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We are given a system $S$ of $m$ equations in variables $x_1,...,x_n$, where each equation is $\\sum_{i \\in I_j}x_i = b_j$ is assigned a positive integral weight $w_j$ and $x_i,b_j \\in \\mathbb{F}_2$, $I_j \\subseteq \\{1,2,...,n\\}$ for $j=1,...,m$. We are required to find an assignment of values to the variables in order to maximize the total weight of the satisfied equations.\n  Let $W$ be the total weight of all equations in $S$. We consider the following parameterized version of MaxLin2: decide whether there is an assignment satisfying equations of "},"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":"1110.5915","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-26T20:02:03Z","cross_cats_sorted":["cs.DM","cs.DS"],"title_canon_sha256":"c48e3db9cbde3ad88f18da92e12e603b1ff295a1d2e2c26f7f2e2ee1117f384f","abstract_canon_sha256":"d06929f317e8cf387b765908d5952279c41ef62e9dbbdb44ab214b0175aa1451"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:29.152637Z","signature_b64":"etWsNvNW0QOJvhJuLsl7GmCwCoOT0ON3jy0GVh/wkQ9VQ+Haodvpq2HeG/PfHQD/OVJcJdFZMbsadZXYA05TCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"771bdaaa07c94c89a8cbd1d2c5283a517ce58f941db73ff9c8656522fa87a88c","last_reissued_at":"2026-05-18T03:39:29.152147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:29.152147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parameterized Complexity of Satisfying Almost All Linear Equations over $\\mathbb{F}_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS"],"primary_cat":"cs.CC","authors_text":"A. Yeo, G. Gutin, M. Jones, R. Crowston","submitted_at":"2011-10-26T20:02:03Z","abstract_excerpt":"The problem MaxLin2 can be stated as follows. We are given a system $S$ of $m$ equations in variables $x_1,...,x_n$, where each equation is $\\sum_{i \\in I_j}x_i = b_j$ is assigned a positive integral weight $w_j$ and $x_i,b_j \\in \\mathbb{F}_2$, $I_j \\subseteq \\{1,2,...,n\\}$ for $j=1,...,m$. We are required to find an assignment of values to the variables in order to maximize the total weight of the satisfied equations.\n  Let $W$ be the total weight of all equations in $S$. We consider the following parameterized version of MaxLin2: decide whether there is an assignment satisfying equations of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5915","kind":"arxiv","version":2},"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":"1110.5915","created_at":"2026-05-18T03:39:29.152220+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.5915v2","created_at":"2026-05-18T03:39:29.152220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5915","created_at":"2026-05-18T03:39:29.152220+00:00"},{"alias_kind":"pith_short_12","alias_value":"O4N5VKQHZFGI","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"O4N5VKQHZFGITKGL","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"O4N5VKQH","created_at":"2026-05-18T12:26:37.096874+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/O4N5VKQHZFGITKGL2HJMKKB2KF","json":"https://pith.science/pith/O4N5VKQHZFGITKGL2HJMKKB2KF.json","graph_json":"https://pith.science/api/pith-number/O4N5VKQHZFGITKGL2HJMKKB2KF/graph.json","events_json":"https://pith.science/api/pith-number/O4N5VKQHZFGITKGL2HJMKKB2KF/events.json","paper":"https://pith.science/paper/O4N5VKQH"},"agent_actions":{"view_html":"https://pith.science/pith/O4N5VKQHZFGITKGL2HJMKKB2KF","download_json":"https://pith.science/pith/O4N5VKQHZFGITKGL2HJMKKB2KF.json","view_paper":"https://pith.science/paper/O4N5VKQH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.5915&json=true","fetch_graph":"https://pith.science/api/pith-number/O4N5VKQHZFGITKGL2HJMKKB2KF/graph.json","fetch_events":"https://pith.science/api/pith-number/O4N5VKQHZFGITKGL2HJMKKB2KF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O4N5VKQHZFGITKGL2HJMKKB2KF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O4N5VKQHZFGITKGL2HJMKKB2KF/action/storage_attestation","attest_author":"https://pith.science/pith/O4N5VKQHZFGITKGL2HJMKKB2KF/action/author_attestation","sign_citation":"https://pith.science/pith/O4N5VKQHZFGITKGL2HJMKKB2KF/action/citation_signature","submit_replication":"https://pith.science/pith/O4N5VKQHZFGITKGL2HJMKKB2KF/action/replication_record"}},"created_at":"2026-05-18T03:39:29.152220+00:00","updated_at":"2026-05-18T03:39:29.152220+00:00"}