Two Levels on the Bench: The Einstein-Cartan Closure in Condensate Variables, With Its Factor of Two Intact
States paper #233's action-decided Einstein-Cartan closure factor (canonical lambda = 1/16 from the stated action; direct-torsion variant 1/4; halved coupling 1/64) and paper #239's exact factor-of-two discrepancy (house density 9.7178e54 g/cm3 at the declared Bohmer coefficient 1/8 against the canonical 1.9436e55 g/cm3 at 1/16, ratio exactly 2, proven a discrepancy and not a convention) in paper #237's condensate bench variables, the dialect neither #233 nor #239 cites. In bench units ((hbar/2)n)^2 a closure coefficient is a level of the bench surface R = P^2 + (1-P^2)/N, by the exact map L = 4 x coef common to every closure: the house closure sits at level 1/2, the curve #237 already drew, and the canonical closure at level 1/4, a new curve unreachable below filling 4, passing P = 0.4082 at N = 10 and P = 0.4971 at the 260-atom voxel, with large-filling asymptote P = 1/2 against the house curve's 1/sqrt(2). The two curves are disjoint, their ratio is exactly 2, and no bench variable (a count and a dimensionless ratio, neither containing a gravitational quantity) can absorb the factor: the bench closure inherits the discrepancy, not a convention. All three parents are gated digit-for-digit first, with #239's exact-gas crossing carried under its standing register flag (5.0625 in print, 5.0624 recomputed from its printed anchor; no verdict rests on the fourth decimal). Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.
Authors
- William Alexander Aldred
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-03
- DOI
- https://doi.org/10.5281/zenodo.23936731
- Primary Topic
- Relativity and Gravitational Theory
- Type
- preprint