{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GXDHC3DWZCW6TODMPR2QQA35OF","short_pith_number":"pith:GXDHC3DW","canonical_record":{"source":{"id":"1112.2000","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T02:02:56Z","cross_cats_sorted":[],"title_canon_sha256":"ec9f05a9610673b6ef251bceed96793094baf30cab5edcbb980db66a27a56c21","abstract_canon_sha256":"d690cad0d570a6d902c2fb00e5934d7e57ff80241b3625eecd731ff6726fc1b5"},"schema_version":"1.0"},"canonical_sha256":"35c6716c76c8ade9b86c7c7508037d71696f3e80984da50b3545135d7db47c43","source":{"kind":"arxiv","id":"1112.2000","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2000","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2000v3","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2000","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"GXDHC3DWZCW6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GXDHC3DWZCW6TODM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GXDHC3DW","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GXDHC3DWZCW6TODMPR2QQA35OF","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2000","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T02:02:56Z","cross_cats_sorted":[],"title_canon_sha256":"ec9f05a9610673b6ef251bceed96793094baf30cab5edcbb980db66a27a56c21","abstract_canon_sha256":"d690cad0d570a6d902c2fb00e5934d7e57ff80241b3625eecd731ff6726fc1b5"},"schema_version":"1.0"},"canonical_sha256":"35c6716c76c8ade9b86c7c7508037d71696f3e80984da50b3545135d7db47c43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:44.944612Z","signature_b64":"8N2P8RC03lzfV9kyddnq0gJRayzu9JTJK/FCiqut1JtkZRNpzPQzWPuIjSJOGVSOBeeh6br9m3R4ckBod0JtBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35c6716c76c8ade9b86c7c7508037d71696f3e80984da50b3545135d7db47c43","last_reissued_at":"2026-05-18T03:53:44.944079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:44.944079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2000","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8wi7oL7qwUX7z5wtCFispQl3kMr0/jhEcJrd0kelZ37/JMVh1uardnLztn1uwoJGt0LMvGGz+jv0bgxuojVjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:13:10.242541Z"},"content_sha256":"0f0ad1afc3e02da78cc1119bb9c4c75050f53ec7b3de504675c5666eddef5d5e","schema_version":"1.0","event_id":"sha256:0f0ad1afc3e02da78cc1119bb9c4c75050f53ec7b3de504675c5666eddef5d5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GXDHC3DWZCW6TODMPR2QQA35OF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A discrepancy lower bound for information complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Mark Braverman, Omri Weinstein","submitted_at":"2011-12-09T02:02:56Z","abstract_excerpt":"This paper provides the first general technique for proving information lower bounds on two-party unbounded-rounds communication problems. We show that the discrepancy lower bound, which applies to randomized communication complexity, also applies to information complexity. More precisely, if the discrepancy of a two-party function $f$ with respect to a distribution $\\mu$ is $Disc_\\mu f$, then any two party randomized protocol computing $f$ must reveal at least $\\Omega(\\log (1/Disc_\\mu f))$ bits of information to the participants. As a corollary, we obtain that any two-party protocol for compu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2000","kind":"arxiv","version":3},"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":"2026-05-18T03:53:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FeX4XkpK4lUnuFG9GSAwf7T4h8WUc0SbYe3X0sBIW7EIchApD8S/Ke+/yBCtHzeSnQ1ig/yPnK6BTzNhjppBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:13:10.243251Z"},"content_sha256":"dad04e06b4ed21c38639619e405ed0ac0d8fa01c1ba3bfe85220e0fe6c8660b8","schema_version":"1.0","event_id":"sha256:dad04e06b4ed21c38639619e405ed0ac0d8fa01c1ba3bfe85220e0fe6c8660b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GXDHC3DWZCW6TODMPR2QQA35OF/bundle.json","state_url":"https://pith.science/pith/GXDHC3DWZCW6TODMPR2QQA35OF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GXDHC3DWZCW6TODMPR2QQA35OF/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":"2026-06-06T21:13:10Z","links":{"resolver":"https://pith.science/pith/GXDHC3DWZCW6TODMPR2QQA35OF","bundle":"https://pith.science/pith/GXDHC3DWZCW6TODMPR2QQA35OF/bundle.json","state":"https://pith.science/pith/GXDHC3DWZCW6TODMPR2QQA35OF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GXDHC3DWZCW6TODMPR2QQA35OF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GXDHC3DWZCW6TODMPR2QQA35OF","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":"d690cad0d570a6d902c2fb00e5934d7e57ff80241b3625eecd731ff6726fc1b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T02:02:56Z","title_canon_sha256":"ec9f05a9610673b6ef251bceed96793094baf30cab5edcbb980db66a27a56c21"},"schema_version":"1.0","source":{"id":"1112.2000","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2000","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2000v3","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2000","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"GXDHC3DWZCW6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GXDHC3DWZCW6TODM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GXDHC3DW","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:dad04e06b4ed21c38639619e405ed0ac0d8fa01c1ba3bfe85220e0fe6c8660b8","target":"graph","created_at":"2026-05-18T03:53:44Z","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":"This paper provides the first general technique for proving information lower bounds on two-party unbounded-rounds communication problems. We show that the discrepancy lower bound, which applies to randomized communication complexity, also applies to information complexity. More precisely, if the discrepancy of a two-party function $f$ with respect to a distribution $\\mu$ is $Disc_\\mu f$, then any two party randomized protocol computing $f$ must reveal at least $\\Omega(\\log (1/Disc_\\mu f))$ bits of information to the participants. As a corollary, we obtain that any two-party protocol for compu","authors_text":"Mark Braverman, Omri Weinstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T02:02:56Z","title":"A discrepancy lower bound for information complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2000","kind":"arxiv","version":3},"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":"sha256:0f0ad1afc3e02da78cc1119bb9c4c75050f53ec7b3de504675c5666eddef5d5e","target":"record","created_at":"2026-05-18T03:53:44Z","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":"d690cad0d570a6d902c2fb00e5934d7e57ff80241b3625eecd731ff6726fc1b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-12-09T02:02:56Z","title_canon_sha256":"ec9f05a9610673b6ef251bceed96793094baf30cab5edcbb980db66a27a56c21"},"schema_version":"1.0","source":{"id":"1112.2000","kind":"arxiv","version":3}},"canonical_sha256":"35c6716c76c8ade9b86c7c7508037d71696f3e80984da50b3545135d7db47c43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35c6716c76c8ade9b86c7c7508037d71696f3e80984da50b3545135d7db47c43","first_computed_at":"2026-05-18T03:53:44.944079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:44.944079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8N2P8RC03lzfV9kyddnq0gJRayzu9JTJK/FCiqut1JtkZRNpzPQzWPuIjSJOGVSOBeeh6br9m3R4ckBod0JtBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:44.944612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2000","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f0ad1afc3e02da78cc1119bb9c4c75050f53ec7b3de504675c5666eddef5d5e","sha256:dad04e06b4ed21c38639619e405ed0ac0d8fa01c1ba3bfe85220e0fe6c8660b8"],"state_sha256":"ee21bcbe883884e17107589c3d80c133feb57ff3136c619e045e19fbfcbe6c1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jF1N57jtHViRrVGuvvIaubeAlvMSLzvNLjvqKvjcOiXHW/rswkqlU9Mmh6ntOQJCgFtUKhhsv4fM6zN8a8A5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:13:10.246763Z","bundle_sha256":"820d5453a17c2ecfdd544ece869d7379419de08c6a92fdc5fb84d4592aae5173"}}