{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Z5UK64CBV3T7BCKYISLHKBROWK","short_pith_number":"pith:Z5UK64CB","schema_version":"1.0","canonical_sha256":"cf68af7041aee7f08958449675062eb2918b6463d6b4908341031fc9decb7ae8","source":{"kind":"arxiv","id":"1501.05115","version":2},"attestation_state":"computed","paper":{"title":"An Isbell Duality Theorem for Type Refinement Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LO","authors_text":"Noam Zeilberger, Paul-Andr\\'e Melli\\`es","submitted_at":"2015-01-21T10:24:16Z","abstract_excerpt":"Any refinement system (= functor) has a fully faithful representation in the refinement system of presheaves, by interpreting types as relative slice categories, and refinement types as presheaves over those categories. Motivated by an analogy between side effects in programming and *context effects* in linear logic, we study logical aspects of this \"positive\" (covariant) representation, as well as of an associated \"negative\" (contravariant) representation. We establish several preservation properties for these representations, including a generalization of Day's embedding theorem for monoidal"},"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":"1501.05115","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-01-21T10:24:16Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"08f7f9838385b50d459040b5986bceb4c8b2a2c851069d65b4cbff59ed916d6a","abstract_canon_sha256":"bf0797491a9594c00840d54181108a9f87bfae60c510f30c747d750e7e79d2d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:01.640925Z","signature_b64":"YSShrrMIhWSrRcbdaapzhyoQ0w8mlAKk6P8IdvhSeSHRGyipaYhx0x5XZsGgehu8ZJdYVhFThvuQfChSByz9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf68af7041aee7f08958449675062eb2918b6463d6b4908341031fc9decb7ae8","last_reissued_at":"2026-05-18T01:36:01.640400Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:01.640400Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Isbell Duality Theorem for Type Refinement Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LO","authors_text":"Noam Zeilberger, Paul-Andr\\'e Melli\\`es","submitted_at":"2015-01-21T10:24:16Z","abstract_excerpt":"Any refinement system (= functor) has a fully faithful representation in the refinement system of presheaves, by interpreting types as relative slice categories, and refinement types as presheaves over those categories. Motivated by an analogy between side effects in programming and *context effects* in linear logic, we study logical aspects of this \"positive\" (covariant) representation, as well as of an associated \"negative\" (contravariant) representation. We establish several preservation properties for these representations, including a generalization of Day's embedding theorem for monoidal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05115","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":"1501.05115","created_at":"2026-05-18T01:36:01.640484+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.05115v2","created_at":"2026-05-18T01:36:01.640484+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05115","created_at":"2026-05-18T01:36:01.640484+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z5UK64CBV3T7","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z5UK64CBV3T7BCKY","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z5UK64CB","created_at":"2026-05-18T12:29:52.810259+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/Z5UK64CBV3T7BCKYISLHKBROWK","json":"https://pith.science/pith/Z5UK64CBV3T7BCKYISLHKBROWK.json","graph_json":"https://pith.science/api/pith-number/Z5UK64CBV3T7BCKYISLHKBROWK/graph.json","events_json":"https://pith.science/api/pith-number/Z5UK64CBV3T7BCKYISLHKBROWK/events.json","paper":"https://pith.science/paper/Z5UK64CB"},"agent_actions":{"view_html":"https://pith.science/pith/Z5UK64CBV3T7BCKYISLHKBROWK","download_json":"https://pith.science/pith/Z5UK64CBV3T7BCKYISLHKBROWK.json","view_paper":"https://pith.science/paper/Z5UK64CB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.05115&json=true","fetch_graph":"https://pith.science/api/pith-number/Z5UK64CBV3T7BCKYISLHKBROWK/graph.json","fetch_events":"https://pith.science/api/pith-number/Z5UK64CBV3T7BCKYISLHKBROWK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z5UK64CBV3T7BCKYISLHKBROWK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z5UK64CBV3T7BCKYISLHKBROWK/action/storage_attestation","attest_author":"https://pith.science/pith/Z5UK64CBV3T7BCKYISLHKBROWK/action/author_attestation","sign_citation":"https://pith.science/pith/Z5UK64CBV3T7BCKYISLHKBROWK/action/citation_signature","submit_replication":"https://pith.science/pith/Z5UK64CBV3T7BCKYISLHKBROWK/action/replication_record"}},"created_at":"2026-05-18T01:36:01.640484+00:00","updated_at":"2026-05-18T01:36:01.640484+00:00"}