{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1993:MC4CMEZEFZFQSUUZNTRNKEEVTI","short_pith_number":"pith:MC4CMEZE","schema_version":"1.0","canonical_sha256":"60b82613242e4b0952996ce2d510959a13e0cf1b30c0a573136df9fa78af7f47","source":{"kind":"arxiv","id":"math/9308213","version":1},"attestation_state":"computed","paper":{"title":"On coherent systems of projections for aleph_1 separable groups","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.LO","authors_text":"Alan H. Mekler, Paul C. Eklof, Saharon Shelah","submitted_at":"1993-08-15T00:00:00Z","abstract_excerpt":"It is proved consistent with either CH or the negation of CH that there is an aleph_1-separable group of cardinality aleph_1 which does not have a coherent system of projections. It had previously been shown that it is consistent with not CH that every aleph_1-separable group of cardinality aleph_1 does have a coherent system of projections."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/9308213","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.LO","submitted_at":"1993-08-15T00:00:00Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"9881a3e4ee2d95210d64f6cfaa6c5ecbce9b6514771ee3f374c6c57cab09a7e0","abstract_canon_sha256":"fc27b4eb3df8ddd8f34047cc4bd368f6eedf267fd680e41a1a76dfa07388d277"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.981298Z","signature_b64":"Tyq+Rhh+xNQ7B4YljKzYibWQyxHKazDEx7dz2eRsG3aDLsOSOK8PggtH6yyDbH2fT2C+u4Ds8FmwZhPxIoxCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60b82613242e4b0952996ce2d510959a13e0cf1b30c0a573136df9fa78af7f47","last_reissued_at":"2026-05-18T01:05:51.980907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.980907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On coherent systems of projections for aleph_1 separable groups","license":"","headline":"","cross_cats":["math.RA"],"primary_cat":"math.LO","authors_text":"Alan H. Mekler, Paul C. Eklof, Saharon Shelah","submitted_at":"1993-08-15T00:00:00Z","abstract_excerpt":"It is proved consistent with either CH or the negation of CH that there is an aleph_1-separable group of cardinality aleph_1 which does not have a coherent system of projections. It had previously been shown that it is consistent with not CH that every aleph_1-separable group of cardinality aleph_1 does have a coherent system of projections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9308213","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/9308213","created_at":"2026-05-18T01:05:51.980965+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9308213v1","created_at":"2026-05-18T01:05:51.980965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9308213","created_at":"2026-05-18T01:05:51.980965+00:00"},{"alias_kind":"pith_short_12","alias_value":"MC4CMEZEFZFQ","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"MC4CMEZEFZFQSUUZ","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"MC4CMEZE","created_at":"2026-05-18T12:25:47.102015+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI","json":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI.json","graph_json":"https://pith.science/api/pith-number/MC4CMEZEFZFQSUUZNTRNKEEVTI/graph.json","events_json":"https://pith.science/api/pith-number/MC4CMEZEFZFQSUUZNTRNKEEVTI/events.json","paper":"https://pith.science/paper/MC4CMEZE"},"agent_actions":{"view_html":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI","download_json":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI.json","view_paper":"https://pith.science/paper/MC4CMEZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9308213&json=true","fetch_graph":"https://pith.science/api/pith-number/MC4CMEZEFZFQSUUZNTRNKEEVTI/graph.json","fetch_events":"https://pith.science/api/pith-number/MC4CMEZEFZFQSUUZNTRNKEEVTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI/action/storage_attestation","attest_author":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI/action/author_attestation","sign_citation":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI/action/citation_signature","submit_replication":"https://pith.science/pith/MC4CMEZEFZFQSUUZNTRNKEEVTI/action/replication_record"}},"created_at":"2026-05-18T01:05:51.980965+00:00","updated_at":"2026-05-18T01:05:51.980965+00:00"}