{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7M35H5GMM3564Y6NJUYXHFGCVU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"58440a8aa4d3503a890f8f5ef66a5e5186a38521d24029a4a6ca46c2029e09ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2011-02-03T18:54:30Z","title_canon_sha256":"fad1a1429e02c0a70d3f7385ff20cd01fe55c525bbcdd0d74c497bf9f51fe3a5"},"schema_version":"1.0","source":{"id":"1102.0749","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0749","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0749v3","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0749","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"pith_short_12","alias_value":"7M35H5GMM356","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7M35H5GMM3564Y6N","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7M35H5GM","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:bdf9a9e072c67c9987f1d3c8c55b366511777b586697133ab8b5118c95d299dd","target":"graph","created_at":"2026-05-18T03:59:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while the latter uses equalities. When given by rewrites, algebraic lambda-calculi are not confluent unless further restrictions are added. We provide a type system for the linear-algebraic lambda-calculus enforcing strong normalisation, which gives back confluence. The type system allows an abstract interpretation in System F.","authors_text":"Alejandro D\\'iaz-Caro, Mauro Jaskelioff, Pablo Buiras","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2011-02-03T18:54:30Z","title":"Confluence via strong normalisation in an algebraic \\lambda-calculus with rewriting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0749","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5feb48c7ff1675bc8910840c244713d63269259a40e25926a3a03f285e36b63f","target":"record","created_at":"2026-05-18T03:59:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"58440a8aa4d3503a890f8f5ef66a5e5186a38521d24029a4a6ca46c2029e09ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2011-02-03T18:54:30Z","title_canon_sha256":"fad1a1429e02c0a70d3f7385ff20cd01fe55c525bbcdd0d74c497bf9f51fe3a5"},"schema_version":"1.0","source":{"id":"1102.0749","kind":"arxiv","version":3}},"canonical_sha256":"fb37d3f4cc66fbee63cd4d317394c2ad27a1d1b67618d0458fcafab38e8fd322","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb37d3f4cc66fbee63cd4d317394c2ad27a1d1b67618d0458fcafab38e8fd322","first_computed_at":"2026-05-18T03:59:12.394962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:12.394962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2D6AQrcrM/eAZP0woT1N08k9h99BljfPrxFe1DXo6eZ2y8lEHIh016gNt3gBDe/YjBPv6+NrdBVvVRyFQA2FCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:12.395446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0749","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5feb48c7ff1675bc8910840c244713d63269259a40e25926a3a03f285e36b63f","sha256:bdf9a9e072c67c9987f1d3c8c55b366511777b586697133ab8b5118c95d299dd"],"state_sha256":"f867c1393bb8019485f436b777a60c8e715778fc21d2add38b63cdc87cdc3b0c"}