{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7DZOOT77EODJLH4SGVLXQ56IAU","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":"51ce69248db8a9806a02ce8da9e9657a7cac7f0addfcc9b346cd5c98a5b62575","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-08-30T14:50:32Z","title_canon_sha256":"8d503cdecaecbbc6e2917785a940024fb9966cdafbcf272a9c7f00c03fc53b2c"},"schema_version":"1.0","source":{"id":"1808.10324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10324","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10324v1","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10324","created_at":"2026-05-18T00:06:49Z"},{"alias_kind":"pith_short_12","alias_value":"7DZOOT77EODJ","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7DZOOT77EODJLH4S","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7DZOOT77","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:0c9d612b3152ff75facad618073ed26e824f676960802aa07497d757f6bd5675","target":"graph","created_at":"2026-05-18T00:06:49Z","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":"We present in this paper a universal method of constructing left-continuous triangular norms (l.-c. t-norms). The starting point is an arbitrary, possibly finite, totally ordered monoid fulfilling the conditions that are characteristic for l.-c. t-norms: commutativity, negativity, and quanticity. We show that, under suitable conditions, we can extend this structure by substituting each element for a real interval. The process can be iterated and if the final structure obtained in this way is order-isomorphic to a closed real interval, its monoidal operation can, up to isomorphism, be identifie","authors_text":"Thomas Vetterlein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-08-30T14:50:32Z","title":"Real coextensions as a tool for constructing triangular norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10324","kind":"arxiv","version":1},"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":"sha256:5556fcf2c8be855adab73286b6cc4ca5e40f54b398bcef126c763a2cb42a5a58","target":"record","created_at":"2026-05-18T00:06:49Z","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":"51ce69248db8a9806a02ce8da9e9657a7cac7f0addfcc9b346cd5c98a5b62575","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-08-30T14:50:32Z","title_canon_sha256":"8d503cdecaecbbc6e2917785a940024fb9966cdafbcf272a9c7f00c03fc53b2c"},"schema_version":"1.0","source":{"id":"1808.10324","kind":"arxiv","version":1}},"canonical_sha256":"f8f2e74fff2386959f9235577877c80537a44d977db74e5fee6c349e6abfb682","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8f2e74fff2386959f9235577877c80537a44d977db74e5fee6c349e6abfb682","first_computed_at":"2026-05-18T00:06:49.140197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:49.140197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hmpMD2IIggPByRiGzcEL5tajCiX+YJ4LHrIfrEU4SrDRdeXrrBuP+SSdpuFbb9iobwsm7JwtRe8GaII5/GZQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:49.140897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.10324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5556fcf2c8be855adab73286b6cc4ca5e40f54b398bcef126c763a2cb42a5a58","sha256:0c9d612b3152ff75facad618073ed26e824f676960802aa07497d757f6bd5675"],"state_sha256":"ecb54da9e3c48af367fc7b146d99389cae52a39b2595a0d9635a25f22e02eac9"}