Papers · William Alexander Aldred

The Aldred Limit: Pinning the Einstein–Cartan Spin–Density Bound — A bottom-up derivation, a prescription verdict, and a falsifiable claim

by William Alexander Aldred — Independent Researcher

Abstract

In Einstein–Cartan (EC) gravity, the spin of fermionic matter sources spacetime torsion, and eliminating torsion through the Cartan equation produces an effective energy density ρ_eff = ρ − κ²⟨S²⟩ in which the spin term opposes compression. We derive the resulting density bound bottom-up, starting from a Tolman–Oppenheimer–Volkoff solver verified against the published SLy equation of state, and we pin the bound rather than quote it to an order of magnitude: under the incoherent (randomly oriented) spin prescription of Böhmer et al., the bound is ρ_A = ρ_Pl (m/m_Pl)²/(8π·coef), which for neutron matter gives a band 2.4×10^54–9.7×10^54 g cm⁻³ depending on the density convention adopted, with headline value ρ_A ≈ 10^55 g cm⁻³. This is the Kopczyński–Trautman bounce density of 1972–73; it is not new, and we claim no novelty for the bound itself.

What is established here is (i) the bottom-up derivation and pinning, (ii) a numerical argument, at the level of the channel estimates of Section 3.2, that the incoherent spin branch is not a modeling choice but is physically forced at bounce conditions, (iii) the equivalence of the density bound with a torsion (“twist”) bound T_A ≈ 1.3×10^16 m⁻¹ through the Cartan equation, and (iv) an exact analysis of the author's earlier entropy-form saturation ansatz against the EC effective density, which fails as a map at the first correction term but calibrates to ρ_Aldred = ρ_A/2.

The falsifiable claim of this paper is: fermion spin caps gravitational compression at ρ_A ≈ 10^55 g cm⁻³ (equivalently T_A ≈ 10^16 m⁻¹), replacing singularities with bounces; and if the progenitor rotates, the galaxy-spin dipole axis and the CMB Cold Spot direction must coincide — a claim that dies to any consistent counterexample above ρ_A, or to the axis failing to coincide with the Cold Spot at catalogue precision. The axis half of that claim has had its first catalogue-level test, reported in Section 7: on the largest public catalogues the registered kill line is not executable at the required precision, and the rotating extension stands neither confirmed nor killed.

Program note

This paper is part of a three-paper program on the vacuum-energy problem in Einstein–Cartan gravity. It is continued by “Two Bounds and an Integration Constant” (DOI 10.5281/zenodo.23485358), whose supplementary memos are at DOI 10.5281/zenodo.23485410, and by “The Constant Changes Address” (DOI 10.5281/zenodo.23610897), an obstruction result that claims no solution to the cosmological constant problem.

The program

• The Aldred Limit (this page)
• Two Bounds and an Integration Constant
• Supplementary Memos for “Two Bounds and an Integration Constant”
• The Constant Changes Address
• The Crossing Charges Nothing
• No Derivation in the Frame
• Static Defects Carry No Nieh–Yan Charge
• Creation Events Are Nieh–Yan Charged
• There Is No Twisted Vacuum
• Propagation Is Not Enough
• Axiom H
• One Flaw, Two Residues
• The ε_eff Turnover
• The Generation Map Has a Fixed Point
• Three Fences Any Λ Mechanism Must Pass