{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IXVOFMY6Q3ULFOVAJS557C5BEY","short_pith_number":"pith:IXVOFMY6","canonical_record":{"source":{"id":"1711.06532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-17T13:45:32Z","cross_cats_sorted":[],"title_canon_sha256":"ac11df4917ead96cce6c57884e66fabbcb0e8ecddbc321acead89d59337ea86d","abstract_canon_sha256":"5516c8e1715fd011d009f0692e70c831c0ddc7e789b9436490fd34f50b5d9646"},"schema_version":"1.0"},"canonical_sha256":"45eae2b31e86e8b2baa04cbbdf8ba12615c7e2003ba521b7757a3275aa7931d7","source":{"kind":"arxiv","id":"1711.06532","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06532","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06532v1","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06532","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"pith_short_12","alias_value":"IXVOFMY6Q3UL","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IXVOFMY6Q3ULFOVA","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IXVOFMY6","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IXVOFMY6Q3ULFOVAJS557C5BEY","target":"record","payload":{"canonical_record":{"source":{"id":"1711.06532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-17T13:45:32Z","cross_cats_sorted":[],"title_canon_sha256":"ac11df4917ead96cce6c57884e66fabbcb0e8ecddbc321acead89d59337ea86d","abstract_canon_sha256":"5516c8e1715fd011d009f0692e70c831c0ddc7e789b9436490fd34f50b5d9646"},"schema_version":"1.0"},"canonical_sha256":"45eae2b31e86e8b2baa04cbbdf8ba12615c7e2003ba521b7757a3275aa7931d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:20.797894Z","signature_b64":"aql6wE3nhpiDBEL94KV3upzZ4pNdwYoMCUlqYFMtBZmVz6EIJaUnQY2N7a4j9wYobL09EEEZmUtf+lQlZqLfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45eae2b31e86e8b2baa04cbbdf8ba12615c7e2003ba521b7757a3275aa7931d7","last_reissued_at":"2026-05-18T00:30:20.797180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:20.797180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.06532","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:30:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wszibpvdiVb0/Qozz0olxN9lEzwT1z+uAYMgE3UgF13ITVwZWc9auZQod04S881cn6iIy6io6BBKtYRUSHoJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:03:59.865530Z"},"content_sha256":"66a1244559bf39777f86992d2eb520838e05e9a95de5525d56b7fd138bb1cede","schema_version":"1.0","event_id":"sha256:66a1244559bf39777f86992d2eb520838e05e9a95de5525d56b7fd138bb1cede"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IXVOFMY6Q3ULFOVAJS557C5BEY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong Reductions between Relatives of the Stable Ramsey's Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Nichols","submitted_at":"2017-11-17T13:45:32Z","abstract_excerpt":"A complete analysis is given of the computable reductions that hold between $\\mathsf{SRT}^2_2$, $\\mathsf{SPT}^2_2$, and $\\mathsf{SIPT}^2_2$. In particular, while $\\mathsf{D}^2_2\\le_{\\rm sW}\\mathsf{SIPT}^2_2\\le_{\\rm sW}\\mathsf{SPT}^2_2\\le_{\\rm sW}\\mathsf{SRT}^2_2$, it is shown that $\\mathsf{SRT}^2_2\\not\\le_{\\rm sc}\\mathsf{SPT}^2_2\\not\\le_{\\rm sc}\\mathsf{SIPT}^2_2\\not\\le_{\\rm sc}\\mathsf{D}^2_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06532","kind":"arxiv","version":1},"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":"2026-05-18T00:30:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whKZ3Q2jNyuZkcpG7Or0ATRE0i3j0j2uPSiSZxMsVqByoAJ7D51lFjHrIi8uKSNd3C4YDm9xc4xa009cQY7ZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:03:59.866208Z"},"content_sha256":"3e5c2fec4be650d9e7cbc6f091b96a45ec7e15f62a8476f5bc60a71803b76efc","schema_version":"1.0","event_id":"sha256:3e5c2fec4be650d9e7cbc6f091b96a45ec7e15f62a8476f5bc60a71803b76efc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IXVOFMY6Q3ULFOVAJS557C5BEY/bundle.json","state_url":"https://pith.science/pith/IXVOFMY6Q3ULFOVAJS557C5BEY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IXVOFMY6Q3ULFOVAJS557C5BEY/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":"2026-06-11T21:03:59Z","links":{"resolver":"https://pith.science/pith/IXVOFMY6Q3ULFOVAJS557C5BEY","bundle":"https://pith.science/pith/IXVOFMY6Q3ULFOVAJS557C5BEY/bundle.json","state":"https://pith.science/pith/IXVOFMY6Q3ULFOVAJS557C5BEY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IXVOFMY6Q3ULFOVAJS557C5BEY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IXVOFMY6Q3ULFOVAJS557C5BEY","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":"5516c8e1715fd011d009f0692e70c831c0ddc7e789b9436490fd34f50b5d9646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-17T13:45:32Z","title_canon_sha256":"ac11df4917ead96cce6c57884e66fabbcb0e8ecddbc321acead89d59337ea86d"},"schema_version":"1.0","source":{"id":"1711.06532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06532","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06532v1","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06532","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"pith_short_12","alias_value":"IXVOFMY6Q3UL","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IXVOFMY6Q3ULFOVA","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IXVOFMY6","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:3e5c2fec4be650d9e7cbc6f091b96a45ec7e15f62a8476f5bc60a71803b76efc","target":"graph","created_at":"2026-05-18T00:30:20Z","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":"A complete analysis is given of the computable reductions that hold between $\\mathsf{SRT}^2_2$, $\\mathsf{SPT}^2_2$, and $\\mathsf{SIPT}^2_2$. In particular, while $\\mathsf{D}^2_2\\le_{\\rm sW}\\mathsf{SIPT}^2_2\\le_{\\rm sW}\\mathsf{SPT}^2_2\\le_{\\rm sW}\\mathsf{SRT}^2_2$, it is shown that $\\mathsf{SRT}^2_2\\not\\le_{\\rm sc}\\mathsf{SPT}^2_2\\not\\le_{\\rm sc}\\mathsf{SIPT}^2_2\\not\\le_{\\rm sc}\\mathsf{D}^2_2$.","authors_text":"David Nichols","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-17T13:45:32Z","title":"Strong Reductions between Relatives of the Stable Ramsey's Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06532","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":"sha256:66a1244559bf39777f86992d2eb520838e05e9a95de5525d56b7fd138bb1cede","target":"record","created_at":"2026-05-18T00:30:20Z","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":"5516c8e1715fd011d009f0692e70c831c0ddc7e789b9436490fd34f50b5d9646","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-11-17T13:45:32Z","title_canon_sha256":"ac11df4917ead96cce6c57884e66fabbcb0e8ecddbc321acead89d59337ea86d"},"schema_version":"1.0","source":{"id":"1711.06532","kind":"arxiv","version":1}},"canonical_sha256":"45eae2b31e86e8b2baa04cbbdf8ba12615c7e2003ba521b7757a3275aa7931d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45eae2b31e86e8b2baa04cbbdf8ba12615c7e2003ba521b7757a3275aa7931d7","first_computed_at":"2026-05-18T00:30:20.797180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:20.797180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aql6wE3nhpiDBEL94KV3upzZ4pNdwYoMCUlqYFMtBZmVz6EIJaUnQY2N7a4j9wYobL09EEEZmUtf+lQlZqLfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:20.797894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66a1244559bf39777f86992d2eb520838e05e9a95de5525d56b7fd138bb1cede","sha256:3e5c2fec4be650d9e7cbc6f091b96a45ec7e15f62a8476f5bc60a71803b76efc"],"state_sha256":"11a655c32f10e8fd1d5c5914deb6f3016a1678589c44e5b7870934c3defeee3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9OkQG3l/GHjfzNkRZ5naA06Q3mwaUTEljoXdkOdXy49+/IaaNVekEvzy3J34VAVz+jlfm9NtdU9lJEt81jhDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:03:59.869919Z","bundle_sha256":"49c3db34dc44fe50d0197a9ed2392ab5b6659196ac10d0ba5b41f4bf1a87b6e2"}}