{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2OGC3TAWCVPUVRMRQGXO7AIHHV","short_pith_number":"pith:2OGC3TAW","schema_version":"1.0","canonical_sha256":"d38c2dcc16155f4ac59181aeef81073d454ddfe7ffc8cea1c135ed7a2471fb91","source":{"kind":"arxiv","id":"2507.10426","version":1},"attestation_state":"computed","paper":{"title":"Communication Complexity is NP-hard","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bruno Loff, Rahul Ilango, Shuichi Hirahara","submitted_at":"2025-07-14T16:15:54Z","abstract_excerpt":"In the paper where he first defined Communication Complexity, Yao asks: \\emph{Is computing $CC(f)$ (the 2-way communication complexity of a given function $f$) NP-complete?} The problem of deciding whether $CC(f) \\le k$, when given the communication matrix for $f$ and a number $k$, is easily seen to be in NP. Kushilevitz and Weinreb have shown that this problem is cryptographically hard. Here we show it is NP-hard."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.10426","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2025-07-14T16:15:54Z","cross_cats_sorted":[],"title_canon_sha256":"ffc9a80111263ae2f887006ff45d233d73e9d9d19d95a48512072669806168b8","abstract_canon_sha256":"7c250d8e7f72001580baa7f6450abaabe9c2d90899f8bc400e4de68dff8e06c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:51.126527Z","signature_b64":"grmEyqUMOzyu4hKHyoXXA8p0bodPhHBar94+FQ8Kew3EReOVCSoij7uVREm9PKdR81x2w01faWfuevxQq93iDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d38c2dcc16155f4ac59181aeef81073d454ddfe7ffc8cea1c135ed7a2471fb91","last_reissued_at":"2026-07-05T11:36:51.126047Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:51.126047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Communication Complexity is NP-hard","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Bruno Loff, Rahul Ilango, Shuichi Hirahara","submitted_at":"2025-07-14T16:15:54Z","abstract_excerpt":"In the paper where he first defined Communication Complexity, Yao asks: \\emph{Is computing $CC(f)$ (the 2-way communication complexity of a given function $f$) NP-complete?} The problem of deciding whether $CC(f) \\le k$, when given the communication matrix for $f$ and a number $k$, is easily seen to be in NP. Kushilevitz and Weinreb have shown that this problem is cryptographically hard. Here we show it is NP-hard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10426","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/2507.10426/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.10426","created_at":"2026-07-05T11:36:51.126108+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.10426v1","created_at":"2026-07-05T11:36:51.126108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10426","created_at":"2026-07-05T11:36:51.126108+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OGC3TAWCVPU","created_at":"2026-07-05T11:36:51.126108+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OGC3TAWCVPUVRMR","created_at":"2026-07-05T11:36:51.126108+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OGC3TAW","created_at":"2026-07-05T11:36:51.126108+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.05327","citing_title":"Computationally Efficient Collaborative Communication Via Regularity-Based Coarsening","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV","json":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV.json","graph_json":"https://pith.science/api/pith-number/2OGC3TAWCVPUVRMRQGXO7AIHHV/graph.json","events_json":"https://pith.science/api/pith-number/2OGC3TAWCVPUVRMRQGXO7AIHHV/events.json","paper":"https://pith.science/paper/2OGC3TAW"},"agent_actions":{"view_html":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV","download_json":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV.json","view_paper":"https://pith.science/paper/2OGC3TAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.10426&json=true","fetch_graph":"https://pith.science/api/pith-number/2OGC3TAWCVPUVRMRQGXO7AIHHV/graph.json","fetch_events":"https://pith.science/api/pith-number/2OGC3TAWCVPUVRMRQGXO7AIHHV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV/action/storage_attestation","attest_author":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV/action/author_attestation","sign_citation":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV/action/citation_signature","submit_replication":"https://pith.science/pith/2OGC3TAWCVPUVRMRQGXO7AIHHV/action/replication_record"}},"created_at":"2026-07-05T11:36:51.126108+00:00","updated_at":"2026-07-05T11:36:51.126108+00:00"}