{"paper":{"title":"Open full-metric formation and local marked first-order asymptotic moduli of FIK blowdown singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Henry Shin","submitted_at":"2026-08-09T07:10:33Z","abstract_excerpt":"We prove that the Feldman--Ilmanen--Knopf (FIK) blowdown singularity has a nonempty open nonlinear formation basin in the full space of smooth Riemannian metrics and, on a smaller neighborhood, local marked first-order asymptotic moduli. Given a closed connected oriented Riemannian four-manifold, an implantation point, and a positive time bound, its oriented blow-up admits a relatively $C^{2,\\alpha}$-open set of smooth metrics whose Ricci flows form, before that time, a localized FIK singularity with global Type-I curvature control. No symmetry, K\\\"ahler condition, or finite-dimensional tuning"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08533","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/2608.08533/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"}