{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WJA6FYJFIAHIPHIHSK7UFBHGSC","short_pith_number":"pith:WJA6FYJF","schema_version":"1.0","canonical_sha256":"b241e2e125400e879d0792bf4284e690abb62411adb24016e97233cb636e4855","source":{"kind":"arxiv","id":"1804.03862","version":1},"attestation_state":"computed","paper":{"title":"Combinatorics of explicit substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.LO","authors_text":"Maciej Bendkowski, Pierre Lescanne","submitted_at":"2018-04-11T08:13:14Z","abstract_excerpt":"$\\lambda\\upsilon$ is an extension of the $\\lambda$-calculus which internalises the calculus of substitutions. In the current paper, we investigate the combinatorial properties of $\\lambda\\upsilon$ focusing on the quantitative aspects of substitution resolution. We exhibit an unexpected correspondence between the counting sequence for $\\lambda\\upsilon$-terms and famous Catalan numbers. As a by-product, we establish effective sampling schemes for random $\\lambda\\upsilon$-terms. We show that typical $\\lambda\\upsilon$-terms represent, in a strong sense, non-strict computations in the classic $\\lam"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.03862","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-04-11T08:13:14Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"69fffa1883cd91dd92b3ea0b68c84a8013406d58e8b870491403503c21c17167","abstract_canon_sha256":"39e9226a2a7a419800f32e1a226b0d950a728accb88c319c16c14d412166a820"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:42.842097Z","signature_b64":"G504Og+y/YMw9TASa24YMYZuV+yBNh8GtgOeHGD7/DEcrtsjFYWFtcLCGsTgfKfxpl4M9T6IdM3ChC8vJfDEDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b241e2e125400e879d0792bf4284e690abb62411adb24016e97233cb636e4855","last_reissued_at":"2026-05-18T00:18:42.841255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:42.841255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorics of explicit substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.LO","authors_text":"Maciej Bendkowski, Pierre Lescanne","submitted_at":"2018-04-11T08:13:14Z","abstract_excerpt":"$\\lambda\\upsilon$ is an extension of the $\\lambda$-calculus which internalises the calculus of substitutions. In the current paper, we investigate the combinatorial properties of $\\lambda\\upsilon$ focusing on the quantitative aspects of substitution resolution. We exhibit an unexpected correspondence between the counting sequence for $\\lambda\\upsilon$-terms and famous Catalan numbers. As a by-product, we establish effective sampling schemes for random $\\lambda\\upsilon$-terms. We show that typical $\\lambda\\upsilon$-terms represent, in a strong sense, non-strict computations in the classic $\\lam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03862","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":"1804.03862","created_at":"2026-05-18T00:18:42.841367+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.03862v1","created_at":"2026-05-18T00:18:42.841367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03862","created_at":"2026-05-18T00:18:42.841367+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJA6FYJFIAHI","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJA6FYJFIAHIPHIH","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJA6FYJF","created_at":"2026-05-18T12:32:59.047623+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/WJA6FYJFIAHIPHIHSK7UFBHGSC","json":"https://pith.science/pith/WJA6FYJFIAHIPHIHSK7UFBHGSC.json","graph_json":"https://pith.science/api/pith-number/WJA6FYJFIAHIPHIHSK7UFBHGSC/graph.json","events_json":"https://pith.science/api/pith-number/WJA6FYJFIAHIPHIHSK7UFBHGSC/events.json","paper":"https://pith.science/paper/WJA6FYJF"},"agent_actions":{"view_html":"https://pith.science/pith/WJA6FYJFIAHIPHIHSK7UFBHGSC","download_json":"https://pith.science/pith/WJA6FYJFIAHIPHIHSK7UFBHGSC.json","view_paper":"https://pith.science/paper/WJA6FYJF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.03862&json=true","fetch_graph":"https://pith.science/api/pith-number/WJA6FYJFIAHIPHIHSK7UFBHGSC/graph.json","fetch_events":"https://pith.science/api/pith-number/WJA6FYJFIAHIPHIHSK7UFBHGSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJA6FYJFIAHIPHIHSK7UFBHGSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJA6FYJFIAHIPHIHSK7UFBHGSC/action/storage_attestation","attest_author":"https://pith.science/pith/WJA6FYJFIAHIPHIHSK7UFBHGSC/action/author_attestation","sign_citation":"https://pith.science/pith/WJA6FYJFIAHIPHIHSK7UFBHGSC/action/citation_signature","submit_replication":"https://pith.science/pith/WJA6FYJFIAHIPHIHSK7UFBHGSC/action/replication_record"}},"created_at":"2026-05-18T00:18:42.841367+00:00","updated_at":"2026-05-18T00:18:42.841367+00:00"}