{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:C6OQ3XBOCKVETKTMEARC6GLEET","short_pith_number":"pith:C6OQ3XBO","canonical_record":{"source":{"id":"1311.7278","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-28T11:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"e6e791e52ca037084a12ff9ae9929da8a532a265161afa841d753a400aed3827","abstract_canon_sha256":"c0c5fc9c0b76b7e8650eff5fd911565203430bb4f910c6ef6133de7f12c14189"},"schema_version":"1.0"},"canonical_sha256":"179d0ddc2e12aa49aa6c20222f196424e3df1db5c347cd7b4d005f23c0278c83","source":{"kind":"arxiv","id":"1311.7278","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7278","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7278v2","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7278","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"C6OQ3XBOCKVE","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C6OQ3XBOCKVETKTM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C6OQ3XBO","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:C6OQ3XBOCKVETKTMEARC6GLEET","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7278","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-28T11:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"e6e791e52ca037084a12ff9ae9929da8a532a265161afa841d753a400aed3827","abstract_canon_sha256":"c0c5fc9c0b76b7e8650eff5fd911565203430bb4f910c6ef6133de7f12c14189"},"schema_version":"1.0"},"canonical_sha256":"179d0ddc2e12aa49aa6c20222f196424e3df1db5c347cd7b4d005f23c0278c83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:02.752658Z","signature_b64":"CXqGBYPNogbGteP6+d90X5Uypy6CsDve5OW7GtqjIVdXzCnan42NzT+ItMOwBqzhRFsizIhSGOGmfRw0/DeHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"179d0ddc2e12aa49aa6c20222f196424e3df1db5c347cd7b4d005f23c0278c83","last_reissued_at":"2026-05-18T02:29:02.752162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:02.752162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7278","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":"2026-05-18T02:29:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3i84urnufHEOROM95B/vYGMUPuPefdzTrehRsWBjlCHyd3NeMCbly6BD75KgcsKBwVBWtjAmlvF07AT0BClBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:02:43.367577Z"},"content_sha256":"3f46564a1ff8deefd3162b55af3c01943f008c688206422becfd22abcda5000a","schema_version":"1.0","event_id":"sha256:3f46564a1ff8deefd3162b55af3c01943f008c688206422becfd22abcda5000a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:C6OQ3XBOCKVETKTMEARC6GLEET","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear list-approximation for short programs (or the power of a few random bits)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bruno Bauwens, Marius Zimand","submitted_at":"2013-11-28T11:28:31Z","abstract_excerpt":"A $c$-short program for a string $x$ is a description of $x$ of length at most $C(x) + c$, where $C(x)$ is the Kolmogorov complexity of $x$. We show that there exists a randomized algorithm that constructs a list of $n$ elements that contains a $O(\\log n)$-short program for $x$. We also show a polynomial-time randomized construction that achieves the same list size for $O(\\log^2 n)$-short programs. These results beat the lower bounds shown by Bauwens et al. \\cite{bmvz:c:shortlist} for deterministic constructions of such lists. We also prove tight lower bounds for the main parameters of our res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7278","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":"2026-05-18T02:29:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gr9/Q9F6b2veVIh2tbaFfnldTqCGlZBnz0euJk7Cf3Tb7Oik3s/KvkPLEe/pF4PRrCenOUXcd5tGGHpL+VvTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T11:02:43.368235Z"},"content_sha256":"dc80e6d676b7a91e59df0480537ac1233581c3e871230eefb82e80df85579e4a","schema_version":"1.0","event_id":"sha256:dc80e6d676b7a91e59df0480537ac1233581c3e871230eefb82e80df85579e4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C6OQ3XBOCKVETKTMEARC6GLEET/bundle.json","state_url":"https://pith.science/pith/C6OQ3XBOCKVETKTMEARC6GLEET/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C6OQ3XBOCKVETKTMEARC6GLEET/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":"2026-06-07T11:02:43Z","links":{"resolver":"https://pith.science/pith/C6OQ3XBOCKVETKTMEARC6GLEET","bundle":"https://pith.science/pith/C6OQ3XBOCKVETKTMEARC6GLEET/bundle.json","state":"https://pith.science/pith/C6OQ3XBOCKVETKTMEARC6GLEET/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C6OQ3XBOCKVETKTMEARC6GLEET/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C6OQ3XBOCKVETKTMEARC6GLEET","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":"c0c5fc9c0b76b7e8650eff5fd911565203430bb4f910c6ef6133de7f12c14189","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-28T11:28:31Z","title_canon_sha256":"e6e791e52ca037084a12ff9ae9929da8a532a265161afa841d753a400aed3827"},"schema_version":"1.0","source":{"id":"1311.7278","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7278","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7278v2","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7278","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"C6OQ3XBOCKVE","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C6OQ3XBOCKVETKTM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C6OQ3XBO","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:dc80e6d676b7a91e59df0480537ac1233581c3e871230eefb82e80df85579e4a","target":"graph","created_at":"2026-05-18T02:29:02Z","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":"A $c$-short program for a string $x$ is a description of $x$ of length at most $C(x) + c$, where $C(x)$ is the Kolmogorov complexity of $x$. We show that there exists a randomized algorithm that constructs a list of $n$ elements that contains a $O(\\log n)$-short program for $x$. We also show a polynomial-time randomized construction that achieves the same list size for $O(\\log^2 n)$-short programs. These results beat the lower bounds shown by Bauwens et al. \\cite{bmvz:c:shortlist} for deterministic constructions of such lists. We also prove tight lower bounds for the main parameters of our res","authors_text":"Bruno Bauwens, Marius Zimand","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-28T11:28:31Z","title":"Linear list-approximation for short programs (or the power of a few random bits)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7278","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":"sha256:3f46564a1ff8deefd3162b55af3c01943f008c688206422becfd22abcda5000a","target":"record","created_at":"2026-05-18T02:29:02Z","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":"c0c5fc9c0b76b7e8650eff5fd911565203430bb4f910c6ef6133de7f12c14189","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-28T11:28:31Z","title_canon_sha256":"e6e791e52ca037084a12ff9ae9929da8a532a265161afa841d753a400aed3827"},"schema_version":"1.0","source":{"id":"1311.7278","kind":"arxiv","version":2}},"canonical_sha256":"179d0ddc2e12aa49aa6c20222f196424e3df1db5c347cd7b4d005f23c0278c83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"179d0ddc2e12aa49aa6c20222f196424e3df1db5c347cd7b4d005f23c0278c83","first_computed_at":"2026-05-18T02:29:02.752162Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:02.752162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CXqGBYPNogbGteP6+d90X5Uypy6CsDve5OW7GtqjIVdXzCnan42NzT+ItMOwBqzhRFsizIhSGOGmfRw0/DeHDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:02.752658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7278","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f46564a1ff8deefd3162b55af3c01943f008c688206422becfd22abcda5000a","sha256:dc80e6d676b7a91e59df0480537ac1233581c3e871230eefb82e80df85579e4a"],"state_sha256":"f764657a919e157f094c86a8749eed1c1061dd0c250b6df862dd91f2679cc516"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8XWUH2JpUPMmSJRbZbdgNoLXnVBCb8Kco0/5ES+BBDnOQqRTLRk9VfR/DcEO1iivo5S2v8JKrldCGkROhWUABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T11:02:43.371643Z","bundle_sha256":"6edc6f601eb5ca28e6c7979ebdabe390bc1856d4bdfc458c39db475fc112e80b"}}