{"paper":{"title":"When infinity stopped being embarrassing: The doubly infinite series of Pierre Alphonse Laurent and the mathematical rehabilitation of singularities","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"B. Sriraman, N. Karjanto","submitted_at":"2026-06-04T05:33:07Z","abstract_excerpt":"For the better part of a century, isolated singularities were treated as pathological obstructions requiring elaborate avoidance strategies. Pierre Alphonse Laurent (1813--1854), a French military engineer at Le Havre, ended this avoidance in 1843 by extending Cauchy's Taylor-type theorem to doubly connected (annular) domains, producing the doubly infinite power series that now bears his name. Negative-power terms in the expansion encode precise geometric information about the singularity rather than signaling a breakdown of the formalism. Laurent's contribution arrived through an unhappy inst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06542","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06542/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"}