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Goldstein et al.~[WADS'2017] conjectured that there is no algorithm for 3SUM-Indexing which uses $n^{2-\\Omega(1)}$ space and $n^{1-\\Omega(1)}$ query time.\n  We show that the conjecture is false by reducing the 3SUM-Indexing problem to the problem of inverting functions, and then applying an algorithm of Fiat and Naor [SICOMP'1999] f"},"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":"1907.11206","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-25T17:11:11Z","cross_cats_sorted":[],"title_canon_sha256":"c486c46e341e6a2b91d44c205b64011739bf64e721979e56b15141094758db6d","abstract_canon_sha256":"c33c3ce5aad5184ee3cd144f3debf87882af18df7bc30114d629eefd748f8df5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:32.951844Z","signature_b64":"vB4eNSrrTRUttO3sKCNnZrbz8yWYpD6JA0+mSfagzUQPs5IH+v5rslm88uUiP0laKNHLLDabT+k3ossnn0I6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0984ee8ffcf65d4698e4f19c21d455a6ba36d2e199360e41f97af94500585c95","last_reissued_at":"2026-05-17T23:39:32.951126Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:32.951126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Strong 3SUM-INDEXING Conjecture is False","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ely Porat, Tsvi Kopelowitz","submitted_at":"2019-07-25T17:11:11Z","abstract_excerpt":"In the 3SUM-Indexing problem the goal is to preprocess two lists of elements from $U$, $A=(a_1,a_2,\\ldots,a_n)$ and $B=(b_1,b_2,...,b_n)$, such that given an element $c\\in U$ one can quickly determine whether there exists a pair $(a,b)\\in A \\times B$ where $a+b=c$. Goldstein et al.~[WADS'2017] conjectured that there is no algorithm for 3SUM-Indexing which uses $n^{2-\\Omega(1)}$ space and $n^{1-\\Omega(1)}$ query time.\n  We show that the conjecture is false by reducing the 3SUM-Indexing problem to the problem of inverting functions, and then applying an algorithm of Fiat and Naor [SICOMP'1999] f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11206","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1907.11206","created_at":"2026-05-17T23:39:32.951233+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.11206v1","created_at":"2026-05-17T23:39:32.951233+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11206","created_at":"2026-05-17T23:39:32.951233+00:00"},{"alias_kind":"pith_short_12","alias_value":"BGCO5D746ZOU","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"BGCO5D746ZOUNGHE","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"BGCO5D74","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2512.04258","citing_title":"Improved Time-Space Tradeoffs for 3SUM-Indexing","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2","json":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2.json","graph_json":"https://pith.science/api/pith-number/BGCO5D746ZOUNGHE6GOCDVCVU2/graph.json","events_json":"https://pith.science/api/pith-number/BGCO5D746ZOUNGHE6GOCDVCVU2/events.json","paper":"https://pith.science/paper/BGCO5D74"},"agent_actions":{"view_html":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2","download_json":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2.json","view_paper":"https://pith.science/paper/BGCO5D74","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.11206&json=true","fetch_graph":"https://pith.science/api/pith-number/BGCO5D746ZOUNGHE6GOCDVCVU2/graph.json","fetch_events":"https://pith.science/api/pith-number/BGCO5D746ZOUNGHE6GOCDVCVU2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2/action/storage_attestation","attest_author":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2/action/author_attestation","sign_citation":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2/action/citation_signature","submit_replication":"https://pith.science/pith/BGCO5D746ZOUNGHE6GOCDVCVU2/action/replication_record"}},"created_at":"2026-05-17T23:39:32.951233+00:00","updated_at":"2026-05-17T23:39:32.951233+00:00"}