{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:EKQLV6IXWTBQHCBP7SQNGQUDFT","short_pith_number":"pith:EKQLV6IX","canonical_record":{"source":{"id":"0712.4009","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-12-24T17:47:44Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"3d369d9fa58c61c5da376bf724394356696743285fa806d1889c186d830272ed","abstract_canon_sha256":"96776a085dd8a08e02ae9299bac11353db174e8fdd7a04d0d9d0925526db890d"},"schema_version":"1.0"},"canonical_sha256":"22a0baf917b4c303882ffca0d342832cfe2129361c814da6098074f19ac17127","source":{"kind":"arxiv","id":"0712.4009","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4009","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4009v3","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4009","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"EKQLV6IXWTBQ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"EKQLV6IXWTBQHCBP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"EKQLV6IX","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:EKQLV6IXWTBQHCBP7SQNGQUDFT","target":"record","payload":{"canonical_record":{"source":{"id":"0712.4009","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-12-24T17:47:44Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"3d369d9fa58c61c5da376bf724394356696743285fa806d1889c186d830272ed","abstract_canon_sha256":"96776a085dd8a08e02ae9299bac11353db174e8fdd7a04d0d9d0925526db890d"},"schema_version":"1.0"},"canonical_sha256":"22a0baf917b4c303882ffca0d342832cfe2129361c814da6098074f19ac17127","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:33.120563Z","signature_b64":"VPxCgL0I5FMy37UQzH1thp7fY1Nq8oZ224Ju0GG9e55Bv/9yOD3IoUvSkULZ69zyZYrC41cMbFZN/KbTRnIZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22a0baf917b4c303882ffca0d342832cfe2129361c814da6098074f19ac17127","last_reissued_at":"2026-05-18T00:04:33.119943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:33.119943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.4009","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zHfIWK8hL3VEbv2OFebwiWsg1gVLR9q+j77YjIFnF+ruxGs951yQCRww6pHa6hwdmvP1rs/QPi0eKixffeSjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:37:52.431344Z"},"content_sha256":"ac5a8da85e2d2544101d4fd9cb1fbc14a278a85bf1bbfb3e4b403e8ffffecc27","schema_version":"1.0","event_id":"sha256:ac5a8da85e2d2544101d4fd9cb1fbc14a278a85bf1bbfb3e4b403e8ffffecc27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:EKQLV6IXWTBQHCBP7SQNGQUDFT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A two-page disproof of the Borsuk partition conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"A. Skopenkov","submitted_at":"2007-12-24T17:47:44Z","abstract_excerpt":"It is presented the simplest known disproof of the Borsuk conjecture stating that if a bounded subset of n-dimensional Euclidean space contains more than n points, then the subset can be partitioned into n+1 nonempty parts of smaller diameter.\n  The argument is due to N. Alon and is a remarkable application of combinatorics and algebra to geometry. This note is purely expository and is accessible for students."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4009","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caFSVRYztCWhqK5H+iQd0+DdQKHwxrGK5kc12GESTUQK0rPwcqJQL/QD4tzckp2d2iX/XT+YRSAlskEjibgEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:37:52.431973Z"},"content_sha256":"6f2d0f291d6404883d993c80b7406704a6a4a15d8444ebd144fb7820456cdcb9","schema_version":"1.0","event_id":"sha256:6f2d0f291d6404883d993c80b7406704a6a4a15d8444ebd144fb7820456cdcb9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKQLV6IXWTBQHCBP7SQNGQUDFT/bundle.json","state_url":"https://pith.science/pith/EKQLV6IXWTBQHCBP7SQNGQUDFT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKQLV6IXWTBQHCBP7SQNGQUDFT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T03:37:52Z","links":{"resolver":"https://pith.science/pith/EKQLV6IXWTBQHCBP7SQNGQUDFT","bundle":"https://pith.science/pith/EKQLV6IXWTBQHCBP7SQNGQUDFT/bundle.json","state":"https://pith.science/pith/EKQLV6IXWTBQHCBP7SQNGQUDFT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKQLV6IXWTBQHCBP7SQNGQUDFT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:EKQLV6IXWTBQHCBP7SQNGQUDFT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"96776a085dd8a08e02ae9299bac11353db174e8fdd7a04d0d9d0925526db890d","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-12-24T17:47:44Z","title_canon_sha256":"3d369d9fa58c61c5da376bf724394356696743285fa806d1889c186d830272ed"},"schema_version":"1.0","source":{"id":"0712.4009","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.4009","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"arxiv_version","alias_value":"0712.4009v3","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.4009","created_at":"2026-05-18T00:04:33Z"},{"alias_kind":"pith_short_12","alias_value":"EKQLV6IXWTBQ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"EKQLV6IXWTBQHCBP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"EKQLV6IX","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:6f2d0f291d6404883d993c80b7406704a6a4a15d8444ebd144fb7820456cdcb9","target":"graph","created_at":"2026-05-18T00:04:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"It is presented the simplest known disproof of the Borsuk conjecture stating that if a bounded subset of n-dimensional Euclidean space contains more than n points, then the subset can be partitioned into n+1 nonempty parts of smaller diameter.\n  The argument is due to N. Alon and is a remarkable application of combinatorics and algebra to geometry. This note is purely expository and is accessible for students.","authors_text":"A. Skopenkov","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-12-24T17:47:44Z","title":"A two-page disproof of the Borsuk partition conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.4009","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ac5a8da85e2d2544101d4fd9cb1fbc14a278a85bf1bbfb3e4b403e8ffffecc27","target":"record","created_at":"2026-05-18T00:04:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"96776a085dd8a08e02ae9299bac11353db174e8fdd7a04d0d9d0925526db890d","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2007-12-24T17:47:44Z","title_canon_sha256":"3d369d9fa58c61c5da376bf724394356696743285fa806d1889c186d830272ed"},"schema_version":"1.0","source":{"id":"0712.4009","kind":"arxiv","version":3}},"canonical_sha256":"22a0baf917b4c303882ffca0d342832cfe2129361c814da6098074f19ac17127","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22a0baf917b4c303882ffca0d342832cfe2129361c814da6098074f19ac17127","first_computed_at":"2026-05-18T00:04:33.119943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:33.119943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VPxCgL0I5FMy37UQzH1thp7fY1Nq8oZ224Ju0GG9e55Bv/9yOD3IoUvSkULZ69zyZYrC41cMbFZN/KbTRnIZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:33.120563Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.4009","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac5a8da85e2d2544101d4fd9cb1fbc14a278a85bf1bbfb3e4b403e8ffffecc27","sha256:6f2d0f291d6404883d993c80b7406704a6a4a15d8444ebd144fb7820456cdcb9"],"state_sha256":"1a40fa48e3f5731c5f37de1f781a1f06301192cfbff31bf20ff4762488cb1a26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4dyWfZ1NVdSadONBTLhQe5uqPtmvz8sDATkfZ3y8WOhZxXNWREIbG8z6Hc2X5QLsIZPpTEWu0Itrl7j5KxegCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:37:52.435471Z","bundle_sha256":"3a2f3af28a96b176846d522d6145a0336121126f0a81ebe2b7d424c078de0179"}}