{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3LKPK77FXCGSCR7FTINEIXT436","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":"c2e78fb00e7b2137b2bea6922576304286a82d8f240afb5e5059031dbf45e971","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-07-29T18:20:03Z","title_canon_sha256":"62a8e680df34c7b6d69a156239aef83025688dfa6b164e249de65a448429092c"},"schema_version":"1.0","source":{"id":"2208.00029","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.00029","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"2208.00029v2","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.00029","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"3LKPK77FXCGS","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_16","alias_value":"3LKPK77FXCGSCR7F","created_at":"2026-07-05T04:47:29Z"},{"alias_kind":"pith_short_8","alias_value":"3LKPK77F","created_at":"2026-07-05T04:47:29Z"}],"graph_snapshots":[{"event_id":"sha256:9199ce30cbe310b2f01de278e5c2c56fc912f1b1529cecca7d3f5db4ee51eae3","target":"graph","created_at":"2026-07-05T04:47:29Z","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/2208.00029/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Collision problem is to decide whether a given list of numbers $(x_1,\\ldots,x_n)\\in[n]^n$ is $1$-to-$1$ or $2$-to-$1$ when promised one of them is the case. We show an $n^{\\Omega(1)}$ randomised communication lower bound for the natural two-party version of Collision where Alice holds the first half of the bits of each $x_i$ and Bob holds the second half. As an application, we also show a similar lower bound for a weak bit-pigeonhole search problem, which answers a question of Itsykson and Riazanov (CCC 2021).","authors_text":"Mika G\\\"o\\\"os, Siddhartha Jain","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-07-29T18:20:03Z","title":"Communication Complexity of Collision"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.00029","kind":"arxiv","version":2},"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":"sha256:2828924961f1f58fffc92f04a6033b8090c30b770f413c95babeb6af04720998","target":"record","created_at":"2026-07-05T04:47:29Z","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":"c2e78fb00e7b2137b2bea6922576304286a82d8f240afb5e5059031dbf45e971","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2022-07-29T18:20:03Z","title_canon_sha256":"62a8e680df34c7b6d69a156239aef83025688dfa6b164e249de65a448429092c"},"schema_version":"1.0","source":{"id":"2208.00029","kind":"arxiv","version":2}},"canonical_sha256":"dad4f57fe5b88d2147e59a1a445e7cdfa8a1f2761ed6894aca95259e759ff550","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dad4f57fe5b88d2147e59a1a445e7cdfa8a1f2761ed6894aca95259e759ff550","first_computed_at":"2026-07-05T04:47:29.207607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:47:29.207607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RbyV9w2vW9ICojChhZYLv4y5j+hwLrYqEvyno9soqx/ggf8fMyvkjNjOAuXYD0mKzc3fpMZ+y+3ftpdcEp64BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:47:29.208040Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.00029","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2828924961f1f58fffc92f04a6033b8090c30b770f413c95babeb6af04720998","sha256:9199ce30cbe310b2f01de278e5c2c56fc912f1b1529cecca7d3f5db4ee51eae3"],"state_sha256":"bc3f311987c4a9549c3a31b55383949c2e145b34192d22e271b14e707e6fa0a4"}