{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6AOKUEPI73XV5JWPIL3FWDIYS4","short_pith_number":"pith:6AOKUEPI","canonical_record":{"source":{"id":"1301.0396","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-03T08:58:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"223d861ca6447810b30b72c3130157df44ed6889ddc052deb286c264022d5236","abstract_canon_sha256":"cef48b76b6b62f84080de8387278c5b7053fdcac5d551c41193398e9ae50d813"},"schema_version":"1.0"},"canonical_sha256":"f01caa11e8feef5ea6cf42f65b0d189720e9606fa235b3cf83d4a003493a653e","source":{"kind":"arxiv","id":"1301.0396","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0396","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0396v3","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0396","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"6AOKUEPI73XV","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6AOKUEPI73XV5JWP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6AOKUEPI","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6AOKUEPI73XV5JWPIL3FWDIYS4","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0396","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-03T08:58:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"223d861ca6447810b30b72c3130157df44ed6889ddc052deb286c264022d5236","abstract_canon_sha256":"cef48b76b6b62f84080de8387278c5b7053fdcac5d551c41193398e9ae50d813"},"schema_version":"1.0"},"canonical_sha256":"f01caa11e8feef5ea6cf42f65b0d189720e9606fa235b3cf83d4a003493a653e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:51.504704Z","signature_b64":"z+kBsub2PnNTPCHazXgXNar/NTy+wClqn7MO+7m/Yb7w8w9Iqw4PRMihwmtbUms946X5S2ZhPxN/MtoYluzsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f01caa11e8feef5ea6cf42f65b0d189720e9606fa235b3cf83d4a003493a653e","last_reissued_at":"2026-05-18T01:37:51.503943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:51.503943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0396","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":"2026-05-18T01:37:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8guz/pnt+PnmLPNGLJu7z+67Hvq44Ftsc9bak2WvBIVJd5bSifOxTwM/yEYClVOrTaUUN0gw3+tNKVyt5s9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:49:47.382270Z"},"content_sha256":"a4c8da6e4a99be2d2efc65b3ae196964fcdf248965cbaad116ebe0d89fb170c2","schema_version":"1.0","event_id":"sha256:a4c8da6e4a99be2d2efc65b3ae196964fcdf248965cbaad116ebe0d89fb170c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6AOKUEPI73XV5JWPIL3FWDIYS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Filter Dichotomy Principle Does not Imply the Semifilter Trichotomy Principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Heike Mildenberger","submitted_at":"2013-01-03T08:58:35Z","abstract_excerpt":"We answer Blass' question from 1989 of whether the inequality $\\gu < \\gro$ is strictly stronger than the filter dichotomy principle affirmatively. We show that there is a forcing extension in which every non-meagre filter on $\\omega$ is ultra by finite-to-one and the semifilter trichotomy does not hold. This trichotomy says: every semifilter is either meagre or comeagre or ultra by finite-to-one. The trichotomy is equivalent to the inequality $\\gu<\\gro$ by work of Blass and Laflamme. Combinatorics of block sequences is used to establish forcing notions that preserve suitable properties of bloc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0396","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":"2026-05-18T01:37:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K8stLv8yLQFMGUPP9uCpOPYAzekTpI+7Xwn3Y4CNjKt63dJMZCXyFfHYNI8osU/DhTAOwzsPdB4h6sSnjAxtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T09:49:47.382632Z"},"content_sha256":"8f39fa8b276a56600c6517e92391e3d54d1855a60014a5e8fbfdbcbf02efc082","schema_version":"1.0","event_id":"sha256:8f39fa8b276a56600c6517e92391e3d54d1855a60014a5e8fbfdbcbf02efc082"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6AOKUEPI73XV5JWPIL3FWDIYS4/bundle.json","state_url":"https://pith.science/pith/6AOKUEPI73XV5JWPIL3FWDIYS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6AOKUEPI73XV5JWPIL3FWDIYS4/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":"2026-06-02T09:49:47Z","links":{"resolver":"https://pith.science/pith/6AOKUEPI73XV5JWPIL3FWDIYS4","bundle":"https://pith.science/pith/6AOKUEPI73XV5JWPIL3FWDIYS4/bundle.json","state":"https://pith.science/pith/6AOKUEPI73XV5JWPIL3FWDIYS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6AOKUEPI73XV5JWPIL3FWDIYS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6AOKUEPI73XV5JWPIL3FWDIYS4","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":"cef48b76b6b62f84080de8387278c5b7053fdcac5d551c41193398e9ae50d813","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-03T08:58:35Z","title_canon_sha256":"223d861ca6447810b30b72c3130157df44ed6889ddc052deb286c264022d5236"},"schema_version":"1.0","source":{"id":"1301.0396","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0396","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0396v3","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0396","created_at":"2026-05-18T01:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"6AOKUEPI73XV","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6AOKUEPI73XV5JWP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6AOKUEPI","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:8f39fa8b276a56600c6517e92391e3d54d1855a60014a5e8fbfdbcbf02efc082","target":"graph","created_at":"2026-05-18T01:37:51Z","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 answer Blass' question from 1989 of whether the inequality $\\gu < \\gro$ is strictly stronger than the filter dichotomy principle affirmatively. We show that there is a forcing extension in which every non-meagre filter on $\\omega$ is ultra by finite-to-one and the semifilter trichotomy does not hold. This trichotomy says: every semifilter is either meagre or comeagre or ultra by finite-to-one. The trichotomy is equivalent to the inequality $\\gu<\\gro$ by work of Blass and Laflamme. Combinatorics of block sequences is used to establish forcing notions that preserve suitable properties of bloc","authors_text":"Heike Mildenberger","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-03T08:58:35Z","title":"The Filter Dichotomy Principle Does not Imply the Semifilter Trichotomy Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0396","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:a4c8da6e4a99be2d2efc65b3ae196964fcdf248965cbaad116ebe0d89fb170c2","target":"record","created_at":"2026-05-18T01:37:51Z","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":"cef48b76b6b62f84080de8387278c5b7053fdcac5d551c41193398e9ae50d813","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-01-03T08:58:35Z","title_canon_sha256":"223d861ca6447810b30b72c3130157df44ed6889ddc052deb286c264022d5236"},"schema_version":"1.0","source":{"id":"1301.0396","kind":"arxiv","version":3}},"canonical_sha256":"f01caa11e8feef5ea6cf42f65b0d189720e9606fa235b3cf83d4a003493a653e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f01caa11e8feef5ea6cf42f65b0d189720e9606fa235b3cf83d4a003493a653e","first_computed_at":"2026-05-18T01:37:51.503943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:51.503943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z+kBsub2PnNTPCHazXgXNar/NTy+wClqn7MO+7m/Yb7w8w9Iqw4PRMihwmtbUms946X5S2ZhPxN/MtoYluzsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:51.504704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0396","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4c8da6e4a99be2d2efc65b3ae196964fcdf248965cbaad116ebe0d89fb170c2","sha256:8f39fa8b276a56600c6517e92391e3d54d1855a60014a5e8fbfdbcbf02efc082"],"state_sha256":"a6b0ff5da29b3e2f62353f2ae5be074b26a00df246c72d3b7b0177cb682e07d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/wDz8ABmL8DFpiRd07HGxcwp4ghfuFVT7yhAdRmQXuDYYqgiP717/z+S2j+SKm4FPf00Qyhwg+kd1jQKkMZaBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T09:49:47.384563Z","bundle_sha256":"3ebfac9aaa712b6221e3c79b2ef0f483e7e4f283efba0437b8e15155f8b693ec"}}