{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I4K4NYB3QRWSAUZENVIOQT7NDH","short_pith_number":"pith:I4K4NYB3","canonical_record":{"source":{"id":"1601.00050","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-01T04:50:58Z","cross_cats_sorted":[],"title_canon_sha256":"2f6d23d658257555796f49079a745e048c8bd40271ac9588896802cb4b555394","abstract_canon_sha256":"1eb24eb96e844ef331a80436ba8a0e79b4d8d709d6a01e4ae6be79c06250dd12"},"schema_version":"1.0"},"canonical_sha256":"4715c6e03b846d2053246d50e84fed19cd926aad21700d42c99e0f71dc59d74d","source":{"kind":"arxiv","id":"1601.00050","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00050","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00050v4","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00050","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"I4K4NYB3QRWS","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I4K4NYB3QRWSAUZE","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I4K4NYB3","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I4K4NYB3QRWSAUZENVIOQT7NDH","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00050","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-01T04:50:58Z","cross_cats_sorted":[],"title_canon_sha256":"2f6d23d658257555796f49079a745e048c8bd40271ac9588896802cb4b555394","abstract_canon_sha256":"1eb24eb96e844ef331a80436ba8a0e79b4d8d709d6a01e4ae6be79c06250dd12"},"schema_version":"1.0"},"canonical_sha256":"4715c6e03b846d2053246d50e84fed19cd926aad21700d42c99e0f71dc59d74d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:49.447181Z","signature_b64":"ERn7ijAG2qbY+vPDwj8sQYGrv9IsrrQ2k3dklEgTRFG42wtGM3X+yf6vqZ+ydczO572oPAvdERA7m4fN0KSOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4715c6e03b846d2053246d50e84fed19cd926aad21700d42c99e0f71dc59d74d","last_reissued_at":"2026-05-18T00:20:49.446676Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:49.446676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00050","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BaChG5drYGJb53LbhUwnbk4sdFuVPKY1qk1Jg0He2ZyVMpf1lR4y+N+9RiSXx9LRB5Jdvx3New54fKz1I1SzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:14:19.936298Z"},"content_sha256":"b1454f7343e5b63aeabf79b4589ba6bfbb9c8a3bc4e323d39c40ab353e0360f7","schema_version":"1.0","event_id":"sha256:b1454f7343e5b63aeabf79b4589ba6bfbb9c8a3bc4e323d39c40ab353e0360f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I4K4NYB3QRWSAUZENVIOQT7NDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The proof-theoretic strength of Ramsey's theorem for pairs and two colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Keita Yokoyama, Ludovic Patey","submitted_at":"2016-01-01T04:50:58Z","abstract_excerpt":"Ramsey's theorem for $n$-tuples and $k$-colors ($\\mathsf{RT}^n_k$) asserts that every k-coloring of $[\\mathbb{N}]^n$ admits an infinite monochromatic subset. We study the proof-theoretic strength of Ramsey's theorem for pairs and two colors, namely, the set of its $\\Pi^0_1$ consequences, and show that $\\mathsf{RT}^2_2$ is $\\Pi^0_3$ conservative over $\\mathsf{I}\\Sigma^0_1$. This strengthens the proof of Chong, Slaman and Yang that $\\mathsf{RT}^2_2$ does not imply $\\mathsf{I}\\Sigma^0_2$, and shows that $\\mathsf{RT}^2_2$ is finitistically reducible, in the sense of Simpson's partial realization o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00050","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"boaeBEvFBKFGV1k+qZ+Y2+u6Im6lMJNpovbIBNc+K/BVIp1WNbeHbZYOb9I15dY8H2e5cuJeGET3D93RaOi8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:14:19.936669Z"},"content_sha256":"577c5ecf973eb6e8ff695df0396cc232b79f74821ae6ad7612ca0122a8e4bcd4","schema_version":"1.0","event_id":"sha256:577c5ecf973eb6e8ff695df0396cc232b79f74821ae6ad7612ca0122a8e4bcd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4K4NYB3QRWSAUZENVIOQT7NDH/bundle.json","state_url":"https://pith.science/pith/I4K4NYB3QRWSAUZENVIOQT7NDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4K4NYB3QRWSAUZENVIOQT7NDH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T01:14:19Z","links":{"resolver":"https://pith.science/pith/I4K4NYB3QRWSAUZENVIOQT7NDH","bundle":"https://pith.science/pith/I4K4NYB3QRWSAUZENVIOQT7NDH/bundle.json","state":"https://pith.science/pith/I4K4NYB3QRWSAUZENVIOQT7NDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4K4NYB3QRWSAUZENVIOQT7NDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I4K4NYB3QRWSAUZENVIOQT7NDH","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":"1eb24eb96e844ef331a80436ba8a0e79b4d8d709d6a01e4ae6be79c06250dd12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-01T04:50:58Z","title_canon_sha256":"2f6d23d658257555796f49079a745e048c8bd40271ac9588896802cb4b555394"},"schema_version":"1.0","source":{"id":"1601.00050","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00050","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00050v4","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00050","created_at":"2026-05-18T00:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"I4K4NYB3QRWS","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I4K4NYB3QRWSAUZE","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I4K4NYB3","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:577c5ecf973eb6e8ff695df0396cc232b79f74821ae6ad7612ca0122a8e4bcd4","target":"graph","created_at":"2026-05-18T00:20:49Z","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"},"paper":{"abstract_excerpt":"Ramsey's theorem for $n$-tuples and $k$-colors ($\\mathsf{RT}^n_k$) asserts that every k-coloring of $[\\mathbb{N}]^n$ admits an infinite monochromatic subset. We study the proof-theoretic strength of Ramsey's theorem for pairs and two colors, namely, the set of its $\\Pi^0_1$ consequences, and show that $\\mathsf{RT}^2_2$ is $\\Pi^0_3$ conservative over $\\mathsf{I}\\Sigma^0_1$. This strengthens the proof of Chong, Slaman and Yang that $\\mathsf{RT}^2_2$ does not imply $\\mathsf{I}\\Sigma^0_2$, and shows that $\\mathsf{RT}^2_2$ is finitistically reducible, in the sense of Simpson's partial realization o","authors_text":"Keita Yokoyama, Ludovic Patey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-01T04:50:58Z","title":"The proof-theoretic strength of Ramsey's theorem for pairs and two colors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00050","kind":"arxiv","version":4},"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:b1454f7343e5b63aeabf79b4589ba6bfbb9c8a3bc4e323d39c40ab353e0360f7","target":"record","created_at":"2026-05-18T00:20:49Z","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":"1eb24eb96e844ef331a80436ba8a0e79b4d8d709d6a01e4ae6be79c06250dd12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-01T04:50:58Z","title_canon_sha256":"2f6d23d658257555796f49079a745e048c8bd40271ac9588896802cb4b555394"},"schema_version":"1.0","source":{"id":"1601.00050","kind":"arxiv","version":4}},"canonical_sha256":"4715c6e03b846d2053246d50e84fed19cd926aad21700d42c99e0f71dc59d74d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4715c6e03b846d2053246d50e84fed19cd926aad21700d42c99e0f71dc59d74d","first_computed_at":"2026-05-18T00:20:49.446676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:49.446676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ERn7ijAG2qbY+vPDwj8sQYGrv9IsrrQ2k3dklEgTRFG42wtGM3X+yf6vqZ+ydczO572oPAvdERA7m4fN0KSOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:49.447181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00050","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1454f7343e5b63aeabf79b4589ba6bfbb9c8a3bc4e323d39c40ab353e0360f7","sha256:577c5ecf973eb6e8ff695df0396cc232b79f74821ae6ad7612ca0122a8e4bcd4"],"state_sha256":"9c593429f808876450268790363b41c948ca0ff2d60d232cd6f8bc254a28ddf6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipHmh1PGO8NqtWB+Om7eH2et2PvhbBWyHp9EZWFkICsjLp6zD4av9Vf9gkc0n0xH8Tlb498cG9IRWmn0wbvvAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:14:19.939409Z","bundle_sha256":"42668543d0e9fc7aedd98c6c6427a5498ce7fafa3df2b8eb03bbf57de60f5dcf"}}