{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q","short_pith_number":"pith:ZWJXIWAL","canonical_record":{"source":{"id":"2608.07800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-08-07T22:45:27Z","cross_cats_sorted":[],"title_canon_sha256":"c1a265ef0dd7387855bdeb0d44a9df86b057101801bf4b7ba1b34f5f5a13d0d5","abstract_canon_sha256":"6e8cf47cc31cdcf07aacbf748eb77a1fb2d0f72a5875c1cbf8bd5713c1159ec9"},"schema_version":"1.0"},"canonical_sha256":"cd9374580b3621f5e5268a7a1e2b98e43f9ddbdc4d81c03d6436bde34fb4aaae","source":{"kind":"arxiv","id":"2608.07800","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07800","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07800v1","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07800","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"pith_short_12","alias_value":"ZWJXIWALGYQ7","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"pith_short_16","alias_value":"ZWJXIWALGYQ7LZJG","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"pith_short_8","alias_value":"ZWJXIWAL","created_at":"2026-08-11T01:18:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q","target":"record","payload":{"canonical_record":{"source":{"id":"2608.07800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-08-07T22:45:27Z","cross_cats_sorted":[],"title_canon_sha256":"c1a265ef0dd7387855bdeb0d44a9df86b057101801bf4b7ba1b34f5f5a13d0d5","abstract_canon_sha256":"6e8cf47cc31cdcf07aacbf748eb77a1fb2d0f72a5875c1cbf8bd5713c1159ec9"},"schema_version":"1.0"},"canonical_sha256":"cd9374580b3621f5e5268a7a1e2b98e43f9ddbdc4d81c03d6436bde34fb4aaae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:18:16.773692Z","signature_b64":"J+KMnK/1CFr1PMywwI5dxBv5qhAK1tU+J4Q4apNK0U5z2zs3IBRDok9phnCf95H/TGi3uCDXMGsoNc0FVRixAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd9374580b3621f5e5268a7a1e2b98e43f9ddbdc4d81c03d6436bde34fb4aaae","last_reissued_at":"2026-08-11T01:18:16.769587Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:18:16.769587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.07800","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":"2026-08-11T01:18:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQNF8mijRfknhlembbxomEH4TVATR4tBUq9ApseMV7qwUEON/7dSP/1KP86+kQeOVmatKaw+VAYlr0gYxNZADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:14:55.706255Z"},"content_sha256":"adc1b725c1348d9065b1603df2dc57e42ab0e1e5a65a2eebb75b43732204cdad","schema_version":"1.0","event_id":"sha256:adc1b725c1348d9065b1603df2dc57e42ab0e1e5a65a2eebb75b43732204cdad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp Analysis of Gaussian Rounding for Boolean Max k-CSP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Yury Makarychev","submitted_at":"2026-08-07T22:45:27Z","abstract_excerpt":"In this note, we show that the approximation algorithm for Boolean Max $k$-CSP presented in [Makarychev and Makarychev 2014] yields a $(1-o_k(1))k/2^k$ approximation, as conjectured in [Makarychev and Makarychev 2017]. This improves the previous guarantee of $(0.626612-o_k(1))k/2^k$ from [Makarychev and Makarychev 2014] and asymptotically matches the known hardness results. The result is a short corollary of the Gaussian stochastic domination theorem of Mulgund."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07800","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/2608.07800/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":"2026-08-11T01:18:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x0tDK/hhlo4rIVupRDV78RpriUhIZ4/zmiyaGySJ5fxziBu7EezpVvZYfZWEQfEjAGGUrnn0ykat7iWu/83aCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:14:55.707294Z"},"content_sha256":"339231d607619f6625fc9843517cde88c9581bdafda08e3f95c6aef8c2088022","schema_version":"1.0","event_id":"sha256:339231d607619f6625fc9843517cde88c9581bdafda08e3f95c6aef8c2088022"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q/bundle.json","state_url":"https://pith.science/pith/ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q/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":"2026-08-17T18:14:55Z","links":{"resolver":"https://pith.science/pith/ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q","bundle":"https://pith.science/pith/ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q/bundle.json","state":"https://pith.science/pith/ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZWJXIWALGYQ7LZJGRJ5B4K4Y4Q","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":"6e8cf47cc31cdcf07aacbf748eb77a1fb2d0f72a5875c1cbf8bd5713c1159ec9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-08-07T22:45:27Z","title_canon_sha256":"c1a265ef0dd7387855bdeb0d44a9df86b057101801bf4b7ba1b34f5f5a13d0d5"},"schema_version":"1.0","source":{"id":"2608.07800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.07800","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"arxiv_version","alias_value":"2608.07800v1","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.07800","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"pith_short_12","alias_value":"ZWJXIWALGYQ7","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"pith_short_16","alias_value":"ZWJXIWALGYQ7LZJG","created_at":"2026-08-11T01:18:16Z"},{"alias_kind":"pith_short_8","alias_value":"ZWJXIWAL","created_at":"2026-08-11T01:18:16Z"}],"graph_snapshots":[{"event_id":"sha256:339231d607619f6625fc9843517cde88c9581bdafda08e3f95c6aef8c2088022","target":"graph","created_at":"2026-08-11T01:18:16Z","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/2608.07800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we show that the approximation algorithm for Boolean Max $k$-CSP presented in [Makarychev and Makarychev 2014] yields a $(1-o_k(1))k/2^k$ approximation, as conjectured in [Makarychev and Makarychev 2017]. This improves the previous guarantee of $(0.626612-o_k(1))k/2^k$ from [Makarychev and Makarychev 2014] and asymptotically matches the known hardness results. The result is a short corollary of the Gaussian stochastic domination theorem of Mulgund.","authors_text":"Yury Makarychev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-08-07T22:45:27Z","title":"Sharp Analysis of Gaussian Rounding for Boolean Max k-CSP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07800","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:adc1b725c1348d9065b1603df2dc57e42ab0e1e5a65a2eebb75b43732204cdad","target":"record","created_at":"2026-08-11T01:18:16Z","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":"6e8cf47cc31cdcf07aacbf748eb77a1fb2d0f72a5875c1cbf8bd5713c1159ec9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-08-07T22:45:27Z","title_canon_sha256":"c1a265ef0dd7387855bdeb0d44a9df86b057101801bf4b7ba1b34f5f5a13d0d5"},"schema_version":"1.0","source":{"id":"2608.07800","kind":"arxiv","version":1}},"canonical_sha256":"cd9374580b3621f5e5268a7a1e2b98e43f9ddbdc4d81c03d6436bde34fb4aaae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd9374580b3621f5e5268a7a1e2b98e43f9ddbdc4d81c03d6436bde34fb4aaae","first_computed_at":"2026-08-11T01:18:16.769587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:18:16.769587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J+KMnK/1CFr1PMywwI5dxBv5qhAK1tU+J4Q4apNK0U5z2zs3IBRDok9phnCf95H/TGi3uCDXMGsoNc0FVRixAQ==","signature_status":"signed_v1","signed_at":"2026-08-11T01:18:16.773692Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.07800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adc1b725c1348d9065b1603df2dc57e42ab0e1e5a65a2eebb75b43732204cdad","sha256:339231d607619f6625fc9843517cde88c9581bdafda08e3f95c6aef8c2088022"],"state_sha256":"133f84fc51d3eedb49bab488ff82a3aad0c7fd6668c5a11b7dbee4cb84e4593c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k7Dpt/EPWuWS6epeaqSXMePtLAmjeBfJDwMStQh0jITG7HKUS3kANH4Ml6b9MhYcQr7MS9AQnMuOIuygJOVrDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T18:14:55.717301Z","bundle_sha256":"9f68b420635d7766102d60d42c853afd1d49761fefefa4c3677899eb180fb935"}}