{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MAKOLA6M7CF6YVJACY3F2I6ZJC","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":"e1d184fe20d83fb85f693a12de6e7223be852dbf8928f8bf0ed802aee82db2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-24T03:05:10Z","title_canon_sha256":"6b74d68334aad0da81be90851984e44fcba8df8b872e43c95ac6cebdc89f8cfd"},"schema_version":"1.0","source":{"id":"1509.07220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07220","created_at":"2026-05-18T01:32:09Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07220v1","created_at":"2026-05-18T01:32:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07220","created_at":"2026-05-18T01:32:09Z"},{"alias_kind":"pith_short_12","alias_value":"MAKOLA6M7CF6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MAKOLA6M7CF6YVJA","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MAKOLA6M","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:df2aa99588c4ef2d3a4dca08a1c609bd78011d179977c5f98d649da766837f95","target":"graph","created_at":"2026-05-18T01:32:09Z","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 1989, Erd\\H{o}s conjectured that for a sufficiently large $n$ it is impossible to place $n$ points in general position in a plane such that for every $1\\le i \\le n-1$ there is a distance that occurs exactly $i$ times. For small $n$ this is possible and in his paper he provided constructions for $n\\leq 8$. The one for $n=5$ was due to Pomerance while Pal\\'{a}sti came up with the constructions for $n=7,8$. Constructions for $n=9$ and above remain undiscovered, and little headway has been made toward a proof that for sufficiently large $n$ no configuration exists. In this paper we consider a n","authors_text":"David Burt, Eli Goldstein, Eyvindur A. Palsson, Hong Suh, Sarah Manski, Steven J. Miller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-24T03:05:10Z","title":"Crescent configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07220","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:c5da039266da7146e3117c1e6be790c5e5697b22c0f4fe228f313b40db62240a","target":"record","created_at":"2026-05-18T01:32:09Z","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":"e1d184fe20d83fb85f693a12de6e7223be852dbf8928f8bf0ed802aee82db2e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-24T03:05:10Z","title_canon_sha256":"6b74d68334aad0da81be90851984e44fcba8df8b872e43c95ac6cebdc89f8cfd"},"schema_version":"1.0","source":{"id":"1509.07220","kind":"arxiv","version":1}},"canonical_sha256":"6014e583ccf88bec552016365d23d9489a30183e9b056076d477de53208821bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6014e583ccf88bec552016365d23d9489a30183e9b056076d477de53208821bd","first_computed_at":"2026-05-18T01:32:09.530593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:09.530593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+5YaOQ9ufKa0v1IP6nmWKzhB3lqE7CQrymYr1D3zCQ4RfDwdbgvPtBn06UPspJtL644S9u3ZuFgNtLSEqd2ZBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:09.531196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5da039266da7146e3117c1e6be790c5e5697b22c0f4fe228f313b40db62240a","sha256:df2aa99588c4ef2d3a4dca08a1c609bd78011d179977c5f98d649da766837f95"],"state_sha256":"b950fe44e306e469ba80e9d6efc374de2e8748d0b067cd3ed6b427d6e3ec04c0"}