{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:E6RMSDUWODDPRAR5CJRG5FAYRQ","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":"74d52aaa2ac0baad1e98b96b78ac0c71b93b6df7a35ada999a109ea66fcc0b6a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-01T16:20:13Z","title_canon_sha256":"7d6dcf3fc7273d11c9e6cf5ad4401dd8e501062fbb5e562b5c04cf08fc450071"},"schema_version":"1.0","source":{"id":"2507.00915","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.00915","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"2507.00915v2","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00915","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"E6RMSDUWODDP","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"pith_short_16","alias_value":"E6RMSDUWODDPRAR5","created_at":"2026-07-05T12:04:37Z"},{"alias_kind":"pith_short_8","alias_value":"E6RMSDUW","created_at":"2026-07-05T12:04:37Z"}],"graph_snapshots":[{"event_id":"sha256:1c18915f0a7e4258ca9c885fb9b8502c9df7989f8486389b1a32e55649d760db","target":"graph","created_at":"2026-07-05T12:04:37Z","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/2507.00915/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Simulating an arbitrary discrete distribution $D \\in [0, 1]^n$ using fair coin tosses incurs trade-offs between entropy complexity and space and time complexity. Shannon's theory suggests that $H(D)$ tosses are necessary and sufficient, but does not guarantee exact distribution. Knuth and Yao showed that a decision tree consumes fewer than $H(D) + 2$ tosses for one exact sample. Draper and Saad's recent work addresses the space and time aspect, showing that $H(D) + 2$ tosses, $O(n \\log(n) \\log(m))$ memory, and $O(H(D))$ operations are all it costs, where $m$ is the common denominator of the pr","authors_text":"Hsin-Po Wang, Jui-Hsiang Shao","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-01T16:20:13Z","title":"MichelangeRoll: Sculpting Rational Distributions Exactly and Efficiently"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00915","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":"sha256:0db99c887954586af04aa24670d5d4145a7968948df5dadd281939599e3d400f","target":"record","created_at":"2026-07-05T12:04:37Z","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":"74d52aaa2ac0baad1e98b96b78ac0c71b93b6df7a35ada999a109ea66fcc0b6a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2025-07-01T16:20:13Z","title_canon_sha256":"7d6dcf3fc7273d11c9e6cf5ad4401dd8e501062fbb5e562b5c04cf08fc450071"},"schema_version":"1.0","source":{"id":"2507.00915","kind":"arxiv","version":2}},"canonical_sha256":"27a2c90e9670c6f8823d12626e94188c32106b26982d5d2a0fad0a10e26f037e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27a2c90e9670c6f8823d12626e94188c32106b26982d5d2a0fad0a10e26f037e","first_computed_at":"2026-07-05T12:04:37.142691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:04:37.142691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o0ZbYQaLEoTBtAnrSvbL5Se7MU8aY1/Inyk0s1tERMVbYDcuGvYhY0Qy2kOFU2ykKdiuyVUq13YvquQLvavdCg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:04:37.143167Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.00915","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db99c887954586af04aa24670d5d4145a7968948df5dadd281939599e3d400f","sha256:1c18915f0a7e4258ca9c885fb9b8502c9df7989f8486389b1a32e55649d760db"],"state_sha256":"d6dcce7aeefee0396e715035071b6fe11c53d1ef99ffec5fa2fbf538b1db4331"}