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We give a positive answer to this problem in $\\mathbb{Z}^2$ under an additional hypothesis that $(2K\\cap \\mathbb{Z}^2)|u^\\perp$ and $(2L\\cap \\mathbb{Z}^2)|u^\\perp$ have the same number of points."},"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":"1602.05574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-02-17T17:37:34Z","cross_cats_sorted":["math.CO","math.FA"],"title_canon_sha256":"d350e39eec3a287be369b14314e6f5e5d6bc005751638a7b03985876c22a6865","abstract_canon_sha256":"f6c7238dc991d871c745561f34bae6eef294b3b666468f194bbbdb1a47fc8a87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:23.729326Z","signature_b64":"yzHD19Ks6csmkKVMfzJxBwaJZBtaBIjNOA5XOpsnY2u9vtDVzdwCRAwwhFnEsxRrsShk9r6fBDwwBykCp5M4Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3908ef87ea389d2747a12f78f500da349cd2af978c3d28d24dd84609ac350ea7","last_reissued_at":"2026-05-18T01:20:23.728717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:23.728717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Aleksandrov projection problem for convex lattice sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.FA"],"primary_cat":"math.MG","authors_text":"Ning Zhang","submitted_at":"2016-02-17T17:37:34Z","abstract_excerpt":"Let $K$ and $L$ be origin-symmetric convex integer polytopes in $\\mathbb{R}^n$. We study a discrete analogue of the Aleksandrov projection problem. If for every $u\\in \\mathbb{Z}^n$, the sets $(K\\cap \\mathbb{Z}^n)|u^\\perp$ and $(L\\cap \\mathbb{Z}^n)|u^\\perp$ have the same number of points, is then $K=L$? We give a positive answer to this problem in $\\mathbb{Z}^2$ under an additional hypothesis that $(2K\\cap \\mathbb{Z}^2)|u^\\perp$ and $(2L\\cap \\mathbb{Z}^2)|u^\\perp$ have the same number of points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05574","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":"1602.05574","created_at":"2026-05-18T01:20:23.728809+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.05574v1","created_at":"2026-05-18T01:20:23.728809+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05574","created_at":"2026-05-18T01:20:23.728809+00:00"},{"alias_kind":"pith_short_12","alias_value":"HEEO7B7KHCOS","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HEEO7B7KHCOSOR5B","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HEEO7B7K","created_at":"2026-05-18T12:30:19.053100+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/HEEO7B7KHCOSOR5BF54PKAG2GS","json":"https://pith.science/pith/HEEO7B7KHCOSOR5BF54PKAG2GS.json","graph_json":"https://pith.science/api/pith-number/HEEO7B7KHCOSOR5BF54PKAG2GS/graph.json","events_json":"https://pith.science/api/pith-number/HEEO7B7KHCOSOR5BF54PKAG2GS/events.json","paper":"https://pith.science/paper/HEEO7B7K"},"agent_actions":{"view_html":"https://pith.science/pith/HEEO7B7KHCOSOR5BF54PKAG2GS","download_json":"https://pith.science/pith/HEEO7B7KHCOSOR5BF54PKAG2GS.json","view_paper":"https://pith.science/paper/HEEO7B7K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.05574&json=true","fetch_graph":"https://pith.science/api/pith-number/HEEO7B7KHCOSOR5BF54PKAG2GS/graph.json","fetch_events":"https://pith.science/api/pith-number/HEEO7B7KHCOSOR5BF54PKAG2GS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HEEO7B7KHCOSOR5BF54PKAG2GS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HEEO7B7KHCOSOR5BF54PKAG2GS/action/storage_attestation","attest_author":"https://pith.science/pith/HEEO7B7KHCOSOR5BF54PKAG2GS/action/author_attestation","sign_citation":"https://pith.science/pith/HEEO7B7KHCOSOR5BF54PKAG2GS/action/citation_signature","submit_replication":"https://pith.science/pith/HEEO7B7KHCOSOR5BF54PKAG2GS/action/replication_record"}},"created_at":"2026-05-18T01:20:23.728809+00:00","updated_at":"2026-05-18T01:20:23.728809+00:00"}