{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2HRHEXQB4745MUHDOZAMPONCPY","short_pith_number":"pith:2HRHEXQB","canonical_record":{"source":{"id":"1305.2584","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-05-12T13:03:34Z","cross_cats_sorted":[],"title_canon_sha256":"3f05dae7185f147cbb6fe2d5d4720000a658ed2c2fa979bb1040e173f52686c6","abstract_canon_sha256":"4dfac8dca94149c58f7ad856b33f1dbaa1ca7f545d3d4f0d56ffd7b26405fad7"},"schema_version":"1.0"},"canonical_sha256":"d1e2725e01e7f9d650e37640c7b9a27e06b53e17a40175e3b66e5eccb70451c3","source":{"kind":"arxiv","id":"1305.2584","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2584","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2584v3","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2584","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"2HRHEXQB4745","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2HRHEXQB4745MUHD","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2HRHEXQB","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2HRHEXQB4745MUHDOZAMPONCPY","target":"record","payload":{"canonical_record":{"source":{"id":"1305.2584","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-05-12T13:03:34Z","cross_cats_sorted":[],"title_canon_sha256":"3f05dae7185f147cbb6fe2d5d4720000a658ed2c2fa979bb1040e173f52686c6","abstract_canon_sha256":"4dfac8dca94149c58f7ad856b33f1dbaa1ca7f545d3d4f0d56ffd7b26405fad7"},"schema_version":"1.0"},"canonical_sha256":"d1e2725e01e7f9d650e37640c7b9a27e06b53e17a40175e3b66e5eccb70451c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:40.762135Z","signature_b64":"E75TUO8RiMmqS8IGBPS9wn800yFQSrCbn+Jkj5J1mJ+IgKzf9RRm8P3LiTkJruACPr6e849c41VaRAE+8dytCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1e2725e01e7f9d650e37640c7b9a27e06b53e17a40175e3b66e5eccb70451c3","last_reissued_at":"2026-05-18T03:14:40.761578Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:40.761578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.2584","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":"2026-05-18T03:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BBrJQSfZimlYl5UCQmxa1LE8PiyOWi+nHGO76SeL5CFBLrgT1IFtiM3w9Pw9SaPGn0WnEvUQc9cRg8MwGG0FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:22:38.033903Z"},"content_sha256":"56b182a027ed3504a76c523f1af2c334c47acdb3ab84448cdb64203c62edeb01","schema_version":"1.0","event_id":"sha256:56b182a027ed3504a76c523f1af2c334c47acdb3ab84448cdb64203c62edeb01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2HRHEXQB4745MUHDOZAMPONCPY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Borsuk's conjecture for two-distance sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Andriy V. Bondarenko","submitted_at":"2013-05-12T13:03:34Z","abstract_excerpt":"In this paper we answer Larman's question on Borsuk's conjecture for two-distance sets. We find a two-distance set consisting of 416 points on the unit sphere in the dimension 65 which cannot be partitioned into 83 parts of smaller diameter. This also reduces the smallest dimension in which Borsuk's conjecture is known to be false. Other examples of two-distance sets with large Borsuk's numbers will be given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2584","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":"2026-05-18T03:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wcRSZImN/z1E36GV5cYKL4tiNNTxXb2ZamggeWYpLKZbNUYzrvjUAdLtHA7ISEyvdHgx6JR+c1fQV75tR7jHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:22:38.034607Z"},"content_sha256":"e87e7dc90e55255d7848b883544a2972022a1da37c9a84db0db7d5fe2f518ed7","schema_version":"1.0","event_id":"sha256:e87e7dc90e55255d7848b883544a2972022a1da37c9a84db0db7d5fe2f518ed7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HRHEXQB4745MUHDOZAMPONCPY/bundle.json","state_url":"https://pith.science/pith/2HRHEXQB4745MUHDOZAMPONCPY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HRHEXQB4745MUHDOZAMPONCPY/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":"2026-05-25T19:22:38Z","links":{"resolver":"https://pith.science/pith/2HRHEXQB4745MUHDOZAMPONCPY","bundle":"https://pith.science/pith/2HRHEXQB4745MUHDOZAMPONCPY/bundle.json","state":"https://pith.science/pith/2HRHEXQB4745MUHDOZAMPONCPY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HRHEXQB4745MUHDOZAMPONCPY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2HRHEXQB4745MUHDOZAMPONCPY","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":"4dfac8dca94149c58f7ad856b33f1dbaa1ca7f545d3d4f0d56ffd7b26405fad7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-05-12T13:03:34Z","title_canon_sha256":"3f05dae7185f147cbb6fe2d5d4720000a658ed2c2fa979bb1040e173f52686c6"},"schema_version":"1.0","source":{"id":"1305.2584","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2584","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2584v3","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2584","created_at":"2026-05-18T03:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"2HRHEXQB4745","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2HRHEXQB4745MUHD","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2HRHEXQB","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:e87e7dc90e55255d7848b883544a2972022a1da37c9a84db0db7d5fe2f518ed7","target":"graph","created_at":"2026-05-18T03:14:40Z","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":"In this paper we answer Larman's question on Borsuk's conjecture for two-distance sets. We find a two-distance set consisting of 416 points on the unit sphere in the dimension 65 which cannot be partitioned into 83 parts of smaller diameter. This also reduces the smallest dimension in which Borsuk's conjecture is known to be false. Other examples of two-distance sets with large Borsuk's numbers will be given.","authors_text":"Andriy V. Bondarenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-05-12T13:03:34Z","title":"On Borsuk's conjecture for two-distance sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2584","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":"sha256:56b182a027ed3504a76c523f1af2c334c47acdb3ab84448cdb64203c62edeb01","target":"record","created_at":"2026-05-18T03:14:40Z","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":"4dfac8dca94149c58f7ad856b33f1dbaa1ca7f545d3d4f0d56ffd7b26405fad7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-05-12T13:03:34Z","title_canon_sha256":"3f05dae7185f147cbb6fe2d5d4720000a658ed2c2fa979bb1040e173f52686c6"},"schema_version":"1.0","source":{"id":"1305.2584","kind":"arxiv","version":3}},"canonical_sha256":"d1e2725e01e7f9d650e37640c7b9a27e06b53e17a40175e3b66e5eccb70451c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1e2725e01e7f9d650e37640c7b9a27e06b53e17a40175e3b66e5eccb70451c3","first_computed_at":"2026-05-18T03:14:40.761578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:40.761578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E75TUO8RiMmqS8IGBPS9wn800yFQSrCbn+Jkj5J1mJ+IgKzf9RRm8P3LiTkJruACPr6e849c41VaRAE+8dytCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:40.762135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2584","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56b182a027ed3504a76c523f1af2c334c47acdb3ab84448cdb64203c62edeb01","sha256:e87e7dc90e55255d7848b883544a2972022a1da37c9a84db0db7d5fe2f518ed7"],"state_sha256":"a615c8ed72acbb951745aacc1ed2a7517b87f21fa28bea8f2d60c230fea83a87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YnGYZ16eR72viwd6uPuADPGMURR3L9/FJrbuLbPcDN/VLbkd6AkxZRt/luHFxYQDrb3qt/0DGvYzwJI91m3eDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:22:38.038526Z","bundle_sha256":"f7f36bf3e6b542018cfb9d9fe52f783e75b4b52409b2d7e06183f00b742de36d"}}