{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:PYZ7VIWBA4KZWFEVDT4AF3C6JD","short_pith_number":"pith:PYZ7VIWB","schema_version":"1.0","canonical_sha256":"7e33faa2c107159b14951cf802ec5e48f7e45a55e9e02e74e6c60c76cfb4d280","source":{"kind":"arxiv","id":"1008.2936","version":3},"attestation_state":"computed","paper":{"title":"On the grasshopper problem with signed jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"G\\'eza K\\'os","submitted_at":"2010-08-17T17:21:31Z","abstract_excerpt":"The 6th problem of the 50th International Mathematical Olympiad (IMO), held in Germany, 2009, was the following.\n  Let $a_1,a_2,...,a_n$ be distinct positive integers and let $M$ be a set of $n-1$ positive integers not containing $s=a_1+a_2+...+a_n$. A grasshopper is to jump along the real axis, starting at the point 0 and making $n$ jumps to the right with lengths $a_1,a_2,...,a_n$ in some order. Prove that the order can be chosen in such a way that the grasshopper never lands on any point in $M$.\n  The problem was discussed in many on-line forums, as well by communities of students as by sen"},"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":"1008.2936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-17T17:21:31Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"2ccc025d13ddbd9a402d36fb5ff8cc05a13d2943e855e00e1a907efa84803072","abstract_canon_sha256":"376c8c9bcaf3a16351336f76c072952cbc3db02d3bc0228f72b491b90a7c6c03"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:36.126803Z","signature_b64":"gg0ZTYeem8vJfOE6nMJAyDlCyDUsgorud15lRNfo8AKi04B00IsGhkOlO2O5Yovu5biB++VpWYmMcCQROyxiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e33faa2c107159b14951cf802ec5e48f7e45a55e9e02e74e6c60c76cfb4d280","last_reissued_at":"2026-05-18T04:15:36.126310Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:36.126310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the grasshopper problem with signed jumps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"G\\'eza K\\'os","submitted_at":"2010-08-17T17:21:31Z","abstract_excerpt":"The 6th problem of the 50th International Mathematical Olympiad (IMO), held in Germany, 2009, was the following.\n  Let $a_1,a_2,...,a_n$ be distinct positive integers and let $M$ be a set of $n-1$ positive integers not containing $s=a_1+a_2+...+a_n$. A grasshopper is to jump along the real axis, starting at the point 0 and making $n$ jumps to the right with lengths $a_1,a_2,...,a_n$ in some order. Prove that the order can be chosen in such a way that the grasshopper never lands on any point in $M$.\n  The problem was discussed in many on-line forums, as well by communities of students as by sen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2936","kind":"arxiv","version":3},"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":"1008.2936","created_at":"2026-05-18T04:15:36.126392+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.2936v3","created_at":"2026-05-18T04:15:36.126392+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2936","created_at":"2026-05-18T04:15:36.126392+00:00"},{"alias_kind":"pith_short_12","alias_value":"PYZ7VIWBA4KZ","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"PYZ7VIWBA4KZWFEV","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"PYZ7VIWB","created_at":"2026-05-18T12:26:12.377268+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/PYZ7VIWBA4KZWFEVDT4AF3C6JD","json":"https://pith.science/pith/PYZ7VIWBA4KZWFEVDT4AF3C6JD.json","graph_json":"https://pith.science/api/pith-number/PYZ7VIWBA4KZWFEVDT4AF3C6JD/graph.json","events_json":"https://pith.science/api/pith-number/PYZ7VIWBA4KZWFEVDT4AF3C6JD/events.json","paper":"https://pith.science/paper/PYZ7VIWB"},"agent_actions":{"view_html":"https://pith.science/pith/PYZ7VIWBA4KZWFEVDT4AF3C6JD","download_json":"https://pith.science/pith/PYZ7VIWBA4KZWFEVDT4AF3C6JD.json","view_paper":"https://pith.science/paper/PYZ7VIWB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.2936&json=true","fetch_graph":"https://pith.science/api/pith-number/PYZ7VIWBA4KZWFEVDT4AF3C6JD/graph.json","fetch_events":"https://pith.science/api/pith-number/PYZ7VIWBA4KZWFEVDT4AF3C6JD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PYZ7VIWBA4KZWFEVDT4AF3C6JD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PYZ7VIWBA4KZWFEVDT4AF3C6JD/action/storage_attestation","attest_author":"https://pith.science/pith/PYZ7VIWBA4KZWFEVDT4AF3C6JD/action/author_attestation","sign_citation":"https://pith.science/pith/PYZ7VIWBA4KZWFEVDT4AF3C6JD/action/citation_signature","submit_replication":"https://pith.science/pith/PYZ7VIWBA4KZWFEVDT4AF3C6JD/action/replication_record"}},"created_at":"2026-05-18T04:15:36.126392+00:00","updated_at":"2026-05-18T04:15:36.126392+00:00"}