{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IJLIHICLBZSGC52MWPZRK4VMVZ","short_pith_number":"pith:IJLIHICL","schema_version":"1.0","canonical_sha256":"425683a04b0e6461774cb3f31572acae5e18b8fc7d587a6117a3ff57a2a87f88","source":{"kind":"arxiv","id":"1705.07621","version":3},"attestation_state":"computed","paper":{"title":"The grasshopper problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adrian Kent, Olga Goulko","submitted_at":"2017-05-22T09:15:19Z","abstract_excerpt":"We introduce and physically motivate the following problem in geometric combinatorics, originally inspired by analysing Bell inequalities. A grasshopper lands at a random point on a planar lawn of area one. It then jumps once, a fixed distance $d$, in a random direction. What shape should the lawn be to maximise the chance that the grasshopper remains on the lawn after jumping? We show that, perhaps surprisingly, a disc shaped lawn is not optimal for any $d>0$. We investigate further by introducing a spin model whose ground state corresponds to the solution of a discrete version of the grassho"},"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":"1705.07621","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-05-22T09:15:19Z","cross_cats_sorted":["math-ph","math.CO","math.MP","quant-ph"],"title_canon_sha256":"9bb57226fe9ed09791f47d6eff424057e9d64531a9bfb3da3b221aaf4df0efb3","abstract_canon_sha256":"f6b8a705c2088812d895a223e474c67297647956621ebf1d1ee26ac560d14a28"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:51.620084Z","signature_b64":"VAUoiJ2eSZTDi6T8Dr2YvAjXUjgpZQDW6Ev2kk0gRJhbcUX3GHlX7MIh2B3O4qEorVUmC9xlPhn8EbPzB3m6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"425683a04b0e6461774cb3f31572acae5e18b8fc7d587a6117a3ff57a2a87f88","last_reissued_at":"2026-05-18T00:29:51.619493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:51.619493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The grasshopper problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","quant-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adrian Kent, Olga Goulko","submitted_at":"2017-05-22T09:15:19Z","abstract_excerpt":"We introduce and physically motivate the following problem in geometric combinatorics, originally inspired by analysing Bell inequalities. A grasshopper lands at a random point on a planar lawn of area one. It then jumps once, a fixed distance $d$, in a random direction. What shape should the lawn be to maximise the chance that the grasshopper remains on the lawn after jumping? We show that, perhaps surprisingly, a disc shaped lawn is not optimal for any $d>0$. We investigate further by introducing a spin model whose ground state corresponds to the solution of a discrete version of the grassho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07621","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":"1705.07621","created_at":"2026-05-18T00:29:51.619576+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.07621v3","created_at":"2026-05-18T00:29:51.619576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07621","created_at":"2026-05-18T00:29:51.619576+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJLIHICLBZSG","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJLIHICLBZSGC52M","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJLIHICL","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2603.08579","citing_title":"The Grasshopper Problem on the Sphere","ref_index":13,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ","json":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ.json","graph_json":"https://pith.science/api/pith-number/IJLIHICLBZSGC52MWPZRK4VMVZ/graph.json","events_json":"https://pith.science/api/pith-number/IJLIHICLBZSGC52MWPZRK4VMVZ/events.json","paper":"https://pith.science/paper/IJLIHICL"},"agent_actions":{"view_html":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ","download_json":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ.json","view_paper":"https://pith.science/paper/IJLIHICL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.07621&json=true","fetch_graph":"https://pith.science/api/pith-number/IJLIHICLBZSGC52MWPZRK4VMVZ/graph.json","fetch_events":"https://pith.science/api/pith-number/IJLIHICLBZSGC52MWPZRK4VMVZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ/action/storage_attestation","attest_author":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ/action/author_attestation","sign_citation":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ/action/citation_signature","submit_replication":"https://pith.science/pith/IJLIHICLBZSGC52MWPZRK4VMVZ/action/replication_record"}},"created_at":"2026-05-18T00:29:51.619576+00:00","updated_at":"2026-05-18T00:29:51.619576+00:00"}