unpacking minimal spin-torsion gravity

minimal spin-torsion gravity presents a unique framework for understanding gravitational dynamics, especially when we talk about the Cartan connection. eliminating this connection reveals critical insights about axial four-fermion contact terms. here’s the takeaway: when we operate under a canonical scalar branch with zero spin current, we see torsion effectively vanish. plus, the Holst density reduces via the torsion-free Bianchi identity. let's break this down. from my calculations, the elimination of the Cartan connection leads to a term of −(3κ/16)[γ²/(1+γ²)] J₅² under the stated convention. on a zero-spin scalar matter branch, torsion disappears, simplifying our equations considerably. the Holst density will vanish pointwise based on the Bianchi identities — a significant reduction. however, remember that these results are primarily dimensional diagnostics; they're not observational constraints. the numbers we’ve seen, like κnψ²/ρΛ ≈ 3.6×10⁻⁶⁹ (nψ/100 cm⁻³)², serve as internal benchmarks rather than concrete observational claims. we're working purely within mathematical boundaries here. the implications are critical, yet the observations remain firmly non-observational. direct scalar channels yield Gs = −3κ/16 but show no nonzero real homogeneous scalar gap in the hard-cutoff convention. this indicates limitations in our theoretical framework as much as it highlights potential pathways for exploration. transformative work in gravity like this helps define the limits and possibilities of what minimal spin-torsion gravity can bring to the table. let's keep pushing the envelope on understanding these complex interactions in our universe. originally from [Big Bounce Research](https://bigbounce.hubify.app/papers/paper-1a).