{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZFMMEWK6BW22BIYEWMCL3QED4H","short_pith_number":"pith:ZFMMEWK6","canonical_record":{"source":{"id":"2607.13828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-15T13:40:27Z","cross_cats_sorted":["cs.IT","math.IT","math.PR","stat.CO"],"title_canon_sha256":"1ad831c4af31a60e7518350f29548b2c190e5997c6738063ed6c51e21c715ce2","abstract_canon_sha256":"08b1ed94269ca2042d91d81288ef17872446a9cd6100f42e321612bb8db8d48b"},"schema_version":"1.0"},"canonical_sha256":"c958c2595e0db5a0a304b304bdc083e1e7817dfbb3c77f0e84b698e17b15a189","source":{"kind":"arxiv","id":"2607.13828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13828","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13828v1","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13828","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZFMMEWK6BW22","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"pith_short_16","alias_value":"ZFMMEWK6BW22BIYE","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"pith_short_8","alias_value":"ZFMMEWK6","created_at":"2026-07-16T01:23:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZFMMEWK6BW22BIYEWMCL3QED4H","target":"record","payload":{"canonical_record":{"source":{"id":"2607.13828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-15T13:40:27Z","cross_cats_sorted":["cs.IT","math.IT","math.PR","stat.CO"],"title_canon_sha256":"1ad831c4af31a60e7518350f29548b2c190e5997c6738063ed6c51e21c715ce2","abstract_canon_sha256":"08b1ed94269ca2042d91d81288ef17872446a9cd6100f42e321612bb8db8d48b"},"schema_version":"1.0"},"canonical_sha256":"c958c2595e0db5a0a304b304bdc083e1e7817dfbb3c77f0e84b698e17b15a189","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:23:08.582085Z","signature_b64":"M/06FHkb4OPP6ZMGDAn/3rvLlo6iXA0I3w/MNFso1t5S8uTjdkL5/D98gk07d4Nfmx1bxOfGM4P9iH6/zrfiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c958c2595e0db5a0a304b304bdc083e1e7817dfbb3c77f0e84b698e17b15a189","last_reissued_at":"2026-07-16T01:23:08.581216Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:23:08.581216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.13828","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-16T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ymtPOBO4XbY4zXVyejkaj66qJ64Rs/1wkxrdb5VO5MWM2WQRcJBTpViRc7JQ0OydTR+mCvFwE0k4oOUz8sxVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T15:29:04.343053Z"},"content_sha256":"35cc3ce3ec32fcb09b2d22165ebfb6377f6d381804bedb05454911d312c42a6d","schema_version":"1.0","event_id":"sha256:35cc3ce3ec32fcb09b2d22165ebfb6377f6d381804bedb05454911d312c42a6d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZFMMEWK6BW22BIYEWMCL3QED4H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Random Sampling with Real Probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR","stat.CO"],"primary_cat":"cs.DS","authors_text":"David G. Harris, Feras A. Saad, Thomas L. Draper","submitted_at":"2026-07-15T13:40:27Z","abstract_excerpt":"We develop an efficient online algorithm to sample a sequence of discrete random variables using an entropy source of i.i.d. fair coin flips, in a standard model of real computation where real-valued probabilities are represented by rational approximations. For any sequence $F_1, F_2, \\dots$ of probability distributions, our sampler generates $n$ outputs $X_1 \\sim F_1, \\dots, X_n \\sim F_n$ using at most $\\mathbb{E}\\left[H(F_1) +\\dots + H(F_n)\\right] + O(\\log n)$ coin flips in expectation while carrying $O(\\log n)$ bits of persistent space, where $H$ is the Shannon entropy. Under standard assum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13828","kind":"arxiv","version":1},"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/2607.13828/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":"2026-07-16T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TmPgc3AM3yLmGz7r9Krv7KxfL/QL9qDU1agFFtn0D4NNs1HIsZqXZrVhZvAr/i0oPjawX7EEUaNVog7dhVnVAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T15:29:04.343585Z"},"content_sha256":"041d2455054add7acdfe220c2fae5577b4a3dda10931aad0a2616afc558d6322","schema_version":"1.0","event_id":"sha256:041d2455054add7acdfe220c2fae5577b4a3dda10931aad0a2616afc558d6322"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFMMEWK6BW22BIYEWMCL3QED4H/bundle.json","state_url":"https://pith.science/pith/ZFMMEWK6BW22BIYEWMCL3QED4H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFMMEWK6BW22BIYEWMCL3QED4H/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":"2026-08-06T15:29:04Z","links":{"resolver":"https://pith.science/pith/ZFMMEWK6BW22BIYEWMCL3QED4H","bundle":"https://pith.science/pith/ZFMMEWK6BW22BIYEWMCL3QED4H/bundle.json","state":"https://pith.science/pith/ZFMMEWK6BW22BIYEWMCL3QED4H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFMMEWK6BW22BIYEWMCL3QED4H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZFMMEWK6BW22BIYEWMCL3QED4H","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":"08b1ed94269ca2042d91d81288ef17872446a9cd6100f42e321612bb8db8d48b","cross_cats_sorted":["cs.IT","math.IT","math.PR","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-15T13:40:27Z","title_canon_sha256":"1ad831c4af31a60e7518350f29548b2c190e5997c6738063ed6c51e21c715ce2"},"schema_version":"1.0","source":{"id":"2607.13828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.13828","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"2607.13828v1","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13828","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZFMMEWK6BW22","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"pith_short_16","alias_value":"ZFMMEWK6BW22BIYE","created_at":"2026-07-16T01:23:08Z"},{"alias_kind":"pith_short_8","alias_value":"ZFMMEWK6","created_at":"2026-07-16T01:23:08Z"}],"graph_snapshots":[{"event_id":"sha256:041d2455054add7acdfe220c2fae5577b4a3dda10931aad0a2616afc558d6322","target":"graph","created_at":"2026-07-16T01:23:08Z","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/2607.13828/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop an efficient online algorithm to sample a sequence of discrete random variables using an entropy source of i.i.d. fair coin flips, in a standard model of real computation where real-valued probabilities are represented by rational approximations. For any sequence $F_1, F_2, \\dots$ of probability distributions, our sampler generates $n$ outputs $X_1 \\sim F_1, \\dots, X_n \\sim F_n$ using at most $\\mathbb{E}\\left[H(F_1) +\\dots + H(F_n)\\right] + O(\\log n)$ coin flips in expectation while carrying $O(\\log n)$ bits of persistent space, where $H$ is the Shannon entropy. Under standard assum","authors_text":"David G. Harris, Feras A. Saad, Thomas L. Draper","cross_cats":["cs.IT","math.IT","math.PR","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-15T13:40:27Z","title":"Online Random Sampling with Real Probabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13828","kind":"arxiv","version":1},"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":"sha256:35cc3ce3ec32fcb09b2d22165ebfb6377f6d381804bedb05454911d312c42a6d","target":"record","created_at":"2026-07-16T01:23:08Z","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":"08b1ed94269ca2042d91d81288ef17872446a9cd6100f42e321612bb8db8d48b","cross_cats_sorted":["cs.IT","math.IT","math.PR","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-15T13:40:27Z","title_canon_sha256":"1ad831c4af31a60e7518350f29548b2c190e5997c6738063ed6c51e21c715ce2"},"schema_version":"1.0","source":{"id":"2607.13828","kind":"arxiv","version":1}},"canonical_sha256":"c958c2595e0db5a0a304b304bdc083e1e7817dfbb3c77f0e84b698e17b15a189","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c958c2595e0db5a0a304b304bdc083e1e7817dfbb3c77f0e84b698e17b15a189","first_computed_at":"2026-07-16T01:23:08.581216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-16T01:23:08.581216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M/06FHkb4OPP6ZMGDAn/3rvLlo6iXA0I3w/MNFso1t5S8uTjdkL5/D98gk07d4Nfmx1bxOfGM4P9iH6/zrfiAA==","signature_status":"signed_v1","signed_at":"2026-07-16T01:23:08.582085Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.13828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35cc3ce3ec32fcb09b2d22165ebfb6377f6d381804bedb05454911d312c42a6d","sha256:041d2455054add7acdfe220c2fae5577b4a3dda10931aad0a2616afc558d6322"],"state_sha256":"5d4452b0966742e9110b0bdb7c1a98161836ccae2ef2fd14e50e073ea62cb0a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SyeNyOJvJXH6pfyXDf+hMH3eXUkkvsGgRnbNqz+FfjDG+7QxIvRXEysQP862qz9/I0nMYUvRLUO+pFWVNA7BDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T15:29:04.349294Z","bundle_sha256":"2824639a371c636fcd056cae3ab2b44198c4ac8dfe312009904537d20cde0d96"}}