A Chemo-Structural Evolutionary Sequence of Disc Galaxies from BTFR Residuals and Baryonic Surface Density: Observational Constraints from SPARC, LittleThings, and MaNGA with TNG100 Progenitor Validation

We present a multi-diagnostic study of the baryonic Tully-Fisher relation (BTFR) and baryonic surface density (Σbar) in a combined sample of N=1172 disc galaxies drawn from SPARC (165 galaxies), LittleThings (25 galaxies), and MaNGA-HI (982 galaxies). We measure the extended BTFR coecient log Vflat = α logMbar + β logRd + c, finding β = −0.136 (IC90% −0.198, −0.072) in the discdominated regime (fgas < 0.627, N=696). On SPARC alone in Rég. D (N=147, true Vflat from extendedrotation curves) we recover β = −0.176 (IC90% −0.243, −0.101), demonstrating that the signal is not an artefact of the MaNGA line-width proxy. In TNG100, |β| decreases monotonically from z=2 to z=0 following |β| ∝ Σ0.21 bar (ρ = +1.000), consistent with inside-out disc growth reducing the kinematic imprint of the initial baryonic compactness. Applying a Gaussian Mixture Model (GMM, k=4 selected by BIC) to (logMbar, log Σbar, fgas), we identify three disc families Σ-A, Σ-B, Σ-C that exhibit eight monotonic sequences (ρ = ±1.000) in variables withheld from the classification: Dn(4000), ZOH, g−r, ΔsSFRMS, Sérsic index n, early-type fraction, stellar metallicity gradient ∇Z⋆ LW, and mass-weighted age gradient ∇AgeMW. Cross-validation confirms stability for Dn(4000) and ZOH (ρCV = −0.93 ± 0.18). TNG100 progenitor tracking reveals that galaxies classified as Σ-A, Σ-B, and Σ-C at z=0 are nearly indistinguishable at z≈2 (fgas ≈ 0.70, g−r ≈ 0.25-0.31, 70-73% all classified as Σ-A at z=2; applying fixed z=0 boundaries in TNG100, Σ-A decreases from 74% at z=2 to 14% at z=0), and that their z=0 ordering in Σbar is entirely reversed at z=2: future-Σ-C galaxies are the most compact proto-discs. The Σ-A/B/C sequence therefore encodes dierential inside-out disc growth rates over 10 Gyr, not pre-existing population segregation. A fourth GMM class (Σ-D) contains a composite of dwarf populations - D1 (dwarf irregulars/BCDs, n=0.77, fgas=0.75, ∇AgeMW=−0.23) and D2 (transitional dwarfs, n=1.26, ΔsSFRMS = −0.87 dex) - separated by mass (ΔlogM = 1.03 dex) and by their dominant physical mechanism (internal SF regulation vs. environmental quenching).