All works → Note

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. As of v1N.0.8, the Introduction and Discussion identify the derived contact term with Popławski's spin-spin bounce mechanism (arXiv:1007.0587; arXiv:1102.5667) as an operator identification only (exact as γ→∞) — the paper does not independently establish the sign of pressure at finite γ. As of v1N.0.9, the separate NJL scalar-projection sign (G_s<0, driving the no-condensate closure) has been independently verified rather than merely presumed; see the v1N.0.9 changelog entry.

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 the same operator as Popławski's torsion-bounce mechanism (Hehl–Datta term, exact as γ→∞) — the positive result; the paper does not independently establish the sign of pressure at finite γ (v1N.0.8)
• 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.