{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NVX5Z5HM7TGG5Q7UX74AVPTNPF","short_pith_number":"pith:NVX5Z5HM","schema_version":"1.0","canonical_sha256":"6d6fdcf4ecfccc6ec3f4bff80abe6d79443e8bdbace2cf6f1560de7070f150c2","source":{"kind":"arxiv","id":"1405.7456","version":2},"attestation_state":"computed","paper":{"title":"Computable structures in generic extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Antonio Montalban, Julia Knight, Noah Schweber","submitted_at":"2014-05-29T04:08:28Z","abstract_excerpt":"In this paper, we investigate connections between structures present in every generic extension of the universe $V$ and computability theory. We introduce the notion of {\\em generic Muchnik reducibility} that can be used to to compare the complexity of uncountable structures; we establish basic properties of this reducibility, and study it in the context of {\\em generic presentability}, the existence of a copy of the structure in every extension by a given forcing. We show that every forcing notion making $\\omega_2$ countable generically presents some countable structure with no copy in the gr"},"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":"1405.7456","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-05-29T04:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"024bac9cbb1e898fd9e22bf39e45a0fb7af9fd78432abd2eb0c2b834836ed04b","abstract_canon_sha256":"a3a51fd2f1ac0973a746914a4ff9bd8a21e9d3225b4d1ba214b984975fe6da97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:38.131112Z","signature_b64":"TNNa5dkD/v3pFVJZS6ZqA4qZUuQ4YUb8wDeE2Z44q/3FyGIEWmLNCUyhtFIYTcfXDFHlcCb4M0oJvSVIpnX+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d6fdcf4ecfccc6ec3f4bff80abe6d79443e8bdbace2cf6f1560de7070f150c2","last_reissued_at":"2026-05-18T02:31:38.130481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:38.130481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computable structures in generic extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Antonio Montalban, Julia Knight, Noah Schweber","submitted_at":"2014-05-29T04:08:28Z","abstract_excerpt":"In this paper, we investigate connections between structures present in every generic extension of the universe $V$ and computability theory. We introduce the notion of {\\em generic Muchnik reducibility} that can be used to to compare the complexity of uncountable structures; we establish basic properties of this reducibility, and study it in the context of {\\em generic presentability}, the existence of a copy of the structure in every extension by a given forcing. We show that every forcing notion making $\\omega_2$ countable generically presents some countable structure with no copy in the gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7456","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1405.7456","created_at":"2026-05-18T02:31:38.130567+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.7456v2","created_at":"2026-05-18T02:31:38.130567+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7456","created_at":"2026-05-18T02:31:38.130567+00:00"},{"alias_kind":"pith_short_12","alias_value":"NVX5Z5HM7TGG","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NVX5Z5HM7TGG5Q7U","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NVX5Z5HM","created_at":"2026-05-18T12:28:41.024544+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/NVX5Z5HM7TGG5Q7UX74AVPTNPF","json":"https://pith.science/pith/NVX5Z5HM7TGG5Q7UX74AVPTNPF.json","graph_json":"https://pith.science/api/pith-number/NVX5Z5HM7TGG5Q7UX74AVPTNPF/graph.json","events_json":"https://pith.science/api/pith-number/NVX5Z5HM7TGG5Q7UX74AVPTNPF/events.json","paper":"https://pith.science/paper/NVX5Z5HM"},"agent_actions":{"view_html":"https://pith.science/pith/NVX5Z5HM7TGG5Q7UX74AVPTNPF","download_json":"https://pith.science/pith/NVX5Z5HM7TGG5Q7UX74AVPTNPF.json","view_paper":"https://pith.science/paper/NVX5Z5HM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.7456&json=true","fetch_graph":"https://pith.science/api/pith-number/NVX5Z5HM7TGG5Q7UX74AVPTNPF/graph.json","fetch_events":"https://pith.science/api/pith-number/NVX5Z5HM7TGG5Q7UX74AVPTNPF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NVX5Z5HM7TGG5Q7UX74AVPTNPF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NVX5Z5HM7TGG5Q7UX74AVPTNPF/action/storage_attestation","attest_author":"https://pith.science/pith/NVX5Z5HM7TGG5Q7UX74AVPTNPF/action/author_attestation","sign_citation":"https://pith.science/pith/NVX5Z5HM7TGG5Q7UX74AVPTNPF/action/citation_signature","submit_replication":"https://pith.science/pith/NVX5Z5HM7TGG5Q7UX74AVPTNPF/action/replication_record"}},"created_at":"2026-05-18T02:31:38.130567+00:00","updated_at":"2026-05-18T02:31:38.130567+00:00"}