{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WFLROV3B5W6DNXGGN56FUR7KM3","short_pith_number":"pith:WFLROV3B","canonical_record":{"source":{"id":"1603.09489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-31T08:42:30Z","cross_cats_sorted":[],"title_canon_sha256":"8803149cfb64d443fc453c43539595ee8751771e8bc8bfaed8433a86400a2680","abstract_canon_sha256":"689e3a5344c6b3f86abd7144bf4e6309ea3b9654e2e2804514dbd6f363447264"},"schema_version":"1.0"},"canonical_sha256":"b157175761edbc36dcc66f7c5a47ea66f76d1ba8696b7712e79ce171d1314cbd","source":{"kind":"arxiv","id":"1603.09489","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09489","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09489v2","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09489","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"WFLROV3B5W6D","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WFLROV3B5W6DNXGG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WFLROV3B","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WFLROV3B5W6DNXGGN56FUR7KM3","target":"record","payload":{"canonical_record":{"source":{"id":"1603.09489","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-31T08:42:30Z","cross_cats_sorted":[],"title_canon_sha256":"8803149cfb64d443fc453c43539595ee8751771e8bc8bfaed8433a86400a2680","abstract_canon_sha256":"689e3a5344c6b3f86abd7144bf4e6309ea3b9654e2e2804514dbd6f363447264"},"schema_version":"1.0"},"canonical_sha256":"b157175761edbc36dcc66f7c5a47ea66f76d1ba8696b7712e79ce171d1314cbd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:37.027755Z","signature_b64":"5Z4KxJEtezUjxr6lfzQCXWmEyPKaE6IIT1wQDZJzNzmQ460lD+aqdtAcKBWEpw4Q72uVmRAY2tX6lR8gLMAABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b157175761edbc36dcc66f7c5a47ea66f76d1ba8696b7712e79ce171d1314cbd","last_reissued_at":"2026-05-18T00:47:37.027209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:37.027209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.09489","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":"2026-05-18T00:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9dCYztLLzlWBhOV5mqJBVqokZnGnY7icy+LVP4L2SpbatN99fvjs2nC13qNo3Rv4nbsERu31nbp6WRFGE+DLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:09:53.391699Z"},"content_sha256":"dce98cb12b48243e332896d54ff4f4aef053014863ab0bb0f60c1049bcc1e070","schema_version":"1.0","event_id":"sha256:dce98cb12b48243e332896d54ff4f4aef053014863ab0bb0f60c1049bcc1e070"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WFLROV3B5W6DNXGGN56FUR7KM3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heterogeneous Ramsey Algebras and Classification of Ramsey Vector Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Wen Chean Teh, Zu Yao Teoh","submitted_at":"2016-03-31T08:42:30Z","abstract_excerpt":"Carlson introduced the notion of a Ramsey space as a generalization to the Ellentuck space. When a Ramsey space is induced by an algebra, Carlson suggested a study of its purely combinatorial version now called Ramsey algebra. Some basic results for homogeneous algebras have been obtained. In this paper, we introduce the notion of a Ramsey algebra for heterogeneous algebras and derive some basic results. Then, we study the Ramsey-algebraic properties of vector spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09489","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":""},"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":"2026-05-18T00:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AI323+fJTQh+vbGdE/JFRab2CyLnYRbiv43+xKGVzs263WJbJZh3AghTHKbRweKrHYvbmdSMsfIRDEDaMxI6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:09:53.392049Z"},"content_sha256":"ad8479d71861c55a6641209fb890105d45a7ca644e43378c4164e5b6cc848666","schema_version":"1.0","event_id":"sha256:ad8479d71861c55a6641209fb890105d45a7ca644e43378c4164e5b6cc848666"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFLROV3B5W6DNXGGN56FUR7KM3/bundle.json","state_url":"https://pith.science/pith/WFLROV3B5W6DNXGGN56FUR7KM3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFLROV3B5W6DNXGGN56FUR7KM3/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":"2026-05-28T11:09:53Z","links":{"resolver":"https://pith.science/pith/WFLROV3B5W6DNXGGN56FUR7KM3","bundle":"https://pith.science/pith/WFLROV3B5W6DNXGGN56FUR7KM3/bundle.json","state":"https://pith.science/pith/WFLROV3B5W6DNXGGN56FUR7KM3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFLROV3B5W6DNXGGN56FUR7KM3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WFLROV3B5W6DNXGGN56FUR7KM3","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":"689e3a5344c6b3f86abd7144bf4e6309ea3b9654e2e2804514dbd6f363447264","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-31T08:42:30Z","title_canon_sha256":"8803149cfb64d443fc453c43539595ee8751771e8bc8bfaed8433a86400a2680"},"schema_version":"1.0","source":{"id":"1603.09489","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.09489","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.09489v2","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.09489","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"WFLROV3B5W6D","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WFLROV3B5W6DNXGG","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WFLROV3B","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:ad8479d71861c55a6641209fb890105d45a7ca644e43378c4164e5b6cc848666","target":"graph","created_at":"2026-05-18T00:47:37Z","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":"Carlson introduced the notion of a Ramsey space as a generalization to the Ellentuck space. When a Ramsey space is induced by an algebra, Carlson suggested a study of its purely combinatorial version now called Ramsey algebra. Some basic results for homogeneous algebras have been obtained. In this paper, we introduce the notion of a Ramsey algebra for heterogeneous algebras and derive some basic results. Then, we study the Ramsey-algebraic properties of vector spaces.","authors_text":"Wen Chean Teh, Zu Yao Teoh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-31T08:42:30Z","title":"Heterogeneous Ramsey Algebras and Classification of Ramsey Vector Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09489","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:dce98cb12b48243e332896d54ff4f4aef053014863ab0bb0f60c1049bcc1e070","target":"record","created_at":"2026-05-18T00:47:37Z","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":"689e3a5344c6b3f86abd7144bf4e6309ea3b9654e2e2804514dbd6f363447264","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-03-31T08:42:30Z","title_canon_sha256":"8803149cfb64d443fc453c43539595ee8751771e8bc8bfaed8433a86400a2680"},"schema_version":"1.0","source":{"id":"1603.09489","kind":"arxiv","version":2}},"canonical_sha256":"b157175761edbc36dcc66f7c5a47ea66f76d1ba8696b7712e79ce171d1314cbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b157175761edbc36dcc66f7c5a47ea66f76d1ba8696b7712e79ce171d1314cbd","first_computed_at":"2026-05-18T00:47:37.027209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:37.027209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Z4KxJEtezUjxr6lfzQCXWmEyPKaE6IIT1wQDZJzNzmQ460lD+aqdtAcKBWEpw4Q72uVmRAY2tX6lR8gLMAABw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:37.027755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.09489","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dce98cb12b48243e332896d54ff4f4aef053014863ab0bb0f60c1049bcc1e070","sha256:ad8479d71861c55a6641209fb890105d45a7ca644e43378c4164e5b6cc848666"],"state_sha256":"d7448ac59ef87df02e7d87b568ed94639e75c650a23c8eb42b6799779473460e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2QfGzfNtMErDDVho0ZL8H2NCmOPU7dyr34wKgwEzsn3/L6XUu99MULlAxGdcu85z+OB2y2VyuAzxMVLewk7hBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:09:53.394045Z","bundle_sha256":"cfad6f197f76525720c6dc4c974ff5c0b88c960397771ce5adb1175a57ff711b"}}