d0e71bc5ab50374ae08598","target":"record","created_at":"2026-07-05T02:25:21Z","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":"7982bc90ac43470d16044a5af6b43ac350125954afc09675ddf6c1fcf089a7ca","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-07-28T19:43:46Z","title_canon_sha256":"333e1fdae4bd8a717e2b93537c12007396704aa79d63e5a32f13a25fd20cf4f1"},"schema_version":"1.0","source":{"id":"2007.14451","kind":"arxiv","version":2}},"canonical_sha256":"8d8d0627c9a720370c159fc2dc689bb18e1fef46807832970e2f2e806df33d67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d8d0627c9a720370c159fc2dc689bb18e1fef46807832970e2f2e806df33d67","first_computed_at":"2026-07-05T02:25:21.174086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:25:21.174086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8iUfUz/coGLWw7RURp1JrNChyl/iIRg3UQk5MAMZvWBPnMpKHDLZCdqwU7Zb8BgwggbuhxGTWAt8wCpYiFyDAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:25:21.174561Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.14451","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48b322750b8a9edda4e90297b745d9977ce8812e80d0e71bc5ab50374ae08598","sha256:28b356a7a449e575dcba123f7793b9d26c78e6b47a8ca2f55c51f91afde8934d"],"state_sha256":"1c9031cf776ac7f92955f1b7f1f1ef51273b0bd3cd85cee9cc141dff1aed960a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rjRWSXAngDwoJ0ETEWTOgP7697asI8iki6dS8xQ9HbRa4GN8u9oarK3C6aeQ77fQk+Xz3Xz6l2Q24vnI1pzUDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T13:32:06.824267Z","bundle_sha256":"ee619daa0b452fab507cbf621bf7311330eaa8b11eec3c8d8eacda692bb8747d"}}