{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HNZSKWKP7UOVT2CUF6XCEPWKD5","short_pith_number":"pith:HNZSKWKP","canonical_record":{"source":{"id":"1101.4555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-01-24T14:53:10Z","cross_cats_sorted":[],"title_canon_sha256":"98c3f8561b8332d0e9551b3854dbbec5a10065e00f160e58e00b07eea24b8084","abstract_canon_sha256":"913479a17474105b2f4210519a83f562889c71ddd8923c354ed0b7621ddffd05"},"schema_version":"1.0"},"canonical_sha256":"3b7325594ffd1d59e8542fae223eca1f5a1a1adcaf20a9bde421c12e80135a7e","source":{"kind":"arxiv","id":"1101.4555","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4555","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4555v1","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4555","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"HNZSKWKP7UOV","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNZSKWKP7UOVT2CU","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNZSKWKP","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HNZSKWKP7UOVT2CUF6XCEPWKD5","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-01-24T14:53:10Z","cross_cats_sorted":[],"title_canon_sha256":"98c3f8561b8332d0e9551b3854dbbec5a10065e00f160e58e00b07eea24b8084","abstract_canon_sha256":"913479a17474105b2f4210519a83f562889c71ddd8923c354ed0b7621ddffd05"},"schema_version":"1.0"},"canonical_sha256":"3b7325594ffd1d59e8542fae223eca1f5a1a1adcaf20a9bde421c12e80135a7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:56.433447Z","signature_b64":"GZDKLteU5aQaOXWU72WHt1j0kzzWbrreNMfriVtixSfnK51S0OvSZUxpDWWTb0IP+MwFUPMseZ/PgHzg7Y88AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b7325594ffd1d59e8542fae223eca1f5a1a1adcaf20a9bde421c12e80135a7e","last_reissued_at":"2026-05-18T04:09:56.432767Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:56.432767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4555","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":"2026-05-18T04:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDsrYwU6lVoI+uVohnCAzzjQzrNGe69LsYhdWOvtpUBNPto7eqq+O0gFcA3S69xh/qcSKJtFsm9pdwyZKc6hBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:42:22.841373Z"},"content_sha256":"ba67fed55fe308acb4bb4ec6cbf15d148c3781413e31945f980e233dd26d189d","schema_version":"1.0","event_id":"sha256:ba67fed55fe308acb4bb4ec6cbf15d148c3781413e31945f980e233dd26d189d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HNZSKWKP7UOVT2CUF6XCEPWKD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tight bounds on the randomized communication complexity of symmetric XOR functions in one-way and SMP models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Ming Lam Leung, Shengyu Zhang, Yang Li","submitted_at":"2011-01-24T14:53:10Z","abstract_excerpt":"We study the communication complexity of symmetric XOR functions, namely functions $f: \\{0,1\\}^n \\times \\{0,1\\}^n \\rightarrow \\{0,1\\}$ that can be formulated as $f(x,y)=D(|x\\oplus y|)$ for some predicate $D: \\{0,1,...,n\\} \\rightarrow \\{0,1\\}$, where $|x\\oplus y|$ is the Hamming weight of the bitwise XOR of $x$ and $y$. We give a public-coin randomized protocol in the Simultaneous Message Passing (SMP) model, with the communication cost matching the known lower bound for the \\emph{quantum} and \\emph{two-way} model up to a logarithm factor. As a corollary, this closes a quadratic gap between qua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4555","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":""},"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":"2026-05-18T04:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3rfwLiWczNo5H1vJp/4K9L8diUIuO6fio1m0VfLK3voNDlR64zHUWSLFyN0qpTA/m2Gq532kJczxUTka5R83Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:42:22.842119Z"},"content_sha256":"890e0d5ca9c36ff811707cccf87bb25d988bb5e742b7ce659eb93d4fb2325008","schema_version":"1.0","event_id":"sha256:890e0d5ca9c36ff811707cccf87bb25d988bb5e742b7ce659eb93d4fb2325008"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNZSKWKP7UOVT2CUF6XCEPWKD5/bundle.json","state_url":"https://pith.science/pith/HNZSKWKP7UOVT2CUF6XCEPWKD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNZSKWKP7UOVT2CUF6XCEPWKD5/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":"2026-05-29T20:42:22Z","links":{"resolver":"https://pith.science/pith/HNZSKWKP7UOVT2CUF6XCEPWKD5","bundle":"https://pith.science/pith/HNZSKWKP7UOVT2CUF6XCEPWKD5/bundle.json","state":"https://pith.science/pith/HNZSKWKP7UOVT2CUF6XCEPWKD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNZSKWKP7UOVT2CUF6XCEPWKD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HNZSKWKP7UOVT2CUF6XCEPWKD5","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":"913479a17474105b2f4210519a83f562889c71ddd8923c354ed0b7621ddffd05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-01-24T14:53:10Z","title_canon_sha256":"98c3f8561b8332d0e9551b3854dbbec5a10065e00f160e58e00b07eea24b8084"},"schema_version":"1.0","source":{"id":"1101.4555","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4555","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4555v1","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4555","created_at":"2026-05-18T04:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"HNZSKWKP7UOV","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HNZSKWKP7UOVT2CU","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HNZSKWKP","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:890e0d5ca9c36ff811707cccf87bb25d988bb5e742b7ce659eb93d4fb2325008","target":"graph","created_at":"2026-05-18T04:09:56Z","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":"We study the communication complexity of symmetric XOR functions, namely functions $f: \\{0,1\\}^n \\times \\{0,1\\}^n \\rightarrow \\{0,1\\}$ that can be formulated as $f(x,y)=D(|x\\oplus y|)$ for some predicate $D: \\{0,1,...,n\\} \\rightarrow \\{0,1\\}$, where $|x\\oplus y|$ is the Hamming weight of the bitwise XOR of $x$ and $y$. We give a public-coin randomized protocol in the Simultaneous Message Passing (SMP) model, with the communication cost matching the known lower bound for the \\emph{quantum} and \\emph{two-way} model up to a logarithm factor. As a corollary, this closes a quadratic gap between qua","authors_text":"Ming Lam Leung, Shengyu Zhang, Yang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-01-24T14:53:10Z","title":"Tight bounds on the randomized communication complexity of symmetric XOR functions in one-way and SMP models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4555","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:ba67fed55fe308acb4bb4ec6cbf15d148c3781413e31945f980e233dd26d189d","target":"record","created_at":"2026-05-18T04:09:56Z","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":"913479a17474105b2f4210519a83f562889c71ddd8923c354ed0b7621ddffd05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-01-24T14:53:10Z","title_canon_sha256":"98c3f8561b8332d0e9551b3854dbbec5a10065e00f160e58e00b07eea24b8084"},"schema_version":"1.0","source":{"id":"1101.4555","kind":"arxiv","version":1}},"canonical_sha256":"3b7325594ffd1d59e8542fae223eca1f5a1a1adcaf20a9bde421c12e80135a7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b7325594ffd1d59e8542fae223eca1f5a1a1adcaf20a9bde421c12e80135a7e","first_computed_at":"2026-05-18T04:09:56.432767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:56.432767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GZDKLteU5aQaOXWU72WHt1j0kzzWbrreNMfriVtixSfnK51S0OvSZUxpDWWTb0IP+MwFUPMseZ/PgHzg7Y88AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:56.433447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4555","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba67fed55fe308acb4bb4ec6cbf15d148c3781413e31945f980e233dd26d189d","sha256:890e0d5ca9c36ff811707cccf87bb25d988bb5e742b7ce659eb93d4fb2325008"],"state_sha256":"e865645e02bed2098624ada3d8c0e5b7e269287e4d6e7ff8983f73960cf561df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kanlQ/E8E2Qmki3dvNitKnC1NX6vR8dvCNLfEydC9I0Kl+uCDVBP08Ullr/nkJyIqr3QZyeaPrmVsevEL3ZgDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:42:22.846096Z","bundle_sha256":"c033f9896f563c2a6c315095cf2a9b973c239a3bc39dbe87287e3f2d697ded38"}}