{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IOCQNNVFV3FAR22H3LK34GUE5L","short_pith_number":"pith:IOCQNNVF","schema_version":"1.0","canonical_sha256":"438506b6a5aeca08eb47dad5be1a84eae8be91a9b67a3442cf577a1bb1203843","source":{"kind":"arxiv","id":"1609.07593","version":2},"attestation_state":"computed","paper":{"title":"Combinatorics of $\\lambda$-terms: a natural approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.LO"],"primary_cat":"cs.LO","authors_text":"Katarzyna Grygiel, Maciej Bendkowski, Marek Zaionc, Pierre Lescanne","submitted_at":"2016-09-24T09:50:25Z","abstract_excerpt":"We consider combinatorial aspects of $\\lambda$-terms in the model based on de Bruijn indices where each building constructor is of size one. Surprisingly, the counting sequence for $\\lambda$-terms corresponds also to two families of binary trees, namely black-white trees and zigzag-free ones. We provide a constructive proof of this fact by exhibiting appropriate bijections. Moreover, we identify the sequence of Motzkin numbers with the counting sequence for neutral $\\lambda$-terms, giving a bijection which, in consequence, results in an exact-size sampler for the latter based on the exact-size"},"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":"1609.07593","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-09-24T09:50:25Z","cross_cats_sorted":["cs.DM","math.CO","math.LO"],"title_canon_sha256":"39854c80cf2227f403ce8eaeb43af558427e539a8f1ac7a9431bbc8062aa5356","abstract_canon_sha256":"bbf8c976f9c464bb80941af748fb955fa57a4a7e0d676fe44e6e444cf8c12114"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:20.434230Z","signature_b64":"JbBC5vxNdI8Z8YJ4HFOQE7nJfOPS9GsSSk6hNiRAVkbVawSQ67V/V+Mk++WNtAnTCz58MOwjfkbz9A8B/najCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"438506b6a5aeca08eb47dad5be1a84eae8be91a9b67a3442cf577a1bb1203843","last_reissued_at":"2026-05-18T01:02:20.433569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:20.433569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorics of $\\lambda$-terms: a natural approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO","math.LO"],"primary_cat":"cs.LO","authors_text":"Katarzyna Grygiel, Maciej Bendkowski, Marek Zaionc, Pierre Lescanne","submitted_at":"2016-09-24T09:50:25Z","abstract_excerpt":"We consider combinatorial aspects of $\\lambda$-terms in the model based on de Bruijn indices where each building constructor is of size one. Surprisingly, the counting sequence for $\\lambda$-terms corresponds also to two families of binary trees, namely black-white trees and zigzag-free ones. We provide a constructive proof of this fact by exhibiting appropriate bijections. Moreover, we identify the sequence of Motzkin numbers with the counting sequence for neutral $\\lambda$-terms, giving a bijection which, in consequence, results in an exact-size sampler for the latter based on the exact-size"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07593","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":"1609.07593","created_at":"2026-05-18T01:02:20.433682+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07593v2","created_at":"2026-05-18T01:02:20.433682+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07593","created_at":"2026-05-18T01:02:20.433682+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOCQNNVFV3FA","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOCQNNVFV3FAR22H","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOCQNNVF","created_at":"2026-05-18T12:30:22.444734+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/IOCQNNVFV3FAR22H3LK34GUE5L","json":"https://pith.science/pith/IOCQNNVFV3FAR22H3LK34GUE5L.json","graph_json":"https://pith.science/api/pith-number/IOCQNNVFV3FAR22H3LK34GUE5L/graph.json","events_json":"https://pith.science/api/pith-number/IOCQNNVFV3FAR22H3LK34GUE5L/events.json","paper":"https://pith.science/paper/IOCQNNVF"},"agent_actions":{"view_html":"https://pith.science/pith/IOCQNNVFV3FAR22H3LK34GUE5L","download_json":"https://pith.science/pith/IOCQNNVFV3FAR22H3LK34GUE5L.json","view_paper":"https://pith.science/paper/IOCQNNVF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07593&json=true","fetch_graph":"https://pith.science/api/pith-number/IOCQNNVFV3FAR22H3LK34GUE5L/graph.json","fetch_events":"https://pith.science/api/pith-number/IOCQNNVFV3FAR22H3LK34GUE5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOCQNNVFV3FAR22H3LK34GUE5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOCQNNVFV3FAR22H3LK34GUE5L/action/storage_attestation","attest_author":"https://pith.science/pith/IOCQNNVFV3FAR22H3LK34GUE5L/action/author_attestation","sign_citation":"https://pith.science/pith/IOCQNNVFV3FAR22H3LK34GUE5L/action/citation_signature","submit_replication":"https://pith.science/pith/IOCQNNVFV3FAR22H3LK34GUE5L/action/replication_record"}},"created_at":"2026-05-18T01:02:20.433682+00:00","updated_at":"2026-05-18T01:02:20.433682+00:00"}