{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SBSTE4JYHJSR4DC74HHAXQDET3","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":"9e29e3c583ea59623cd0a119204d4de7540639ab441e40c006c3cfebd87ff91d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-27T19:45:01Z","title_canon_sha256":"175ff232c3d48b2277efbfdc699fde7dd94bcdb69d1f743160f73652e00e0e40"},"schema_version":"1.0","source":{"id":"1603.08249","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08249","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08249v1","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08249","created_at":"2026-05-18T01:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"SBSTE4JYHJSR","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SBSTE4JYHJSR4DC7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SBSTE4JY","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:689b3b39317ebd0cc44fdf11402dc419f4fc043b1b46e751d82cf6e6cc8879a0","target":"graph","created_at":"2026-05-18T01:18:12Z","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 consider the strength and effective content of restricted versions of Hindman's Theorem in which the number of colors is specified and the length of the sums has a specified finite bound. Let $\\mathsf{HT}^{\\leq n}_k$ denote the assertion that for each $k$-coloring $c$ of $\\mathbb{N}$ there is an infinite set $X \\subseteq \\mathbb{N}$ such that all sums $\\sum_{x \\in F} x$ for $F \\subseteq X$ and $0 < |F| \\leq n$ have the same color. We prove that there is a computable $2$-coloring $c$ of $\\mathbb{N}$ such that there is no infinite computable set $X$ such that all nonempty sums of at most $2$ ","authors_text":"Carl G. Jockusch, Damir D. Dzhafarov, Jr., Linda Brown Westrick, Reed Solomon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-27T19:45:01Z","title":"Effectiveness of Hindman's theorem for bounded sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08249","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":"sha256:8fc9b92ef313117c281ecb94c4532eeead6075fcf504c95568c8bdef8d608327","target":"record","created_at":"2026-05-18T01:18:12Z","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":"9e29e3c583ea59623cd0a119204d4de7540639ab441e40c006c3cfebd87ff91d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-27T19:45:01Z","title_canon_sha256":"175ff232c3d48b2277efbfdc699fde7dd94bcdb69d1f743160f73652e00e0e40"},"schema_version":"1.0","source":{"id":"1603.08249","kind":"arxiv","version":1}},"canonical_sha256":"90653271383a651e0c5fe1ce0bc0649ec435fb9233286b4bdcc3bc829caf850f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90653271383a651e0c5fe1ce0bc0649ec435fb9233286b4bdcc3bc829caf850f","first_computed_at":"2026-05-18T01:18:12.767928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:12.767928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFibQxYhm/d/JCeO3ITzL2ACvzapBThE9KeXG0+LfbuaJMezRIqCDbpyjnIutubyVhw0IX4A3Wa+YT7bGc42Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:12.768495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08249","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fc9b92ef313117c281ecb94c4532eeead6075fcf504c95568c8bdef8d608327","sha256:689b3b39317ebd0cc44fdf11402dc419f4fc043b1b46e751d82cf6e6cc8879a0"],"state_sha256":"ab1b6cd3a059d4e062acd6f8c7a1e2e66d2d2f82be48255238310e918715b7aa"}