{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WGESVHNQSWETH3G4E4YJSRHM7Z","short_pith_number":"pith:WGESVHNQ","canonical_record":{"source":{"id":"2606.00996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-31T04:24:33Z","cross_cats_sorted":[],"title_canon_sha256":"553f2a32dee4faf6179681af9391a50fbf69e4e58018fea431445cfb2d812c8a","abstract_canon_sha256":"f8e14281ca72ce1a96b323c69bbe9430904a7a248de2ecc10614d9728cfbbf24"},"schema_version":"1.0"},"canonical_sha256":"b1892a9db0958933ecdc27309944ecfe4f569dd0f1db597c786ca188791ebb56","source":{"kind":"arxiv","id":"2606.00996","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00996","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00996v1","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00996","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"WGESVHNQSWET","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"pith_short_16","alias_value":"WGESVHNQSWETH3G4","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"pith_short_8","alias_value":"WGESVHNQ","created_at":"2026-06-02T01:04:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WGESVHNQSWETH3G4E4YJSRHM7Z","target":"record","payload":{"canonical_record":{"source":{"id":"2606.00996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-31T04:24:33Z","cross_cats_sorted":[],"title_canon_sha256":"553f2a32dee4faf6179681af9391a50fbf69e4e58018fea431445cfb2d812c8a","abstract_canon_sha256":"f8e14281ca72ce1a96b323c69bbe9430904a7a248de2ecc10614d9728cfbbf24"},"schema_version":"1.0"},"canonical_sha256":"b1892a9db0958933ecdc27309944ecfe4f569dd0f1db597c786ca188791ebb56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:17.434930Z","signature_b64":"hhKiVZs1CyWYOXckCe2LXAy3m1iHhOZ230ZH/O1uuHMDGpWst1yalsI7Y115uBon4F3QaLApwb10mmP3NbkSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1892a9db0958933ecdc27309944ecfe4f569dd0f1db597c786ca188791ebb56","last_reissued_at":"2026-06-02T01:04:17.434385Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:17.434385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.00996","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":"2026-06-02T01:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7MmdTPQGWnR1oz78Np/J/TAWc6AFkw+E4m1jEY1chcqyycDeXFP7490QMK3BroOF5VMyxDGY/XAEsz/px1nyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:13:25.184697Z"},"content_sha256":"63c3b9a088bde2555615a56ae5c9becf7a36897a17396befa2216a083f5d788f","schema_version":"1.0","event_id":"sha256:63c3b9a088bde2555615a56ae5c9becf7a36897a17396befa2216a083f5d788f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WGESVHNQSWETH3G4E4YJSRHM7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant-Stretch Rounding on the Hypersimplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alireza Haqi, Eric Ma, Nima Anari","submitted_at":"2026-05-31T04:24:33Z","abstract_excerpt":"We study correlated rounding on the hypersimplex, the base polytope of the uniform matroid. For each point $x$ in the hypersimplex, the goal is to sample a $k$-subset $A(x)$ with marginals $x$, while coupling the samples for all choices of $x$ so that nearby inputs produce nearby sets. We give a constant-stretch scheme. Our scheme samples the maximum-entropy $k$-subset distribution with prescribed marginals using a common random ordering and common uniform thresholds. For every $x,y\\in[0,1]^n$ with $\\sum_i x_i=\\sum_i y_i=k$, it satisfies $\\mathbb{E}[|A(x)\\triangle A(y)|]\\le 6\\|x-y\\|_1$. This i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00996","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/2606.00996/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":"2026-06-02T01:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CN+QIiAutATfz4jH+KEp2InuXlWyRDeKVXb/17T2qz6Ztui1B8FJaSbBF3eCVH+aywPo9pH5JPYKTnQtPvQQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:13:25.185065Z"},"content_sha256":"bcdf841844d60940b74262bdaae4a81e89e7130b1a2cc4f481f6d00036b53b0b","schema_version":"1.0","event_id":"sha256:bcdf841844d60940b74262bdaae4a81e89e7130b1a2cc4f481f6d00036b53b0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGESVHNQSWETH3G4E4YJSRHM7Z/bundle.json","state_url":"https://pith.science/pith/WGESVHNQSWETH3G4E4YJSRHM7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGESVHNQSWETH3G4E4YJSRHM7Z/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":"2026-06-06T17:13:25Z","links":{"resolver":"https://pith.science/pith/WGESVHNQSWETH3G4E4YJSRHM7Z","bundle":"https://pith.science/pith/WGESVHNQSWETH3G4E4YJSRHM7Z/bundle.json","state":"https://pith.science/pith/WGESVHNQSWETH3G4E4YJSRHM7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGESVHNQSWETH3G4E4YJSRHM7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WGESVHNQSWETH3G4E4YJSRHM7Z","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":"f8e14281ca72ce1a96b323c69bbe9430904a7a248de2ecc10614d9728cfbbf24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-31T04:24:33Z","title_canon_sha256":"553f2a32dee4faf6179681af9391a50fbf69e4e58018fea431445cfb2d812c8a"},"schema_version":"1.0","source":{"id":"2606.00996","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00996","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00996v1","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00996","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"WGESVHNQSWET","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"pith_short_16","alias_value":"WGESVHNQSWETH3G4","created_at":"2026-06-02T01:04:17Z"},{"alias_kind":"pith_short_8","alias_value":"WGESVHNQ","created_at":"2026-06-02T01:04:17Z"}],"graph_snapshots":[{"event_id":"sha256:bcdf841844d60940b74262bdaae4a81e89e7130b1a2cc4f481f6d00036b53b0b","target":"graph","created_at":"2026-06-02T01:04:17Z","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/2606.00996/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study correlated rounding on the hypersimplex, the base polytope of the uniform matroid. For each point $x$ in the hypersimplex, the goal is to sample a $k$-subset $A(x)$ with marginals $x$, while coupling the samples for all choices of $x$ so that nearby inputs produce nearby sets. We give a constant-stretch scheme. Our scheme samples the maximum-entropy $k$-subset distribution with prescribed marginals using a common random ordering and common uniform thresholds. For every $x,y\\in[0,1]^n$ with $\\sum_i x_i=\\sum_i y_i=k$, it satisfies $\\mathbb{E}[|A(x)\\triangle A(y)|]\\le 6\\|x-y\\|_1$. This i","authors_text":"Alireza Haqi, Eric Ma, Nima Anari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-31T04:24:33Z","title":"Constant-Stretch Rounding on the Hypersimplex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00996","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":"sha256:63c3b9a088bde2555615a56ae5c9becf7a36897a17396befa2216a083f5d788f","target":"record","created_at":"2026-06-02T01:04:17Z","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":"f8e14281ca72ce1a96b323c69bbe9430904a7a248de2ecc10614d9728cfbbf24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-31T04:24:33Z","title_canon_sha256":"553f2a32dee4faf6179681af9391a50fbf69e4e58018fea431445cfb2d812c8a"},"schema_version":"1.0","source":{"id":"2606.00996","kind":"arxiv","version":1}},"canonical_sha256":"b1892a9db0958933ecdc27309944ecfe4f569dd0f1db597c786ca188791ebb56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1892a9db0958933ecdc27309944ecfe4f569dd0f1db597c786ca188791ebb56","first_computed_at":"2026-06-02T01:04:17.434385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:04:17.434385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hhKiVZs1CyWYOXckCe2LXAy3m1iHhOZ230ZH/O1uuHMDGpWst1yalsI7Y115uBon4F3QaLApwb10mmP3NbkSDw==","signature_status":"signed_v1","signed_at":"2026-06-02T01:04:17.434930Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00996","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63c3b9a088bde2555615a56ae5c9becf7a36897a17396befa2216a083f5d788f","sha256:bcdf841844d60940b74262bdaae4a81e89e7130b1a2cc4f481f6d00036b53b0b"],"state_sha256":"631ede563a6d83d0bd33dd8f15f140b485575515fccee5e109a7c5a53877219d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrXR2700vgILZI2J3oDYnu35quTIJ3y4Nldyx3xyEnjwHNiMMO+u1PZ1gg5oj3jg0y2mhC0xVRI2b7/utmfWDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:13:25.187431Z","bundle_sha256":"a4efa007e589dfaf96864db790456b348fe2841c9ef9eed5b1b09f2d0458f5fa"}}