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Let $L_1, \\ldots, L_r$ be linear forms with real coefficients such that if $\\boldsymbol{\\alpha} \\in \\mathbb{R}^r \\setminus \\{ \\boldsymbol{0} \\}$ then $\\boldsymbol{\\alpha} \\cdot \\mathbf{L}$ is not a rational form. Assume that $h > 16 + 8 r$. Let $\\boldsymbol{\\tau} \\in \\mathbb{R}^r$, and let $\\eta$ be a positive real number. We prove an asymptotic formula for the weighted number of integer solutions $\\mathbf{x} \\in [-P,P]^n$ to the system $C(\\mathbf{x}) = 0, \\: |\\mathbf{L}(\\mathbf{x}) - "},"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":"1504.07837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-29T12:48:14Z","cross_cats_sorted":[],"title_canon_sha256":"06a8f4f741a1280a2751f076f2b79ca344a3c11b0b75ecdfb27a83fbce661bf6","abstract_canon_sha256":"e03e424491ad75b81516a75d40f791a8d876941af0b7bab7793088e0b3218f65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:09.849498Z","signature_b64":"c9BjBhwmzpHkoSdvg6r4Q5rkjaQNk/kv8ImS//2E9P+cWvqMxAIBrw4WqzHw7ojwwaGjwC0gxs02OWq9zbbABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97e858d85232801ff9adc7507c513714b0aca64743d63ba701b47c388425af46","last_reissued_at":"2026-05-18T01:18:09.849051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:09.849051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equidistribution of values of linear forms on a cubic hypersurface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Sam Chow","submitted_at":"2015-04-29T12:48:14Z","abstract_excerpt":"Let $C$ be a cubic form with rational coefficients in $n$ variables, and let $h$ be the $h$-invariant of $C$. Let $L_1, \\ldots, L_r$ be linear forms with real coefficients such that if $\\boldsymbol{\\alpha} \\in \\mathbb{R}^r \\setminus \\{ \\boldsymbol{0} \\}$ then $\\boldsymbol{\\alpha} \\cdot \\mathbf{L}$ is not a rational form. Assume that $h > 16 + 8 r$. Let $\\boldsymbol{\\tau} \\in \\mathbb{R}^r$, and let $\\eta$ be a positive real number. We prove an asymptotic formula for the weighted number of integer solutions $\\mathbf{x} \\in [-P,P]^n$ to the system $C(\\mathbf{x}) = 0, \\: |\\mathbf{L}(\\mathbf{x}) - "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07837","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":"1504.07837","created_at":"2026-05-18T01:18:09.849112+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.07837v1","created_at":"2026-05-18T01:18:09.849112+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07837","created_at":"2026-05-18T01:18:09.849112+00:00"},{"alias_kind":"pith_short_12","alias_value":"S7UFRWCSGKAB","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"S7UFRWCSGKAB76NN","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"S7UFRWCS","created_at":"2026-05-18T12:29:39.896362+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/S7UFRWCSGKAB76NNY5IHYUJXCS","json":"https://pith.science/pith/S7UFRWCSGKAB76NNY5IHYUJXCS.json","graph_json":"https://pith.science/api/pith-number/S7UFRWCSGKAB76NNY5IHYUJXCS/graph.json","events_json":"https://pith.science/api/pith-number/S7UFRWCSGKAB76NNY5IHYUJXCS/events.json","paper":"https://pith.science/paper/S7UFRWCS"},"agent_actions":{"view_html":"https://pith.science/pith/S7UFRWCSGKAB76NNY5IHYUJXCS","download_json":"https://pith.science/pith/S7UFRWCSGKAB76NNY5IHYUJXCS.json","view_paper":"https://pith.science/paper/S7UFRWCS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.07837&json=true","fetch_graph":"https://pith.science/api/pith-number/S7UFRWCSGKAB76NNY5IHYUJXCS/graph.json","fetch_events":"https://pith.science/api/pith-number/S7UFRWCSGKAB76NNY5IHYUJXCS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S7UFRWCSGKAB76NNY5IHYUJXCS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S7UFRWCSGKAB76NNY5IHYUJXCS/action/storage_attestation","attest_author":"https://pith.science/pith/S7UFRWCSGKAB76NNY5IHYUJXCS/action/author_attestation","sign_citation":"https://pith.science/pith/S7UFRWCSGKAB76NNY5IHYUJXCS/action/citation_signature","submit_replication":"https://pith.science/pith/S7UFRWCSGKAB76NNY5IHYUJXCS/action/replication_record"}},"created_at":"2026-05-18T01:18:09.849112+00:00","updated_at":"2026-05-18T01:18:09.849112+00:00"}