{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5NB2UE6IY5ADUUUX6CWYP64F6N","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":"59b5f6c2ffa0cc829483a71745e6a7625bf25a5bad1fc87c60f85e334ca9054a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-12-19T08:05:28Z","title_canon_sha256":"e11197dc940db247151d66275dd72bd3ac0bcfae45ec8293abe2fd2cbc92790f"},"schema_version":"1.0","source":{"id":"1912.09049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.09049","created_at":"2026-07-05T00:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1912.09049v1","created_at":"2026-07-05T00:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.09049","created_at":"2026-07-05T00:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"5NB2UE6IY5AD","created_at":"2026-07-05T00:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"5NB2UE6IY5ADUUUX","created_at":"2026-07-05T00:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"5NB2UE6I","created_at":"2026-07-05T00:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:ced76369105f27481a1c90893434f82192a1b184c4d39c1a03c0abae27e07eb2","target":"graph","created_at":"2026-07-05T00:27:23Z","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/1912.09049/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathsf{TT}^2_k$ denote the combinatorial principle stating that every $k$-coloring of pairs of compatible nodes in the full binary tree has a homogeneous solution, i.e. an isomorphic subtree in which all pairs of compatible nodes have the same color. Let $\\mathsf{WKL}_0$ be the subsystem of second order arithmetic consisting of the base system $\\mathsf{RCA}_0$ together with the principle (called Weak K\\\"onig's Lemma) stating that every infinite subtree of the full binary tree has an infinite path. We show that over $\\mathsf{RCA}_0$,\n  $\\mathsf{TT}^2_k$ doe not imply $\\mathsf{WKL}_0$. Thi","authors_text":"Chi Tat Chong, Lu Liu, Wei Li, Yue Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-12-19T08:05:28Z","title":"The Strength of Ramsey's Theorem For Pairs over trees: I. Weak K\\\"onig's Lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.09049","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":"sha256:5acc7ebb66136ff85d650c79a274c38acf200fcf68fca9614122944ed65047ac","target":"record","created_at":"2026-07-05T00:27:23Z","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":"59b5f6c2ffa0cc829483a71745e6a7625bf25a5bad1fc87c60f85e334ca9054a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-12-19T08:05:28Z","title_canon_sha256":"e11197dc940db247151d66275dd72bd3ac0bcfae45ec8293abe2fd2cbc92790f"},"schema_version":"1.0","source":{"id":"1912.09049","kind":"arxiv","version":1}},"canonical_sha256":"eb43aa13c8c7403a5297f0ad87fb85f36f5ab632f36e4d851fb8501bfb46558c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb43aa13c8c7403a5297f0ad87fb85f36f5ab632f36e4d851fb8501bfb46558c","first_computed_at":"2026-07-05T00:27:23.126828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:27:23.126828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PX7ONN0ofXXZJVlN3YaOOtedTB4Uu36cTc8Zz4RZsW8hUOefP2WCX0/yjbHD+cp+NU98905ajBY3b8z1t+Z8DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:27:23.127168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.09049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5acc7ebb66136ff85d650c79a274c38acf200fcf68fca9614122944ed65047ac","sha256:ced76369105f27481a1c90893434f82192a1b184c4d39c1a03c0abae27e07eb2"],"state_sha256":"5937ea2dcc9fe292dc277f59de3ef74642e2d5783b80fa49426bc511e0605eca"}