{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HTMKJTNB7KR7JBT67WRHZFOJWR","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":"9aceb13869f838cd2f55a67b8920de2e02ebd3a30c1af0211e4c705d1571e011","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-20T04:46:35Z","title_canon_sha256":"8ba457e958ba42e54327708fd49c34585a4e84ea957dde6e38524c3abd19bc89"},"schema_version":"1.0","source":{"id":"2605.20695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.20695","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"2605.20695v1","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20695","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"HTMKJTNB7KR7","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_16","alias_value":"HTMKJTNB7KR7JBT6","created_at":"2026-05-21T01:04:49Z"},{"alias_kind":"pith_short_8","alias_value":"HTMKJTNB","created_at":"2026-05-21T01:04:49Z"}],"graph_snapshots":[{"event_id":"sha256:c9d06252f2991c25708f54047bd39a0b6c88e95cd4fb787a723b360641b08e10","target":"graph","created_at":"2026-05-21T01:04:49Z","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/2605.20695/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erd\\H{o}s unit distance conjecture, and a sequence of reflections on it. The argument relies crucially on ideas that may, at least in retrospect, be attributed to Ellenberg-Venkatesh, Golod-Shafarevich, and Hajir-Maire-Ramakrishna.","authors_text":"Arul Shankar, Daniel Litt, Jacob Tsimerman, Melanie Matchett Wood, Noga Alon, Thomas F. Bloom, Victor Wang, Will Sawin, W. T. Gowers","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-20T04:46:35Z","title":"Remarks on the disproof of the unit distance conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20695","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":"sha256:853af5c9356e0bb7d50a0d9f6d1bdca6c999b6b2e894759e7ffa4efbd2d6609d","target":"record","created_at":"2026-05-21T01:04:49Z","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":"9aceb13869f838cd2f55a67b8920de2e02ebd3a30c1af0211e4c705d1571e011","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-20T04:46:35Z","title_canon_sha256":"8ba457e958ba42e54327708fd49c34585a4e84ea957dde6e38524c3abd19bc89"},"schema_version":"1.0","source":{"id":"2605.20695","kind":"arxiv","version":1}},"canonical_sha256":"3cd8a4cda1faa3f4867efda27c95c9b46e5c413cc6b27192c86c99cd371133d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cd8a4cda1faa3f4867efda27c95c9b46e5c413cc6b27192c86c99cd371133d0","first_computed_at":"2026-05-21T01:04:49.618109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:49.618109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AHs1xOO96l6upntS2dWtDWTk6ps7DUFvWs/gRX2cLF619Mow8SYPsiYEx5pWGnBfmIQHaCCsn/yS+ImjMS/pBw==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:49.618779Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.20695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:853af5c9356e0bb7d50a0d9f6d1bdca6c999b6b2e894759e7ffa4efbd2d6609d","sha256:c9d06252f2991c25708f54047bd39a0b6c88e95cd4fb787a723b360641b08e10"],"state_sha256":"955769f7f10cc8c4f98bce9ed910f27c06d6d5597233a0dd2f5fd80c3a67de33"}