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.

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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
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preprint

Two Levels on the Bench: The Einstein-Cartan Closure in Condensate Variables, With Its Factor of Two Intact

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

Two Levels on the Bench: The Einstein-Cartan Closure in Condensate Variables, With Its Factor of Two Intact

William Alexander Aldred
preprint en

Abstract

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.

Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
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Two Levels on the Bench: The Einstein-Cartan Closure in Condensate Variables, With Its Factor of Two Intact — William Alexander Aldred · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS