{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PACQVE5FR74GFUOZ6BWBAH27OC","short_pith_number":"pith:PACQVE5F","schema_version":"1.0","canonical_sha256":"78050a93a58ff862d1d9f06c101f5f70b539abc5919437cc099808f63eebd115","source":{"kind":"arxiv","id":"2605.23638","version":1},"attestation_state":"computed","paper":{"title":"List Reconstruction Problem with List Size Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"(2) National University of Singapore, Binh Vu (1), Hanoi, Shuche Wang (2), Singapore), Van Khu Vu (1) ((1) VinUniversity, Vietnam","submitted_at":"2026-05-22T13:52:06Z","abstract_excerpt":"The problem of computing the cardinality of the intersection of multiple balls in the Hamming space has attracted a lot of attention recently due to their applications in the list reconstruction problem and information retrieval in Associative Memories. In previous work, most of the results are for the cases where the radii of each ball, $r$ and the distance between the centers of these balls, $k$ are fixed when the length $n$ of each codeword tend to infinity. In this work, we focus on the case where $r = \\alpha n$ and $k=\\beta n$ for some constants $\\alpha$ and $\\beta$ and compute the maximu"},"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":"2605.23638","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-22T13:52:06Z","cross_cats_sorted":[],"title_canon_sha256":"fc7b28883fe69fe0bfc7e6876131ed8f9f78c0495def7e6f65a17dbe3e70e381","abstract_canon_sha256":"d262107a5abf925c0698a9646ee8286c9d02ed740913074bf704413f131b9772"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:23.307715Z","signature_b64":"dRDcMsFvtt3qKnxsm652gzzuZdSnBZ3pkTqWrIc1zrV7zJzHVJ+LJmut1T+7A6hJogzZW1j/LLlmrXViXdNbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78050a93a58ff862d1d9f06c101f5f70b539abc5919437cc099808f63eebd115","last_reissued_at":"2026-05-25T02:02:23.306944Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:23.306944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"List Reconstruction Problem with List Size Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"(2) National University of Singapore, Binh Vu (1), Hanoi, Shuche Wang (2), Singapore), Van Khu Vu (1) ((1) VinUniversity, Vietnam","submitted_at":"2026-05-22T13:52:06Z","abstract_excerpt":"The problem of computing the cardinality of the intersection of multiple balls in the Hamming space has attracted a lot of attention recently due to their applications in the list reconstruction problem and information retrieval in Associative Memories. In previous work, most of the results are for the cases where the radii of each ball, $r$ and the distance between the centers of these balls, $k$ are fixed when the length $n$ of each codeword tend to infinity. In this work, we focus on the case where $r = \\alpha n$ and $k=\\beta n$ for some constants $\\alpha$ and $\\beta$ and compute the maximu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23638","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/2605.23638/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":"2605.23638","created_at":"2026-05-25T02:02:23.307065+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.23638v1","created_at":"2026-05-25T02:02:23.307065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23638","created_at":"2026-05-25T02:02:23.307065+00:00"},{"alias_kind":"pith_short_12","alias_value":"PACQVE5FR74G","created_at":"2026-05-25T02:02:23.307065+00:00"},{"alias_kind":"pith_short_16","alias_value":"PACQVE5FR74GFUOZ","created_at":"2026-05-25T02:02:23.307065+00:00"},{"alias_kind":"pith_short_8","alias_value":"PACQVE5F","created_at":"2026-05-25T02:02:23.307065+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC","json":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC.json","graph_json":"https://pith.science/api/pith-number/PACQVE5FR74GFUOZ6BWBAH27OC/graph.json","events_json":"https://pith.science/api/pith-number/PACQVE5FR74GFUOZ6BWBAH27OC/events.json","paper":"https://pith.science/paper/PACQVE5F"},"agent_actions":{"view_html":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC","download_json":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC.json","view_paper":"https://pith.science/paper/PACQVE5F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.23638&json=true","fetch_graph":"https://pith.science/api/pith-number/PACQVE5FR74GFUOZ6BWBAH27OC/graph.json","fetch_events":"https://pith.science/api/pith-number/PACQVE5FR74GFUOZ6BWBAH27OC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC/action/storage_attestation","attest_author":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC/action/author_attestation","sign_citation":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC/action/citation_signature","submit_replication":"https://pith.science/pith/PACQVE5FR74GFUOZ6BWBAH27OC/action/replication_record"}},"created_at":"2026-05-25T02:02:23.307065+00:00","updated_at":"2026-05-25T02:02:23.307065+00:00"}