{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TES2E56IN5DYQ4HMNA2LPPQKIH","short_pith_number":"pith:TES2E56I","canonical_record":{"source":{"id":"1710.00070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-29T19:45:11Z","cross_cats_sorted":[],"title_canon_sha256":"814dbba3c2fb654d15b5485fe78e00489ac04efde346a3ea8bee782cefa72a0c","abstract_canon_sha256":"58018fef90eb3df9e8c9267fb4e7d37521a22c72d0d19548de6b8fa6d774a26a"},"schema_version":"1.0"},"canonical_sha256":"9925a277c86f478870ec6834b7be0a41cc53ead007722b59e8b27087133f24fd","source":{"kind":"arxiv","id":"1710.00070","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00070","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00070v2","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00070","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"TES2E56IN5DY","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"pith_short_16","alias_value":"TES2E56IN5DYQ4HM","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"pith_short_8","alias_value":"TES2E56I","created_at":"2026-07-05T02:41:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TES2E56IN5DYQ4HMNA2LPPQKIH","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-29T19:45:11Z","cross_cats_sorted":[],"title_canon_sha256":"814dbba3c2fb654d15b5485fe78e00489ac04efde346a3ea8bee782cefa72a0c","abstract_canon_sha256":"58018fef90eb3df9e8c9267fb4e7d37521a22c72d0d19548de6b8fa6d774a26a"},"schema_version":"1.0"},"canonical_sha256":"9925a277c86f478870ec6834b7be0a41cc53ead007722b59e8b27087133f24fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:41:45.291371Z","signature_b64":"2yk1NWPmr0R95JsHBmBaZdz4zsDcsNb+W50uyNdhZOQUmnjCxJb9aRoRtTePgr8J1nBt6ZNrz/usGY7+0G7EBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9925a277c86f478870ec6834b7be0a41cc53ead007722b59e8b27087133f24fd","last_reissued_at":"2026-07-05T02:41:45.290962Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:41:45.290962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00070","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t13eTyx2RwD9mz/GCIJP9V06lbG82KxT8und/3WtK06ZdPTbGcbWhYZvOCLXCBxk9x9Ao+JIQTCpwcWhCQoSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:56:27.432558Z"},"content_sha256":"85d74830930466372dc00a7b3b0a8499f9b929acca58771da82e29125a4499ee","schema_version":"1.0","event_id":"sha256:85d74830930466372dc00a7b3b0a8499f9b929acca58771da82e29125a4499ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TES2E56IN5DYQ4HMNA2LPPQKIH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effectiveness for the Dual Ramsey Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Damir Dzhafarov, Linda Brown Westrick, Reed Solomon, Stephen Flood","submitted_at":"2017-09-29T19:45:11Z","abstract_excerpt":"We analyze the Dual Ramsey Theorem for $k$ partitions and $\\ell$ colors ($\\mathsf{DRT}^k_\\ell$) in the context of reverse math, effective analysis, and strong reductions. Over $\\mathsf{RCA}_0$, the Dual Ramsey Theorem stated for Baire colorings is equivalent to the statement for clopen colorings and to a purely combinatorial theorem $\\mathsf{cDRT}^k_\\ell$. When the theorem is stated for Borel colorings and $k\\geq 3$, the resulting principles are essentially relativizations of $\\mathsf{cDRT}^k_\\ell$. For each $\\alpha$, there is a computable Borel code for a $\\Delta^0_\\alpha$ coloring such that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00070","kind":"arxiv","version":2},"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/1710.00070/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":"2026-07-05T02:41:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K54oCdzbGQjN6+pZInsDwPMPs3KIz9hvayC2proWqH7eRv3P2OwqBs1unpZuiCZ9vkro2z85bAvqbMlhVPs8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T05:56:27.432936Z"},"content_sha256":"cc32655f200a7f73c18d185aa58b62062cc5f9a6996006556d01d76f14ccd82d","schema_version":"1.0","event_id":"sha256:cc32655f200a7f73c18d185aa58b62062cc5f9a6996006556d01d76f14ccd82d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TES2E56IN5DYQ4HMNA2LPPQKIH/bundle.json","state_url":"https://pith.science/pith/TES2E56IN5DYQ4HMNA2LPPQKIH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TES2E56IN5DYQ4HMNA2LPPQKIH/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":"2026-07-07T05:56:27Z","links":{"resolver":"https://pith.science/pith/TES2E56IN5DYQ4HMNA2LPPQKIH","bundle":"https://pith.science/pith/TES2E56IN5DYQ4HMNA2LPPQKIH/bundle.json","state":"https://pith.science/pith/TES2E56IN5DYQ4HMNA2LPPQKIH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TES2E56IN5DYQ4HMNA2LPPQKIH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TES2E56IN5DYQ4HMNA2LPPQKIH","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":"58018fef90eb3df9e8c9267fb4e7d37521a22c72d0d19548de6b8fa6d774a26a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-29T19:45:11Z","title_canon_sha256":"814dbba3c2fb654d15b5485fe78e00489ac04efde346a3ea8bee782cefa72a0c"},"schema_version":"1.0","source":{"id":"1710.00070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00070","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00070v2","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00070","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"pith_short_12","alias_value":"TES2E56IN5DY","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"pith_short_16","alias_value":"TES2E56IN5DYQ4HM","created_at":"2026-07-05T02:41:45Z"},{"alias_kind":"pith_short_8","alias_value":"TES2E56I","created_at":"2026-07-05T02:41:45Z"}],"graph_snapshots":[{"event_id":"sha256:cc32655f200a7f73c18d185aa58b62062cc5f9a6996006556d01d76f14ccd82d","target":"graph","created_at":"2026-07-05T02:41:45Z","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/1710.00070/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the Dual Ramsey Theorem for $k$ partitions and $\\ell$ colors ($\\mathsf{DRT}^k_\\ell$) in the context of reverse math, effective analysis, and strong reductions. Over $\\mathsf{RCA}_0$, the Dual Ramsey Theorem stated for Baire colorings is equivalent to the statement for clopen colorings and to a purely combinatorial theorem $\\mathsf{cDRT}^k_\\ell$. When the theorem is stated for Borel colorings and $k\\geq 3$, the resulting principles are essentially relativizations of $\\mathsf{cDRT}^k_\\ell$. For each $\\alpha$, there is a computable Borel code for a $\\Delta^0_\\alpha$ coloring such that ","authors_text":"Damir Dzhafarov, Linda Brown Westrick, Reed Solomon, Stephen Flood","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-29T19:45:11Z","title":"Effectiveness for the Dual Ramsey Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00070","kind":"arxiv","version":2},"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":"sha256:85d74830930466372dc00a7b3b0a8499f9b929acca58771da82e29125a4499ee","target":"record","created_at":"2026-07-05T02:41:45Z","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":"58018fef90eb3df9e8c9267fb4e7d37521a22c72d0d19548de6b8fa6d774a26a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-29T19:45:11Z","title_canon_sha256":"814dbba3c2fb654d15b5485fe78e00489ac04efde346a3ea8bee782cefa72a0c"},"schema_version":"1.0","source":{"id":"1710.00070","kind":"arxiv","version":2}},"canonical_sha256":"9925a277c86f478870ec6834b7be0a41cc53ead007722b59e8b27087133f24fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9925a277c86f478870ec6834b7be0a41cc53ead007722b59e8b27087133f24fd","first_computed_at":"2026-07-05T02:41:45.290962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:41:45.290962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2yk1NWPmr0R95JsHBmBaZdz4zsDcsNb+W50uyNdhZOQUmnjCxJb9aRoRtTePgr8J1nBt6ZNrz/usGY7+0G7EBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:41:45.291371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85d74830930466372dc00a7b3b0a8499f9b929acca58771da82e29125a4499ee","sha256:cc32655f200a7f73c18d185aa58b62062cc5f9a6996006556d01d76f14ccd82d"],"state_sha256":"251d84be4a6e74923701092b936ab5745ae5765ff4c7dd7b82aafbbea622de87"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qv1gdycwnSqNnjrzPHiMM5hG6NP2JCRFrtd6n2E1zVDAKkg7HgUlvTSsS2Kp7g32LITUn13qNSmzylLcq+mQAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T05:56:27.437045Z","bundle_sha256":"1aaab29b0da01afe211736c387484ed89be4fea07828df5c997a57c9060d00c9"}}