The manuscript addresses a methodological question in the inverse-problem reconstruction of optical geometry from supernova distance–redshift data. In a static, spherically symmetric reference geometry, one may ask how the leading Taylor coefficients of an effective optical potential Ψ (r) relate to the observer-side cosmographic parameters H₀, q₀, j₀. The mapping is structurally non-trivial: it must run through the data-side luminosity-distance series dL (z), requiring both an inversion of z (r) to r (z) and a multiplication by (1+z) ². A naive identification of z (r) Taylor coefficients with cosmographic parameters does not reproduce that expansion, and the resulting numerical disagreement is not perturbative at representative coefficient values.
Eric Levin (Mon,) studied this question.