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Eddy viscosity (EV) ROMs (e.g., Smagorinsky ROM (S-ROM)) are LES-ROMs whose closure model consists of a diffusion-like operator in which the viscosity depends on the ROM velocity. We propose the Ladyzhenskaya ROM (L-ROM), which is a generalization of the S-ROM. Furthermore, we prove two fundamental numerical analysis results for the new L-ROM and the classical S-ROM: (i) We prove the verifiability of the L-ROM and S-ROM, i.e., that the ROM error is bounded (up to a constant) by the ROM closure error. (ii) We introduce the concept of ROM limit consistency (in a discrete sense), and prove that the L-ROM and S-ROM are limit consistent, i.e., that as the ROM dimension approaches the rank of the snapshot matrix,\n                    <jats:italic>d<\/jats:italic>\n                    , and the ROM lengthscale goes to zero, the ROM solution converges to the\n                    <jats:italic>\u201ctrue solution\"<\/jats:italic>\n                    , i.e., the solution of the\n                    <jats:italic>d<\/jats:italic>\n                    -dimensional ROM. Finally, we illustrate numerically the verifiability and limit consistency of the new L-ROM and S-ROM in two under-resolved convection-dominated problems that display sharp gradients:\n                    <jats:list list-type=\"order\">\n                      <jats:list-item>\n                        <jats:p>the 1D Burgers equation with a small diffusion coefficient; and<\/jats:p>\n                      <\/jats:list-item>\n                      <jats:list-item>\n                        <jats:p>\n                          the 2D lid-driven cavity flow at Reynolds number\n                          <jats:inline-formula>\n                            <jats:alternatives>\n                              <jats:tex-math>$$\\textrm{Re}=15,000$$<\/jats:tex-math>\n                              <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                                <mml:mrow>\n                                  <mml:mtext>Re<\/mml:mtext>\n                                  <mml:mo>=<\/mml:mo>\n                                  <mml:mn>15<\/mml:mn>\n                                  <mml:mo>,<\/mml:mo>\n                                  <mml:mn>000<\/mml:mn>\n                                <\/mml:mrow>\n                              <\/mml:math>\n                            <\/jats:alternatives>\n                          <\/jats:inline-formula>\n                          .\n                        <\/jats:p>\n                      <\/jats:list-item>\n                    <\/jats:list>\n                  <\/jats:p>","DOI":"10.1007\/s10915-025-03106-6","type":"journal-article","created":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T07:36:26Z","timestamp":1762241786000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Verifiability and Limit Consistency of Eddy Viscosity Large Eddy Simulation Reduced Order Models"],"prefix":"10.1007","volume":"105","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5096-2297","authenticated-orcid":false,"given":"Jorge","family":"Reyes","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0003-2388-7580","authenticated-orcid":false,"given":"Ping-Hsuan","family":"Tsai","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1121-1979","authenticated-orcid":false,"given":"Ian","family":"Moore","sequence":"additional","affiliation":[]},{"given":"Honghu","family":"Liu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1437-7362","authenticated-orcid":false,"given":"Traian","family":"Iliescu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,4]]},"reference":[{"key":"3106_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2024.113577","volume":"522","author":"S Agdestein","year":"2025","unstructured":"Agdestein, S., Sanderse, B.: Discretize first, filter next:learning divergence-consistent closure models for large-eddy simulation. 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