{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5WGZEWIVPOIXH4LTM5LBPTPQDX","short_pith_number":"pith:5WGZEWIV","canonical_record":{"source":{"id":"1609.00092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-01T02:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"8e5d14661ad9b6f43c2b213f33b168a2d15149eed1b321a0b577fdb12e4f9c0c","abstract_canon_sha256":"ddab8e69c02f158d538d56f3af75950ca3fe8eeb4ef91a54ff94bf6d0bfb16ec"},"schema_version":"1.0"},"canonical_sha256":"ed8d9259157b9173f173675617cdf01dec6145ab077fb77dfb8f8d628ef409d4","source":{"kind":"arxiv","id":"1609.00092","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00092","created_at":"2026-05-18T01:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00092v1","created_at":"2026-05-18T01:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00092","created_at":"2026-05-18T01:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"5WGZEWIVPOIX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5WGZEWIVPOIXH4LT","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5WGZEWIV","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5WGZEWIVPOIXH4LTM5LBPTPQDX","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-01T02:28:40Z","cross_cats_sorted":[],"title_canon_sha256":"8e5d14661ad9b6f43c2b213f33b168a2d15149eed1b321a0b577fdb12e4f9c0c","abstract_canon_sha256":"ddab8e69c02f158d538d56f3af75950ca3fe8eeb4ef91a54ff94bf6d0bfb16ec"},"schema_version":"1.0"},"canonical_sha256":"ed8d9259157b9173f173675617cdf01dec6145ab077fb77dfb8f8d628ef409d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:27.963054Z","signature_b64":"Mi+7aLuWHfwjPM52szChm9BrUqeCZh5GxlBNwKP9YLA7V+IiChJRa9KOyhhxofZmGq45Gcc43Mrro6xe4DO1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed8d9259157b9173f173675617cdf01dec6145ab077fb77dfb8f8d628ef409d4","last_reissued_at":"2026-05-18T01:06:27.962457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:27.962457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00092","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":"2026-05-18T01:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RSWaAxg7B8dOxKIyl2RNXLREKzUUg32SakaYvWirHrsTwmzpj9zIzYV4LzoXzYY/IuWJxs4Fo5CDnOOWD7IMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:40:57.915747Z"},"content_sha256":"0db40fc6051c6e1fb7c6df7a8b2dde39ff5781d63879718a62d8686694539f4d","schema_version":"1.0","event_id":"sha256:0db40fc6051c6e1fb7c6df7a8b2dde39ff5781d63879718a62d8686694539f4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5WGZEWIVPOIXH4LTM5LBPTPQDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Representation of convex geometries by circles on a plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kira Adaricheva, Madina Bolat","submitted_at":"2016-09-01T02:28:40Z","abstract_excerpt":"Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the result of K. Kashiwabara, M.Nakamura and Y.Okamoto (2005). Allowing circles rather than points, as was suggested by G.Cz\\'edli (2014), may presumably reduce the dimension for representation. This paper introduces a property, the Weak $2\\times 3$-Carousel rule, which is satisfied by all convex geometries of circles on a plane, and we show that it does not hold i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00092","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":"2026-05-18T01:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIQC/cDRHXoFmijrN9LzaofzfpqqYrgW0VApYf1GA/3sKob5XS+bU3QzXMgBGlzDvK0ksu2I4HsYcOS46dxJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:40:57.916401Z"},"content_sha256":"8ddda59734cd21f5731bd8e19da918c5397c3ecea839efb7d0b441d360d76bb2","schema_version":"1.0","event_id":"sha256:8ddda59734cd21f5731bd8e19da918c5397c3ecea839efb7d0b441d360d76bb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5WGZEWIVPOIXH4LTM5LBPTPQDX/bundle.json","state_url":"https://pith.science/pith/5WGZEWIVPOIXH4LTM5LBPTPQDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5WGZEWIVPOIXH4LTM5LBPTPQDX/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":"2026-05-26T15:40:57Z","links":{"resolver":"https://pith.science/pith/5WGZEWIVPOIXH4LTM5LBPTPQDX","bundle":"https://pith.science/pith/5WGZEWIVPOIXH4LTM5LBPTPQDX/bundle.json","state":"https://pith.science/pith/5WGZEWIVPOIXH4LTM5LBPTPQDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5WGZEWIVPOIXH4LTM5LBPTPQDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5WGZEWIVPOIXH4LTM5LBPTPQDX","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":"ddab8e69c02f158d538d56f3af75950ca3fe8eeb4ef91a54ff94bf6d0bfb16ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-01T02:28:40Z","title_canon_sha256":"8e5d14661ad9b6f43c2b213f33b168a2d15149eed1b321a0b577fdb12e4f9c0c"},"schema_version":"1.0","source":{"id":"1609.00092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00092","created_at":"2026-05-18T01:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00092v1","created_at":"2026-05-18T01:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00092","created_at":"2026-05-18T01:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"5WGZEWIVPOIX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5WGZEWIVPOIXH4LT","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5WGZEWIV","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:8ddda59734cd21f5731bd8e19da918c5397c3ecea839efb7d0b441d360d76bb2","target":"graph","created_at":"2026-05-18T01:06:27Z","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":"Convex geometries are closure systems satisfying the anti-exchange axiom. Every finite convex geometry can be embedded into a convex geometry of finitely many points in an n-dimensional space equipped with a convex hull operator, by the result of K. Kashiwabara, M.Nakamura and Y.Okamoto (2005). Allowing circles rather than points, as was suggested by G.Cz\\'edli (2014), may presumably reduce the dimension for representation. This paper introduces a property, the Weak $2\\times 3$-Carousel rule, which is satisfied by all convex geometries of circles on a plane, and we show that it does not hold i","authors_text":"Kira Adaricheva, Madina Bolat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-01T02:28:40Z","title":"Representation of convex geometries by circles on a plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00092","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":"sha256:0db40fc6051c6e1fb7c6df7a8b2dde39ff5781d63879718a62d8686694539f4d","target":"record","created_at":"2026-05-18T01:06:27Z","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":"ddab8e69c02f158d538d56f3af75950ca3fe8eeb4ef91a54ff94bf6d0bfb16ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-01T02:28:40Z","title_canon_sha256":"8e5d14661ad9b6f43c2b213f33b168a2d15149eed1b321a0b577fdb12e4f9c0c"},"schema_version":"1.0","source":{"id":"1609.00092","kind":"arxiv","version":1}},"canonical_sha256":"ed8d9259157b9173f173675617cdf01dec6145ab077fb77dfb8f8d628ef409d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed8d9259157b9173f173675617cdf01dec6145ab077fb77dfb8f8d628ef409d4","first_computed_at":"2026-05-18T01:06:27.962457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:27.962457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mi+7aLuWHfwjPM52szChm9BrUqeCZh5GxlBNwKP9YLA7V+IiChJRa9KOyhhxofZmGq45Gcc43Mrro6xe4DO1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:27.963054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db40fc6051c6e1fb7c6df7a8b2dde39ff5781d63879718a62d8686694539f4d","sha256:8ddda59734cd21f5731bd8e19da918c5397c3ecea839efb7d0b441d360d76bb2"],"state_sha256":"a625543898ac4caf7ea3f637a193d3e492f60f940b004e124526dcdb463e348e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cKbSYarYN9IRF7pPHilyac6gnmsnp0iXcELFDrpIyjQ2yVPyAzcP9DQ1IEWK3vDfPyjw9xLsPSkDQv6iZUN/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:40:57.919936Z","bundle_sha256":"da5b2df00869bc3bbaf5fff1d199a5a41b184d629b253fe22683895b5e247877"}}