{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HNF77Y6NI7G3LUMN7SJXPWM3GS","short_pith_number":"pith:HNF77Y6N","schema_version":"1.0","canonical_sha256":"3b4bffe3cd47cdb5d18dfc9377d99b349f5144c40f82c768aa759401ccd050f9","source":{"kind":"arxiv","id":"1303.7329","version":1},"attestation_state":"computed","paper":{"title":"Minimal lambda-theories by ultraproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alberto Carraro (PPS, Antonino Salibra (DAIS, Antonio Bucciarelli (PPS, Universit\\`a Ca' Foscari Venezia), Universit\\'e Paris Diderot)","submitted_at":"2013-03-29T09:01:59Z","abstract_excerpt":"A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating all the unsolvable terms). A related question is whether, given a class of lambda models, there is a minimal lambda-theory represented by it. In this paper, we give a general tool to answer positively to this question and we apply it to a wide class of webbed models: the i-models. The method then applies also to graph models, Krivine models, coherent models "},"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":"1303.7329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2013-03-29T09:01:59Z","cross_cats_sorted":[],"title_canon_sha256":"997774d2a0846d3b86c14980dff85bb5e430243a02a2157fe7e6361de03beb3d","abstract_canon_sha256":"32823d730f3b4020e47cd888fd1dcf6f485352fe6e6a458c10da0da4155e445f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:28.833381Z","signature_b64":"HnZWOdLUNR5uESSnggQdxEgdRxd+ZQHt8JDqr/BmwyatYQ1GzmmsZ3IEqJn5KW53BjEV1vzxzHvXZ4umg8+mBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b4bffe3cd47cdb5d18dfc9377d99b349f5144c40f82c768aa759401ccd050f9","last_reissued_at":"2026-05-18T03:29:28.832635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:28.832635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal lambda-theories by ultraproducts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alberto Carraro (PPS, Antonino Salibra (DAIS, Antonio Bucciarelli (PPS, Universit\\`a Ca' Foscari Venezia), Universit\\'e Paris Diderot)","submitted_at":"2013-03-29T09:01:59Z","abstract_excerpt":"A longstanding open problem in lambda calculus is whether there exist continuous models of the untyped lambda calculus whose theory is exactly the least lambda-theory lambda-beta or the least sensible lambda-theory H (generated by equating all the unsolvable terms). A related question is whether, given a class of lambda models, there is a minimal lambda-theory represented by it. In this paper, we give a general tool to answer positively to this question and we apply it to a wide class of webbed models: the i-models. The method then applies also to graph models, Krivine models, coherent models "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7329","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":"1303.7329","created_at":"2026-05-18T03:29:28.832746+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.7329v1","created_at":"2026-05-18T03:29:28.832746+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7329","created_at":"2026-05-18T03:29:28.832746+00:00"},{"alias_kind":"pith_short_12","alias_value":"HNF77Y6NI7G3","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HNF77Y6NI7G3LUMN","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HNF77Y6N","created_at":"2026-05-18T12:27:46.883200+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/HNF77Y6NI7G3LUMN7SJXPWM3GS","json":"https://pith.science/pith/HNF77Y6NI7G3LUMN7SJXPWM3GS.json","graph_json":"https://pith.science/api/pith-number/HNF77Y6NI7G3LUMN7SJXPWM3GS/graph.json","events_json":"https://pith.science/api/pith-number/HNF77Y6NI7G3LUMN7SJXPWM3GS/events.json","paper":"https://pith.science/paper/HNF77Y6N"},"agent_actions":{"view_html":"https://pith.science/pith/HNF77Y6NI7G3LUMN7SJXPWM3GS","download_json":"https://pith.science/pith/HNF77Y6NI7G3LUMN7SJXPWM3GS.json","view_paper":"https://pith.science/paper/HNF77Y6N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.7329&json=true","fetch_graph":"https://pith.science/api/pith-number/HNF77Y6NI7G3LUMN7SJXPWM3GS/graph.json","fetch_events":"https://pith.science/api/pith-number/HNF77Y6NI7G3LUMN7SJXPWM3GS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HNF77Y6NI7G3LUMN7SJXPWM3GS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HNF77Y6NI7G3LUMN7SJXPWM3GS/action/storage_attestation","attest_author":"https://pith.science/pith/HNF77Y6NI7G3LUMN7SJXPWM3GS/action/author_attestation","sign_citation":"https://pith.science/pith/HNF77Y6NI7G3LUMN7SJXPWM3GS/action/citation_signature","submit_replication":"https://pith.science/pith/HNF77Y6NI7G3LUMN7SJXPWM3GS/action/replication_record"}},"created_at":"2026-05-18T03:29:28.832746+00:00","updated_at":"2026-05-18T03:29:28.832746+00:00"}