{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZN6LNQJ4CS2DTXA7NZK7KTXVKI","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":"60369e5b3583da1475159c89bf45b48c878f5c8e27d6d0ac50b833db749bc2c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-09-30T01:55:58Z","title_canon_sha256":"5e5a7b24636f504b0810cb706a2764a49dff153975fb3924d2820ef28cbb3e21"},"schema_version":"1.0","source":{"id":"1409.8361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8361","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8361v1","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8361","created_at":"2026-05-18T02:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZN6LNQJ4CS2D","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZN6LNQJ4CS2DTXA7","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZN6LNQJ4","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:5891762742f396d13c6e9334dcfa4ecd56307d4b51dbc6f86403b43ee2eec9a4","target":"graph","created_at":"2026-05-18T02:41:25Z","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":"For any $m \\geq 1$, let $H_m$ denote the quantity $H_m := \\liminf_{n \\to \\infty} (p_{n+m}-p_n)$, where $p_n$ denotes the $n^{\\operatorname{th}}$ prime; thus for instance the twin prime conjecture is equivalent to the assertion that $H_1$ is equal to two. In a recent breakthrough paper of Zhang, a finite upper bound was obtained for the first time on $H_1$; more specifically, Zhang showed that $H_1 \\leq 70000000$.\n  Almost immediately after the appearance of Zhang's paper, improvements to the upper bound on $H_1$ were made. In order to pool together these various efforts, a \\emph{Polymath proje","authors_text":"D.H.J. Polymath","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-09-30T01:55:58Z","title":"The \"bounded gaps between primes\" Polymath project - a retrospective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8361","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":"sha256:5694f3a64220ee3f87c671f856cb564a24935323add12546a412b97a9e9c784a","target":"record","created_at":"2026-05-18T02:41:25Z","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":"60369e5b3583da1475159c89bf45b48c878f5c8e27d6d0ac50b833db749bc2c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-09-30T01:55:58Z","title_canon_sha256":"5e5a7b24636f504b0810cb706a2764a49dff153975fb3924d2820ef28cbb3e21"},"schema_version":"1.0","source":{"id":"1409.8361","kind":"arxiv","version":1}},"canonical_sha256":"cb7cb6c13c14b439dc1f6e55f54ef55217b57817a5f7f7033ac57e8cff8a7c58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb7cb6c13c14b439dc1f6e55f54ef55217b57817a5f7f7033ac57e8cff8a7c58","first_computed_at":"2026-05-18T02:41:25.517910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:25.517910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A9T1Q7pYwDxmkCuTWkfGm3w6zHEhPEovvqBnC1KboRRQ0h9gCPlkggkcJZJTVfehj0irQ2Y6J+DT9BbcXhmsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:25.518383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5694f3a64220ee3f87c671f856cb564a24935323add12546a412b97a9e9c784a","sha256:5891762742f396d13c6e9334dcfa4ecd56307d4b51dbc6f86403b43ee2eec9a4"],"state_sha256":"38e30231be7073a438be36971bd19564a4b81b4e9b20b7e7a463f05f19e5221a"}