{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CW4CTXJW54Y2VRAAF2E5U472J2","short_pith_number":"pith:CW4CTXJW","canonical_record":{"source":{"id":"1905.00321","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-01T14:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"2394c8c23f165e381646e1c1f51d631a7eb349b3f2fbd1e03d7aac489ea5d01f","abstract_canon_sha256":"55301a4b3c6089990a2530c17bbff526a57ce9d0973b41a7113dd18797de1e57"},"schema_version":"1.0"},"canonical_sha256":"15b829dd36ef31aac4002e89da73fa4ebe2419f29e697e85c64bd3e8d935a430","source":{"kind":"arxiv","id":"1905.00321","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00321","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00321v3","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00321","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"CW4CTXJW54Y2","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"pith_short_16","alias_value":"CW4CTXJW54Y2VRAA","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"pith_short_8","alias_value":"CW4CTXJW","created_at":"2026-07-05T01:15:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CW4CTXJW54Y2VRAAF2E5U472J2","target":"record","payload":{"canonical_record":{"source":{"id":"1905.00321","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-01T14:12:43Z","cross_cats_sorted":[],"title_canon_sha256":"2394c8c23f165e381646e1c1f51d631a7eb349b3f2fbd1e03d7aac489ea5d01f","abstract_canon_sha256":"55301a4b3c6089990a2530c17bbff526a57ce9d0973b41a7113dd18797de1e57"},"schema_version":"1.0"},"canonical_sha256":"15b829dd36ef31aac4002e89da73fa4ebe2419f29e697e85c64bd3e8d935a430","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:15:49.596752Z","signature_b64":"cOKzfDuoSNJvS2Dzilbsnf5hD3rS+lL4P/3yRym+rvNuVurBNeXwd40ISvSV+N/BZlOBMN//c9bDiszPr+AkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15b829dd36ef31aac4002e89da73fa4ebe2419f29e697e85c64bd3e8d935a430","last_reissued_at":"2026-07-05T01:15:49.596381Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:15:49.596381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.00321","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBfiXk9xmC6Z1NtzzfjNrrZeLmf8jCV4ZFQMiqV0KEZPHGcFsOw9upNPyBXLBgNFp5qznsy6xK1gWRzQ1v4DCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T14:02:36.178364Z"},"content_sha256":"c86d5f08dbc91555810c235b49ca06649e0f09bad57c9c17edaf10c79f47a6e5","schema_version":"1.0","event_id":"sha256:c86d5f08dbc91555810c235b49ca06649e0f09bad57c9c17edaf10c79f47a6e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CW4CTXJW54Y2VRAAF2E5U472J2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"COH, SRT22, and multiple functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Damir Dzhafarov, Ludovic Patey","submitted_at":"2019-05-01T14:12:43Z","abstract_excerpt":"We prove the following result: there is a family $R = \\langle R_0,R_1,\\ldots \\rangle$ of subsets of $\\omega$ such that for every stable coloring $c : [\\omega]^2 \\to k$ hyperarithmetical in $R$ and every finite collection of Turing functionals, there is an infinite homogeneous set $H$ for $c$ such that none of the finitely many functionals map $R \\oplus H$ to an infinite cohesive set for $R$. This extends the current best partial results towards the $\\mathsf{SRT}^2_2$ vs. $\\mathsf{COH}$ problem in reverse mathematics, and is also a partial result towards the resolution of several related proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00321","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.00321/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uGHC21AJmwjdIKCB7+iil/Z/SrcWmz151bJ95jHUi1VtQNjysBTqe7rLWvz3wjYIEkh/bgep5jxWUtQsammdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T14:02:36.179013Z"},"content_sha256":"2639ac0f6006321e186c848f9b91c3678dfbd77567ec33f0eaf6b1ac032caf8f","schema_version":"1.0","event_id":"sha256:2639ac0f6006321e186c848f9b91c3678dfbd77567ec33f0eaf6b1ac032caf8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CW4CTXJW54Y2VRAAF2E5U472J2/bundle.json","state_url":"https://pith.science/pith/CW4CTXJW54Y2VRAAF2E5U472J2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CW4CTXJW54Y2VRAAF2E5U472J2/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":"2026-08-15T14:02:36Z","links":{"resolver":"https://pith.science/pith/CW4CTXJW54Y2VRAAF2E5U472J2","bundle":"https://pith.science/pith/CW4CTXJW54Y2VRAAF2E5U472J2/bundle.json","state":"https://pith.science/pith/CW4CTXJW54Y2VRAAF2E5U472J2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CW4CTXJW54Y2VRAAF2E5U472J2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CW4CTXJW54Y2VRAAF2E5U472J2","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":"55301a4b3c6089990a2530c17bbff526a57ce9d0973b41a7113dd18797de1e57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-01T14:12:43Z","title_canon_sha256":"2394c8c23f165e381646e1c1f51d631a7eb349b3f2fbd1e03d7aac489ea5d01f"},"schema_version":"1.0","source":{"id":"1905.00321","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.00321","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1905.00321v3","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.00321","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"CW4CTXJW54Y2","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"pith_short_16","alias_value":"CW4CTXJW54Y2VRAA","created_at":"2026-07-05T01:15:49Z"},{"alias_kind":"pith_short_8","alias_value":"CW4CTXJW","created_at":"2026-07-05T01:15:49Z"}],"graph_snapshots":[{"event_id":"sha256:2639ac0f6006321e186c848f9b91c3678dfbd77567ec33f0eaf6b1ac032caf8f","target":"graph","created_at":"2026-07-05T01:15:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1905.00321/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the following result: there is a family $R = \\langle R_0,R_1,\\ldots \\rangle$ of subsets of $\\omega$ such that for every stable coloring $c : [\\omega]^2 \\to k$ hyperarithmetical in $R$ and every finite collection of Turing functionals, there is an infinite homogeneous set $H$ for $c$ such that none of the finitely many functionals map $R \\oplus H$ to an infinite cohesive set for $R$. This extends the current best partial results towards the $\\mathsf{SRT}^2_2$ vs. $\\mathsf{COH}$ problem in reverse mathematics, and is also a partial result towards the resolution of several related proble","authors_text":"Damir Dzhafarov, Ludovic Patey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-01T14:12:43Z","title":"COH, SRT22, and multiple functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00321","kind":"arxiv","version":3},"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:c86d5f08dbc91555810c235b49ca06649e0f09bad57c9c17edaf10c79f47a6e5","target":"record","created_at":"2026-07-05T01:15:49Z","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":"55301a4b3c6089990a2530c17bbff526a57ce9d0973b41a7113dd18797de1e57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-05-01T14:12:43Z","title_canon_sha256":"2394c8c23f165e381646e1c1f51d631a7eb349b3f2fbd1e03d7aac489ea5d01f"},"schema_version":"1.0","source":{"id":"1905.00321","kind":"arxiv","version":3}},"canonical_sha256":"15b829dd36ef31aac4002e89da73fa4ebe2419f29e697e85c64bd3e8d935a430","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15b829dd36ef31aac4002e89da73fa4ebe2419f29e697e85c64bd3e8d935a430","first_computed_at":"2026-07-05T01:15:49.596381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:15:49.596381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cOKzfDuoSNJvS2Dzilbsnf5hD3rS+lL4P/3yRym+rvNuVurBNeXwd40ISvSV+N/BZlOBMN//c9bDiszPr+AkAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:15:49.596752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.00321","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c86d5f08dbc91555810c235b49ca06649e0f09bad57c9c17edaf10c79f47a6e5","sha256:2639ac0f6006321e186c848f9b91c3678dfbd77567ec33f0eaf6b1ac032caf8f"],"state_sha256":"0c0f24924a595abf4d27622bd328e1b2c3b9c24c5540bb9795c0a9e36c56b07e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5HmQlbTQ+xunt9anuGKi1vILt0EQ/j81S1mBWv1v5iCJFRUwtKWKshsh/30GJi8ma+O66j2RaP4pioY/2yE5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T14:02:36.183962Z","bundle_sha256":"aa636c6af4091ca7ad2dcefe90feab8b6c55f9988a3d506724e31fd951ec38fc"}}