{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:GROFRWZAT5K4PHMDYKWK3GKQMS","short_pith_number":"pith:GROFRWZA","canonical_record":{"source":{"id":"2206.00889","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-02T06:11:04Z","cross_cats_sorted":[],"title_canon_sha256":"1369b0ae617274a84dd15b92acd40be6b65aa18a9fa8eae99bcd8b52321b5b9a","abstract_canon_sha256":"a3c06d4f4148b4b706a8c8b55eda33b1bfa28bd57ae88324b44890c61e4d35b2"},"schema_version":"1.0"},"canonical_sha256":"345c58db209f55c79d83c2acad995064b92b217365879912a395967c94a0b068","source":{"kind":"arxiv","id":"2206.00889","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.00889","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"2206.00889v3","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.00889","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"GROFRWZAT5K4","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"pith_short_16","alias_value":"GROFRWZAT5K4PHMD","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"pith_short_8","alias_value":"GROFRWZA","created_at":"2026-07-05T06:33:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:GROFRWZAT5K4PHMDYKWK3GKQMS","target":"record","payload":{"canonical_record":{"source":{"id":"2206.00889","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-02T06:11:04Z","cross_cats_sorted":[],"title_canon_sha256":"1369b0ae617274a84dd15b92acd40be6b65aa18a9fa8eae99bcd8b52321b5b9a","abstract_canon_sha256":"a3c06d4f4148b4b706a8c8b55eda33b1bfa28bd57ae88324b44890c61e4d35b2"},"schema_version":"1.0"},"canonical_sha256":"345c58db209f55c79d83c2acad995064b92b217365879912a395967c94a0b068","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:33:40.147085Z","signature_b64":"yh8UeP7ueNP1EGGi31BznKrIqg2tHSvWqCPmihcz0xhO3XdWzMdZ3pB8N0WEJ6aGuUOMFJX0LNqyRmomLPEFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"345c58db209f55c79d83c2acad995064b92b217365879912a395967c94a0b068","last_reissued_at":"2026-07-05T06:33:40.146734Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:33:40.146734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.00889","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":"2026-07-05T06:33:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TEles0zPRnjX01OtEoQUrNZjT8L0gjDNZDN3/FzKuPEHR/pLge/9tDmdmTfyCf0PtsScqHdk+PZcigEI4M/6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:44:50.811408Z"},"content_sha256":"f453406a59ca3e387abd520b101f3aaccdcd14d33cdc451cabaa63b9e83ea452","schema_version":"1.0","event_id":"sha256:f453406a59ca3e387abd520b101f3aaccdcd14d33cdc451cabaa63b9e83ea452"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:GROFRWZAT5K4PHMDYKWK3GKQMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the structure of pointsets with many collinear triples","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jozsef Solymosi","submitted_at":"2022-06-02T06:11:04Z","abstract_excerpt":"It is conjectured that if a finite set of points in the plane contains many collinear triples then there is some structure in the set. We are going to show that under some combinatorial conditions such pointsets contain special configurations of triples, proving a case of Elekes' conjecture. Using the techniques applied in the proof we show a density version of Jamison's theorem. If the number of distinct directions between many pairs of points of a pointset in convex position is small, then many points are on a conic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.00889","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.00889/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:33:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKnmDZ1v58YU4ZmQ44M+XADO8Ik/w1tZO3EYuETu9i7Jyv6Ssk7H3KcSB3adR5X4g9v2Arm+wLAWwYebwQY+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:44:50.812331Z"},"content_sha256":"d633c3db29fa8119a44948a31958e3349e7f9f8266c2f54a34bbdd076b4290e6","schema_version":"1.0","event_id":"sha256:d633c3db29fa8119a44948a31958e3349e7f9f8266c2f54a34bbdd076b4290e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GROFRWZAT5K4PHMDYKWK3GKQMS/bundle.json","state_url":"https://pith.science/pith/GROFRWZAT5K4PHMDYKWK3GKQMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GROFRWZAT5K4PHMDYKWK3GKQMS/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":"2026-08-04T18:44:50Z","links":{"resolver":"https://pith.science/pith/GROFRWZAT5K4PHMDYKWK3GKQMS","bundle":"https://pith.science/pith/GROFRWZAT5K4PHMDYKWK3GKQMS/bundle.json","state":"https://pith.science/pith/GROFRWZAT5K4PHMDYKWK3GKQMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GROFRWZAT5K4PHMDYKWK3GKQMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GROFRWZAT5K4PHMDYKWK3GKQMS","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":"a3c06d4f4148b4b706a8c8b55eda33b1bfa28bd57ae88324b44890c61e4d35b2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-02T06:11:04Z","title_canon_sha256":"1369b0ae617274a84dd15b92acd40be6b65aa18a9fa8eae99bcd8b52321b5b9a"},"schema_version":"1.0","source":{"id":"2206.00889","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.00889","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"arxiv_version","alias_value":"2206.00889v3","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.00889","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"pith_short_12","alias_value":"GROFRWZAT5K4","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"pith_short_16","alias_value":"GROFRWZAT5K4PHMD","created_at":"2026-07-05T06:33:40Z"},{"alias_kind":"pith_short_8","alias_value":"GROFRWZA","created_at":"2026-07-05T06:33:40Z"}],"graph_snapshots":[{"event_id":"sha256:d633c3db29fa8119a44948a31958e3349e7f9f8266c2f54a34bbdd076b4290e6","target":"graph","created_at":"2026-07-05T06:33:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.00889/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is conjectured that if a finite set of points in the plane contains many collinear triples then there is some structure in the set. We are going to show that under some combinatorial conditions such pointsets contain special configurations of triples, proving a case of Elekes' conjecture. Using the techniques applied in the proof we show a density version of Jamison's theorem. If the number of distinct directions between many pairs of points of a pointset in convex position is small, then many points are on a conic.","authors_text":"Jozsef Solymosi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-02T06:11:04Z","title":"On the structure of pointsets with many collinear triples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.00889","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:f453406a59ca3e387abd520b101f3aaccdcd14d33cdc451cabaa63b9e83ea452","target":"record","created_at":"2026-07-05T06:33:40Z","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":"a3c06d4f4148b4b706a8c8b55eda33b1bfa28bd57ae88324b44890c61e4d35b2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-06-02T06:11:04Z","title_canon_sha256":"1369b0ae617274a84dd15b92acd40be6b65aa18a9fa8eae99bcd8b52321b5b9a"},"schema_version":"1.0","source":{"id":"2206.00889","kind":"arxiv","version":3}},"canonical_sha256":"345c58db209f55c79d83c2acad995064b92b217365879912a395967c94a0b068","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"345c58db209f55c79d83c2acad995064b92b217365879912a395967c94a0b068","first_computed_at":"2026-07-05T06:33:40.146734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:33:40.146734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yh8UeP7ueNP1EGGi31BznKrIqg2tHSvWqCPmihcz0xhO3XdWzMdZ3pB8N0WEJ6aGuUOMFJX0LNqyRmomLPEFAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:33:40.147085Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.00889","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f453406a59ca3e387abd520b101f3aaccdcd14d33cdc451cabaa63b9e83ea452","sha256:d633c3db29fa8119a44948a31958e3349e7f9f8266c2f54a34bbdd076b4290e6"],"state_sha256":"0cbbdb625205b6eacbfa0ba8d3142822d0d2d5ad54993fd8a14252b7430a63cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+pKrCP8NlGz2x/MeAqoX1hUcZ+77Q8SxKoe2UIufFZFO/yF6nckpFKn2VWwlbyBjFiXZ3hVYoNfRxX9ZRlePDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T18:44:50.822311Z","bundle_sha256":"d3524e30c28e3ff97ecf6cc9ac02954a0dd45a853ff7db217e0d556d9054e034"}}