| Summary: | We use an up-to-date compilation of Tully–Fisher data to search for transitions in the evolution of the Tully–Fisher relation. Using an up-to-date data compilation, we find hints at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>≈</mo><mn>3</mn><mi>σ</mi></mrow></semantics></math></inline-formula> level for a transition at critical distances <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>D</mi><mi>c</mi></msub><mo>≃</mo><mn>9</mn></mrow></semantics></math></inline-formula> Mpc and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>D</mi><mi>c</mi></msub><mo>≃</mo><mn>17</mn></mrow></semantics></math></inline-formula> Mpc. We split the full sample in two subsamples, according to the measured galaxy distance with respect to splitting distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>c</mi></msub></semantics></math></inline-formula>, and identify the likelihood of the best-fit slope and intercept of one sample with respect to the best-fit corresponding values of the other sample. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>D</mi><mi>c</mi></msub><mo>≃</mo><mn>9</mn></mrow></semantics></math></inline-formula> Mpc and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>D</mi><mi>c</mi></msub><mo>≃</mo><mn>17</mn></mrow></semantics></math></inline-formula> Mpc, we find a tension between the two subsamples at a level of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msup><mi>χ</mi><mn>2</mn></msup><mo>></mo><mn>17</mn><mspace width="0.277778em"></mspace><mrow><mo>(</mo><mn>3.5</mn><mi>σ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Using Monte Carlo simulations, we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances and is unlikely in the context of a homogeneous dataset constructed using the Tully–Fisher relation. If the tension is interpreted as being due to a gravitational strength transition, it would imply a shift in the effective gravitational constant to lower values for distances larger than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>c</mi></msub></semantics></math></inline-formula> by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><mo>Δ</mo><mi>G</mi></mrow><mi>G</mi></mfrac><mo>≃</mo><mo>−</mo><mn>0.1</mn></mrow></semantics></math></inline-formula>. Such a shift is of the anticipated sign and magnitude but at a somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mfrac><mrow><mo>Δ</mo><mi>G</mi></mrow><mi>G</mi></mfrac><mo>≃</mo><mo>−</mo><mn>0.1</mn></mrow></semantics></math></inline-formula> at the transition redshift of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>z</mi><mi>t</mi></msub><mo>≲</mo><mn>0.01</mn></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>D</mi><mi>c</mi></msub><mo>≲</mo><mn>40</mn></mrow></semantics></math></inline-formula> Mpc)).
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