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We focus on lower-main-sequence stars, where other age-dating tools become ineffective. Our age distributions are compared to those derived from asteroseismic and giant samples and solar analogs. We are able to recover gyrochronological ages for old, lower-main-sequence stars, a remarkable improvement over prior work in hotter stars. Under our model assumptions, our ages have a median relative uncertainty of 14%, comparable to the age precision inferred for more massive stars using traditional methods. We investigate trends of Galactic <jats:italic>\u03b1<\/jats:italic>-enhancement with age, finding evidence of a detection threshold between the age of the oldest <jats:italic>\u03b1<\/jats:italic>-poor stars and that of the bulk <jats:italic>\u03b1<\/jats:italic>-rich population. We argue that gyrochronology is an effective tool reaching ages of 10\u201312 Gyr in K and early M dwarfs. 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We estimate a \u223c15% bias in age for cool, <jats:italic>\u03b1<\/jats:italic>-enhanced (+0.4 dex) stars when standard solar-abundance-pattern rotational models are used for age inference, rather than models that appropriately account for <jats:italic>\u03b1<\/jats:italic>-enrichment.<\/jats:p>","DOI":"10.3847\/1538-4357\/ab5c24","type":"journal-article","created":{"date-parts":[[2020,1,7]],"date-time":"2020-01-07T16:48:21Z","timestamp":1578415701000},"page":"43","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":59,"title":["Chemical Evolution in the Milky Way: Rotation-based Ages for APOGEE-Kepler Cool Dwarf Stars"],"prefix":"10.3847","volume":"888","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9879-3904","authenticated-orcid":false,"given":"Zachary R.","family":"Claytor","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4284-8638","authenticated-orcid":false,"given":"Jennifer L. van","family":"Saders","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7195-6542","authenticated-orcid":false,"given":"\u00c2ngela R. 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