{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4OMU573HRQXVOU4HCAUCR6LEZS","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":"941c6f67f3c7d61991a72347de142af0d0d3c548e5c0eb898d6b7b15c65ac751","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-07-12T10:03:45Z","title_canon_sha256":"9e0806198c58e1147523e9d8d94781b86f64d1a40b12018ba3efab9744ec074d"},"schema_version":"1.0","source":{"id":"1607.03291","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03291","created_at":"2026-05-18T00:27:22Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03291v3","created_at":"2026-05-18T00:27:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03291","created_at":"2026-05-18T00:27:22Z"},{"alias_kind":"pith_short_12","alias_value":"4OMU573HRQXV","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4OMU573HRQXVOU4H","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4OMU573H","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:a82a244fc6fe7c683ed9c2ee2c1cf95946ebde9370545acad5932a359587cb66","target":"graph","created_at":"2026-05-18T00:27:22Z","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":"Given a family $\\mathcal{F}$ of subsets of $\\{1,\\ldots,m\\}$, we try to compute the least natural number $n$ such that for every function $S:[\\aleph_n]^{<\\omega}\\longrightarrow [\\aleph_n]^{<\\omega}$ there exists a bijection $u:\\{1,\\ldots,m\\}\\longrightarrow Y\\subset \\aleph_n$ such that $Su(A)\\cap Y \\subset u(A)$ for all $A\\in\\mathcal{F}$.","authors_text":"Antonio Avil\\'es, Claribet Pi\\~na","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-07-12T10:03:45Z","title":"Free sets for a set-mapping relative to a family of sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03291","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":"sha256:519ce846025459c6b7c6162e07327ccf810bcb53934e01fae1afb4911bf91e72","target":"record","created_at":"2026-05-18T00:27:22Z","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":"941c6f67f3c7d61991a72347de142af0d0d3c548e5c0eb898d6b7b15c65ac751","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-07-12T10:03:45Z","title_canon_sha256":"9e0806198c58e1147523e9d8d94781b86f64d1a40b12018ba3efab9744ec074d"},"schema_version":"1.0","source":{"id":"1607.03291","kind":"arxiv","version":3}},"canonical_sha256":"e3994eff678c2f575387102828f964cc9475a770a54cd91bc9f76a5369565620","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3994eff678c2f575387102828f964cc9475a770a54cd91bc9f76a5369565620","first_computed_at":"2026-05-18T00:27:22.220999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:22.220999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AlQLW7ZFJUcGNtvW2ylRELhFOB3IOW5JiMuLioX8xyjLzXY9puDe/5FExJZwErcqv11QCUwSLX0GyR8MkSpMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:22.221571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03291","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:519ce846025459c6b7c6162e07327ccf810bcb53934e01fae1afb4911bf91e72","sha256:a82a244fc6fe7c683ed9c2ee2c1cf95946ebde9370545acad5932a359587cb66"],"state_sha256":"0055590ca495d37005d3ea19f63e97c5f08caa202d11282c44df42e95bdf42f0"}