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Note
What Minimal Einstein–Cartan–Holst Torsion Does for the Bounce and Cannot Do for Dark Energy
One closed-line Note: spin-torsion gravity's contact repulsion powers a bounce mechanism, but not dark energy
Abstract
Track B of the 2026-09-02 portfolio restructure (directive R3): P1A's algebraic Cartan elimination (spin-sourced axial contact term, zero-spin scalar branch) merged with P1C's 14-entry structural no-go survey (Route-2/Route-3 amplitude-budget closures, six-member dimension-4 parity-odd operator list) into one Note that states both readings of the same result — what minimal ECH gravity does for the bounce, and what it cannot do for dark energy. The Introduction and Discussion explicitly identify the derived contact term with Popławski's spin-spin repulsion mechanism (arXiv:1007.0587; arXiv:1102.5667).
Result summary
- openMinimal ECH Cartan elimination yields the axial contact term −(3κ/16)[γ²/(1+γ²)]J₅² in the stated convention
- derivedThe derived contact term is identified with Popławski's torsion-bounce spin-spin repulsion mechanism — the positive result
- open14-entry barrier catalog across 7 foundation mechanism classes and 6 observational branches closes four candidate dark-energy routes (R1–R4) — the negative result
- openSix-member dimension-4 parity-odd operator list corrected to a rank-4 spanning/generating list (rank 2 modulo total derivatives), matching the settled theory-audit record
Readiness
0B / 0M / 0m / 0C open
Readiness is publication readiness only — science, evidence, review convergence, packaging, and Houston’s final sign-off. Venue and submission are tracked separately below, and never subtract from this number (directive P).
Publishing
Not part of readiness.
Lineage
Track B · The ECH Note (closed line). This work does not claim beyond its stated target and scope above.