{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QMAT5O26JV2BCYOUZN4HEMECR6","short_pith_number":"pith:QMAT5O26","canonical_record":{"source":{"id":"1512.02954","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-09T17:20:42Z","cross_cats_sorted":[],"title_canon_sha256":"58753fb0cf224ed392a93fcf8d014735819537980db81095560c0f2f7874d4f7","abstract_canon_sha256":"0c1eced3df36bde02cb6dd139cfed8e3f65e7c73d950fa90a7d7698294d884ff"},"schema_version":"1.0"},"canonical_sha256":"83013ebb5e4d741161d4cb787230828f86cbe3b4a354a5a426eedf2859d72077","source":{"kind":"arxiv","id":"1512.02954","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02954","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02954v3","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02954","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"pith_short_12","alias_value":"QMAT5O26JV2B","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QMAT5O26JV2BCYOU","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QMAT5O26","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QMAT5O26JV2BCYOUZN4HEMECR6","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02954","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-09T17:20:42Z","cross_cats_sorted":[],"title_canon_sha256":"58753fb0cf224ed392a93fcf8d014735819537980db81095560c0f2f7874d4f7","abstract_canon_sha256":"0c1eced3df36bde02cb6dd139cfed8e3f65e7c73d950fa90a7d7698294d884ff"},"schema_version":"1.0"},"canonical_sha256":"83013ebb5e4d741161d4cb787230828f86cbe3b4a354a5a426eedf2859d72077","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:05.965347Z","signature_b64":"Hs3+kgv9Ii23Ig4y4/UcSyNpy9d6Yq+UXdKvhIoJX/Sf6e1KRLCmuvvK9xro1yRk9wJjUv99fcMOU6Z9XRoQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83013ebb5e4d741161d4cb787230828f86cbe3b4a354a5a426eedf2859d72077","last_reissued_at":"2026-05-18T00:09:05.964693Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:05.964693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02954","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":"2026-05-18T00:09:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fp2eh+k8/B7+NcdprQjUbQxIzN+lQNiH2Uf0oA0wPpaCNOoWewDKO5BihsCowPxOYqURz9cIfyUFX4oCJKDIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:56:12.392367Z"},"content_sha256":"89cff3f4fa80dfc3cc36e2c5cf1677c24eb11c8c7b56f9920d0c73f0c47fb11b","schema_version":"1.0","event_id":"sha256:89cff3f4fa80dfc3cc36e2c5cf1677c24eb11c8c7b56f9920d0c73f0c47fb11b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QMAT5O26JV2BCYOUZN4HEMECR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dickson's lemma and weak Ramsey theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Florian Pelupessy, Yasuhiko Omata","submitted_at":"2015-12-09T17:20:42Z","abstract_excerpt":"We explore the connections between Dickson's lemma and weak Ramsey theory. We show that a weak version of the Paris--Harrington principle for pairs in $c$ colors and miniaturized Dickson's lemma for $c$-tuples are equivalent over $\\mathsf{RCA}_0^{\\ast}$. Furthermore, we look at a cascade of consequences for several variants of weak Ramsey's theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02954","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":""},"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":"2026-05-18T00:09:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SeQHZpcrpTDn8c8FYPiBvkRd5mBsBNQtLZANuHwqXRCppP49wNjkd3++HFtyZYzwjvkpEExF34qS0OEXQkA5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:56:12.393001Z"},"content_sha256":"0ea374cda3a2b856794b28d5886f8ffa01b2226b040c161a854fd86efb6d3c84","schema_version":"1.0","event_id":"sha256:0ea374cda3a2b856794b28d5886f8ffa01b2226b040c161a854fd86efb6d3c84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QMAT5O26JV2BCYOUZN4HEMECR6/bundle.json","state_url":"https://pith.science/pith/QMAT5O26JV2BCYOUZN4HEMECR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QMAT5O26JV2BCYOUZN4HEMECR6/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":"2026-05-26T09:56:12Z","links":{"resolver":"https://pith.science/pith/QMAT5O26JV2BCYOUZN4HEMECR6","bundle":"https://pith.science/pith/QMAT5O26JV2BCYOUZN4HEMECR6/bundle.json","state":"https://pith.science/pith/QMAT5O26JV2BCYOUZN4HEMECR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QMAT5O26JV2BCYOUZN4HEMECR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QMAT5O26JV2BCYOUZN4HEMECR6","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":"0c1eced3df36bde02cb6dd139cfed8e3f65e7c73d950fa90a7d7698294d884ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-09T17:20:42Z","title_canon_sha256":"58753fb0cf224ed392a93fcf8d014735819537980db81095560c0f2f7874d4f7"},"schema_version":"1.0","source":{"id":"1512.02954","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02954","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02954v3","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02954","created_at":"2026-05-18T00:09:05Z"},{"alias_kind":"pith_short_12","alias_value":"QMAT5O26JV2B","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QMAT5O26JV2BCYOU","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QMAT5O26","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:0ea374cda3a2b856794b28d5886f8ffa01b2226b040c161a854fd86efb6d3c84","target":"graph","created_at":"2026-05-18T00:09:05Z","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":"We explore the connections between Dickson's lemma and weak Ramsey theory. We show that a weak version of the Paris--Harrington principle for pairs in $c$ colors and miniaturized Dickson's lemma for $c$-tuples are equivalent over $\\mathsf{RCA}_0^{\\ast}$. Furthermore, we look at a cascade of consequences for several variants of weak Ramsey's theorem.","authors_text":"Florian Pelupessy, Yasuhiko Omata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-09T17:20:42Z","title":"Dickson's lemma and weak Ramsey theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02954","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":"sha256:89cff3f4fa80dfc3cc36e2c5cf1677c24eb11c8c7b56f9920d0c73f0c47fb11b","target":"record","created_at":"2026-05-18T00:09:05Z","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":"0c1eced3df36bde02cb6dd139cfed8e3f65e7c73d950fa90a7d7698294d884ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-12-09T17:20:42Z","title_canon_sha256":"58753fb0cf224ed392a93fcf8d014735819537980db81095560c0f2f7874d4f7"},"schema_version":"1.0","source":{"id":"1512.02954","kind":"arxiv","version":3}},"canonical_sha256":"83013ebb5e4d741161d4cb787230828f86cbe3b4a354a5a426eedf2859d72077","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83013ebb5e4d741161d4cb787230828f86cbe3b4a354a5a426eedf2859d72077","first_computed_at":"2026-05-18T00:09:05.964693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:05.964693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hs3+kgv9Ii23Ig4y4/UcSyNpy9d6Yq+UXdKvhIoJX/Sf6e1KRLCmuvvK9xro1yRk9wJjUv99fcMOU6Z9XRoQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:05.965347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02954","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89cff3f4fa80dfc3cc36e2c5cf1677c24eb11c8c7b56f9920d0c73f0c47fb11b","sha256:0ea374cda3a2b856794b28d5886f8ffa01b2226b040c161a854fd86efb6d3c84"],"state_sha256":"69f0f33b8a504da3c0ed871b61e05bd9154418c2b296189a33e109418b2ce77f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aLOdRSnkLjPR266zxCLZsBPsw/EBB+GdxUu2OGwXUIffA72vUmzGQEP1FGC4t4TR4NuOcH51uULSyHgPBCerDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:56:12.396422Z","bundle_sha256":"1af09d9afe5ef6fffeb96e5921f189a5d889d5b8f8c50851886bfcffe8b99df6"}}