{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:R5CBWEH2VIVRGGJC3OWUXIQT67","short_pith_number":"pith:R5CBWEH2","canonical_record":{"source":{"id":"1008.2988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-18T00:13:39Z","cross_cats_sorted":[],"title_canon_sha256":"95b2d1679354e4ced56e86a7f3b04856c66f8ef6d2d1de0c13b2d8838327d72b","abstract_canon_sha256":"b3f7c2421c8373a6d0937b0ef1126c446a8ce3a893634db9b85adb3d4eb407b2"},"schema_version":"1.0"},"canonical_sha256":"8f441b10faaa2b131922dbad4ba213f7d45788c34fc1c82c8e578b16c391ba52","source":{"kind":"arxiv","id":"1008.2988","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2988","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2988v1","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2988","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"pith_short_12","alias_value":"R5CBWEH2VIVR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"R5CBWEH2VIVRGGJC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"R5CBWEH2","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:R5CBWEH2VIVRGGJC3OWUXIQT67","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2988","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-18T00:13:39Z","cross_cats_sorted":[],"title_canon_sha256":"95b2d1679354e4ced56e86a7f3b04856c66f8ef6d2d1de0c13b2d8838327d72b","abstract_canon_sha256":"b3f7c2421c8373a6d0937b0ef1126c446a8ce3a893634db9b85adb3d4eb407b2"},"schema_version":"1.0"},"canonical_sha256":"8f441b10faaa2b131922dbad4ba213f7d45788c34fc1c82c8e578b16c391ba52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:03.770799Z","signature_b64":"oN3Tz11/ca3NF0Cd6RiIPlS34J42ICLnh8CFxMJmSfUuQJOwGT2czw1q9i+/2RkpvdIEfhlRavTZEwJ7vmXmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f441b10faaa2b131922dbad4ba213f7d45788c34fc1c82c8e578b16c391ba52","last_reissued_at":"2026-05-18T04:42:03.770297Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:03.770297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2988","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:42:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HWTR4eZnN3aFFwGk7ageejVaA+icZncDBPX04Tbpvb72SM+YC6NISsBg9+QZW8NKB4Jw8CshFjXeZhFH6k3PAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T14:14:51.371355Z"},"content_sha256":"c35994187b80f41af6d1054c5c7cdcbd9c56cf05a258598705f33c92cf8a54cd","schema_version":"1.0","event_id":"sha256:c35994187b80f41af6d1054c5c7cdcbd9c56cf05a258598705f33c92cf8a54cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:R5CBWEH2VIVRGGJC3OWUXIQT67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Attila~P\\'or, David R. Wood","submitted_at":"2010-08-18T00:13:39Z","abstract_excerpt":"The big-line-big-clique conjecture states that for all $k,\\ell\\geq2$ there is an integer $n$ such that every finite set of at least $n$ points in the plane contains $\\ell$ collinear points or $k$ pairwise visible points. We show that this conjecture is false for infinite point sets, by constructing a countably infinite point set with no 4 collinear points and no 3 pairwise visible points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2988","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:42:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tUHN/ez42A7TE1Wc/XiXJlJD+HB3UXpG1gKauhXFKotT678G2TPzvgDtrrOLcV+58RAcp//HQvpBDjXMQChrBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T14:14:51.371699Z"},"content_sha256":"10ad304d8b58f218c1ee35382ebde2400dbdb3d790520bb3aaede39a4d293d33","schema_version":"1.0","event_id":"sha256:10ad304d8b58f218c1ee35382ebde2400dbdb3d790520bb3aaede39a4d293d33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R5CBWEH2VIVRGGJC3OWUXIQT67/bundle.json","state_url":"https://pith.science/pith/R5CBWEH2VIVRGGJC3OWUXIQT67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R5CBWEH2VIVRGGJC3OWUXIQT67/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":"2026-06-10T14:14:51Z","links":{"resolver":"https://pith.science/pith/R5CBWEH2VIVRGGJC3OWUXIQT67","bundle":"https://pith.science/pith/R5CBWEH2VIVRGGJC3OWUXIQT67/bundle.json","state":"https://pith.science/pith/R5CBWEH2VIVRGGJC3OWUXIQT67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R5CBWEH2VIVRGGJC3OWUXIQT67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:R5CBWEH2VIVRGGJC3OWUXIQT67","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":"b3f7c2421c8373a6d0937b0ef1126c446a8ce3a893634db9b85adb3d4eb407b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-18T00:13:39Z","title_canon_sha256":"95b2d1679354e4ced56e86a7f3b04856c66f8ef6d2d1de0c13b2d8838327d72b"},"schema_version":"1.0","source":{"id":"1008.2988","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2988","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2988v1","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2988","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"pith_short_12","alias_value":"R5CBWEH2VIVR","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"R5CBWEH2VIVRGGJC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"R5CBWEH2","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:10ad304d8b58f218c1ee35382ebde2400dbdb3d790520bb3aaede39a4d293d33","target":"graph","created_at":"2026-05-18T04:42:03Z","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":"The big-line-big-clique conjecture states that for all $k,\\ell\\geq2$ there is an integer $n$ such that every finite set of at least $n$ points in the plane contains $\\ell$ collinear points or $k$ pairwise visible points. We show that this conjecture is false for infinite point sets, by constructing a countably infinite point set with no 4 collinear points and no 3 pairwise visible points.","authors_text":"Attila~P\\'or, David R. Wood","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-18T00:13:39Z","title":"The Big-Line-Big-Clique Conjecture is False for Infinite Point Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2988","kind":"arxiv","version":1},"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:c35994187b80f41af6d1054c5c7cdcbd9c56cf05a258598705f33c92cf8a54cd","target":"record","created_at":"2026-05-18T04:42:03Z","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":"b3f7c2421c8373a6d0937b0ef1126c446a8ce3a893634db9b85adb3d4eb407b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-18T00:13:39Z","title_canon_sha256":"95b2d1679354e4ced56e86a7f3b04856c66f8ef6d2d1de0c13b2d8838327d72b"},"schema_version":"1.0","source":{"id":"1008.2988","kind":"arxiv","version":1}},"canonical_sha256":"8f441b10faaa2b131922dbad4ba213f7d45788c34fc1c82c8e578b16c391ba52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f441b10faaa2b131922dbad4ba213f7d45788c34fc1c82c8e578b16c391ba52","first_computed_at":"2026-05-18T04:42:03.770297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:03.770297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oN3Tz11/ca3NF0Cd6RiIPlS34J42ICLnh8CFxMJmSfUuQJOwGT2czw1q9i+/2RkpvdIEfhlRavTZEwJ7vmXmAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:03.770799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2988","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c35994187b80f41af6d1054c5c7cdcbd9c56cf05a258598705f33c92cf8a54cd","sha256:10ad304d8b58f218c1ee35382ebde2400dbdb3d790520bb3aaede39a4d293d33"],"state_sha256":"4dc54124b33ae7823b2d64dabce16f8c9672bef564b683589eafef454e38d244"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Da0wFF6gc29o76NgeTeiwzJVXeDHUhJRWbOJez8FCzEkufrriW1F9qYUg7NSqe83IK9RvspvTFX7+dYro4mgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T14:14:51.373996Z","bundle_sha256":"3a1aa8b79e7452c5211eda8a738286758d049f8fca7220b08906a5a15fdb334a"}}