{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GVRFH4EMPEGR2IWVF2OZ2RVDGA","short_pith_number":"pith:GVRFH4EM","schema_version":"1.0","canonical_sha256":"356253f08c790d1d22d52e9d9d46a3303baeab56e9592f426abd7b8570114a16","source":{"kind":"arxiv","id":"1807.10906","version":1},"attestation_state":"computed","paper":{"title":"No bullying! A playful proof of Brouwer's fixed-point theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Henrik Petri, Mark Voorneveld","submitted_at":"2018-07-28T07:48:59Z","abstract_excerpt":"We give an elementary proof of Brouwer's fixed-point theorem. The only mathematical prerequisite is a version of the Bolzano-Weierstrass theorem: a sequence in a compact subset of $n$-dimensional Euclidean space has a convergent subsequence with a limit in that set. Our main tool is a `no-bullying' lemma for agents with preferences over indivisible goods. What does this lemma claim? Consider a finite number of children, each with a single indivisible good (a toy) and preferences over those toys. Let's say that a group of children, possibly after exchanging toys, could bully some poor kid if al"},"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":"1807.10906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2018-07-28T07:48:59Z","cross_cats_sorted":[],"title_canon_sha256":"7119c717a086d61eb45ba1ff7fdf7744f75ff82d57ab9b0de7f348911dee8321","abstract_canon_sha256":"0134745e982b4c646cfd76ea2f8d6bb8222d25496a0d3775a0c2fbc333b94e02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:35.065627Z","signature_b64":"W0VnWz60WOYPgVZVUUvQRslMCLbWRk+inueo5u5J54nrfpQZhvy5XHLwm1iYF4wFy4TQ24etiaNzTdtne4hAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"356253f08c790d1d22d52e9d9d46a3303baeab56e9592f426abd7b8570114a16","last_reissued_at":"2026-05-18T00:09:35.065062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:35.065062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"No bullying! A playful proof of Brouwer's fixed-point theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Henrik Petri, Mark Voorneveld","submitted_at":"2018-07-28T07:48:59Z","abstract_excerpt":"We give an elementary proof of Brouwer's fixed-point theorem. The only mathematical prerequisite is a version of the Bolzano-Weierstrass theorem: a sequence in a compact subset of $n$-dimensional Euclidean space has a convergent subsequence with a limit in that set. Our main tool is a `no-bullying' lemma for agents with preferences over indivisible goods. What does this lemma claim? Consider a finite number of children, each with a single indivisible good (a toy) and preferences over those toys. Let's say that a group of children, possibly after exchanging toys, could bully some poor kid if al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10906","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":"1807.10906","created_at":"2026-05-18T00:09:35.065132+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.10906v1","created_at":"2026-05-18T00:09:35.065132+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10906","created_at":"2026-05-18T00:09:35.065132+00:00"},{"alias_kind":"pith_short_12","alias_value":"GVRFH4EMPEGR","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GVRFH4EMPEGR2IWV","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GVRFH4EM","created_at":"2026-05-18T12:32:25.280505+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/GVRFH4EMPEGR2IWVF2OZ2RVDGA","json":"https://pith.science/pith/GVRFH4EMPEGR2IWVF2OZ2RVDGA.json","graph_json":"https://pith.science/api/pith-number/GVRFH4EMPEGR2IWVF2OZ2RVDGA/graph.json","events_json":"https://pith.science/api/pith-number/GVRFH4EMPEGR2IWVF2OZ2RVDGA/events.json","paper":"https://pith.science/paper/GVRFH4EM"},"agent_actions":{"view_html":"https://pith.science/pith/GVRFH4EMPEGR2IWVF2OZ2RVDGA","download_json":"https://pith.science/pith/GVRFH4EMPEGR2IWVF2OZ2RVDGA.json","view_paper":"https://pith.science/paper/GVRFH4EM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.10906&json=true","fetch_graph":"https://pith.science/api/pith-number/GVRFH4EMPEGR2IWVF2OZ2RVDGA/graph.json","fetch_events":"https://pith.science/api/pith-number/GVRFH4EMPEGR2IWVF2OZ2RVDGA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GVRFH4EMPEGR2IWVF2OZ2RVDGA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GVRFH4EMPEGR2IWVF2OZ2RVDGA/action/storage_attestation","attest_author":"https://pith.science/pith/GVRFH4EMPEGR2IWVF2OZ2RVDGA/action/author_attestation","sign_citation":"https://pith.science/pith/GVRFH4EMPEGR2IWVF2OZ2RVDGA/action/citation_signature","submit_replication":"https://pith.science/pith/GVRFH4EMPEGR2IWVF2OZ2RVDGA/action/replication_record"}},"created_at":"2026-05-18T00:09:35.065132+00:00","updated_at":"2026-05-18T00:09:35.065132+00:00"}