{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:L4A7UKJD3IXAJCITVYV3SP5AXM","short_pith_number":"pith:L4A7UKJD","canonical_record":{"source":{"id":"1412.8314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-29T11:28:55Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"11809e968dd6cadce9e0cfc6b176545f3fc794479a22fa0fac6795a9e19ccbf9","abstract_canon_sha256":"f5f447d5c958c72b175b3680acf9fc24e822ec977d86ca4a0f8810fc486b293e"},"schema_version":"1.0"},"canonical_sha256":"5f01fa2923da2e048913ae2bb93fa0bb065a89f4710cb32992472c1206d71325","source":{"kind":"arxiv","id":"1412.8314","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8314","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8314v2","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8314","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"L4A7UKJD3IXA","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L4A7UKJD3IXAJCIT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L4A7UKJD","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:L4A7UKJD3IXAJCITVYV3SP5AXM","target":"record","payload":{"canonical_record":{"source":{"id":"1412.8314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-29T11:28:55Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"11809e968dd6cadce9e0cfc6b176545f3fc794479a22fa0fac6795a9e19ccbf9","abstract_canon_sha256":"f5f447d5c958c72b175b3680acf9fc24e822ec977d86ca4a0f8810fc486b293e"},"schema_version":"1.0"},"canonical_sha256":"5f01fa2923da2e048913ae2bb93fa0bb065a89f4710cb32992472c1206d71325","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:38.845924Z","signature_b64":"3y9J0FXhgZVjstms7x9HK9ECplBUHIbaiC3b46BOOIbIUm6yADPh9DbtHDQOKrIZ109v5YKRRRb8uOJGzTxhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f01fa2923da2e048913ae2bb93fa0bb065a89f4710cb32992472c1206d71325","last_reissued_at":"2026-05-18T01:15:38.845130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:38.845130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.8314","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+LEhgmLFrSsIABlZmaHgCmbPdOjPAjZuM9DSZKQ5D/S4VfmateIVvTWL5u0fS+zMKUdd4kpBVZGtndaFRIxzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:37:51.935963Z"},"content_sha256":"66de02349c87407a373c76929a9c5541898cf52c91f6a63c4bcad48018d52267","schema_version":"1.0","event_id":"sha256:66de02349c87407a373c76929a9c5541898cf52c91f6a63c4bcad48018d52267"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:L4A7UKJD3IXAJCITVYV3SP5AXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the number of ordinary circles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Frank de Zeeuw, Hossein Nassajian Mojarrad","submitted_at":"2014-12-29T11:28:55Z","abstract_excerpt":"We prove that any $n$ points in $\\mathbb{R}^2$, not all on a line or circle, determine at least $\\frac{1}{4}n^2-O(n)$ ordinary circles (circles containing exactly three of the $n$ points). The main term of this bound is best possible for even $n$. Our proof relies on a recent result of Green and Tao on ordinary lines."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8314","kind":"arxiv","version":2},"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":"2026-05-18T01:15:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEj1ZEMFRDPqrH5UU2bIWxH3VFseKjg99fXMP17P7vHhfwOc7LvkZZCEIBHkj14HxQ7Q8kImkDo3o6mT82cNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:37:51.936345Z"},"content_sha256":"a50fb95273d8524042299b78f0ca0742272961d296689c588dfa744b80196884","schema_version":"1.0","event_id":"sha256:a50fb95273d8524042299b78f0ca0742272961d296689c588dfa744b80196884"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L4A7UKJD3IXAJCITVYV3SP5AXM/bundle.json","state_url":"https://pith.science/pith/L4A7UKJD3IXAJCITVYV3SP5AXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L4A7UKJD3IXAJCITVYV3SP5AXM/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":"2026-06-26T12:37:51Z","links":{"resolver":"https://pith.science/pith/L4A7UKJD3IXAJCITVYV3SP5AXM","bundle":"https://pith.science/pith/L4A7UKJD3IXAJCITVYV3SP5AXM/bundle.json","state":"https://pith.science/pith/L4A7UKJD3IXAJCITVYV3SP5AXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L4A7UKJD3IXAJCITVYV3SP5AXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L4A7UKJD3IXAJCITVYV3SP5AXM","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":"f5f447d5c958c72b175b3680acf9fc24e822ec977d86ca4a0f8810fc486b293e","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-29T11:28:55Z","title_canon_sha256":"11809e968dd6cadce9e0cfc6b176545f3fc794479a22fa0fac6795a9e19ccbf9"},"schema_version":"1.0","source":{"id":"1412.8314","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8314","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8314v2","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8314","created_at":"2026-05-18T01:15:38Z"},{"alias_kind":"pith_short_12","alias_value":"L4A7UKJD3IXA","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L4A7UKJD3IXAJCIT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L4A7UKJD","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:a50fb95273d8524042299b78f0ca0742272961d296689c588dfa744b80196884","target":"graph","created_at":"2026-05-18T01:15:38Z","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":"We prove that any $n$ points in $\\mathbb{R}^2$, not all on a line or circle, determine at least $\\frac{1}{4}n^2-O(n)$ ordinary circles (circles containing exactly three of the $n$ points). The main term of this bound is best possible for even $n$. Our proof relies on a recent result of Green and Tao on ordinary lines.","authors_text":"Frank de Zeeuw, Hossein Nassajian Mojarrad","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-29T11:28:55Z","title":"On the number of ordinary circles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8314","kind":"arxiv","version":2},"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":"sha256:66de02349c87407a373c76929a9c5541898cf52c91f6a63c4bcad48018d52267","target":"record","created_at":"2026-05-18T01:15:38Z","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":"f5f447d5c958c72b175b3680acf9fc24e822ec977d86ca4a0f8810fc486b293e","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-29T11:28:55Z","title_canon_sha256":"11809e968dd6cadce9e0cfc6b176545f3fc794479a22fa0fac6795a9e19ccbf9"},"schema_version":"1.0","source":{"id":"1412.8314","kind":"arxiv","version":2}},"canonical_sha256":"5f01fa2923da2e048913ae2bb93fa0bb065a89f4710cb32992472c1206d71325","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f01fa2923da2e048913ae2bb93fa0bb065a89f4710cb32992472c1206d71325","first_computed_at":"2026-05-18T01:15:38.845130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:38.845130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3y9J0FXhgZVjstms7x9HK9ECplBUHIbaiC3b46BOOIbIUm6yADPh9DbtHDQOKrIZ109v5YKRRRb8uOJGzTxhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:38.845924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.8314","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66de02349c87407a373c76929a9c5541898cf52c91f6a63c4bcad48018d52267","sha256:a50fb95273d8524042299b78f0ca0742272961d296689c588dfa744b80196884"],"state_sha256":"5dcfdc643cc484f9774d2fe5a5d27cbb020eb82e3961c12672f080960eaccfb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KaRoaenGvBJ1NE+CU+qUVU8uaw39VWVpf55u8Fu5e8CUIP90UmBZRWMqvd6CcelslUF9hqmNXZ1suflLYx/jAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:37:51.938327Z","bundle_sha256":"4f3b31d41000eb97d1de516e29bd76f7cc3410dd36abb7bab47afafea34b804d"}}