{"paper":{"title":"On real log canonical thresholds","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Morihiko Saito","submitted_at":"2007-07-16T12:14:06Z","abstract_excerpt":"We introduce real log canonical threshold and real jumping numbers for real algebraic functions. A real jumping number is a root of the $b$-function up to a sign if its difference with the minimal one is less than 1. The real log canonical threshold, which is the minimal real jumping number, coincides up to a sign with the maximal pole of the distribution defined by the complex power of the absolute value of the function. However, this number may be greater than 1 if the codimension of the real zero locus of the function is greater than 1. So it does not necessarily coincide with the maximal r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2308","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0707.2308/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}