What is the Aldred Limit?
The short answer. The Aldred Limit is the maximum density matter can reach in Einstein–Cartan gravity — the point where the spin of fermionic matter pushes back hard enough to stop gravitational compression: ρA ≈ 1055 g/cm³. Past it, collapse does not end in a singularity; it bounces. The value is the bounce density Kopczyński and Trautman found in 1972–73 — William Alexander Aldred's first paper, The Aldred Limit (DOI 10.5281/zenodo.23485325), derives it bottom-up and pins it, instead of quoting it to an order of magnitude.
In plain words
Einstein–Cartan gravity is Einstein's theory with one addition: matter's spin twists the space it sits in, and that twist carries energy. Squeeze matter hard enough and the spin term grows faster than the squeeze — it opposes compression. There is therefore a density the squeeze cannot pass. That ceiling is the Aldred Limit: not a wall put in by hand, but the place the theory's own arithmetic turns the fall around.
The pinning
The paper derives the bound from a Tolman–Oppenheimer–Volkoff solver verified against the published SLy equation of state, and pins it to a band — 2.4×1054 to 9.7×1054 g/cm³ for neutron matter, depending on the density convention, headline ρA ≈ 1055 g/cm³. Through the Cartan equation the same bound is a torsion bound: 𝒯A ≈ 1.3×1016 m−1. It also shows the incoherent (randomly oriented) spin branch is not a modeling choice but physically forced at bounce conditions.
What is new, and what is not
The density itself is not new, and the paper claims no novelty for it: it is the Kopczyński–Trautman bounce density of 1972–73. What is Aldred's is the bottom-up derivation, the pinning to a band, the forced-branch argument, and the falsifiable claim stated at full size: fermion spin caps compression at ρA — and if the progenitor rotates, the galaxy-spin dipole axis and the CMB Cold Spot direction must coincide. That axis test has had its first catalogue-level run: the registered kill line is not executable at the required precision on today's catalogues, so the rotating extension stands open — neither confirmed nor killed.
The paper: “The Aldred Limit: Pinning the Einstein–Cartan Spin–Density Bound,” published October 20, 2026, 7 pp, DOI 10.5281/zenodo.23485325. It is Paper 1 of a three-paper program on the vacuum-energy problem — the program's summit, the vacuum catastrophe, stands open, and the work continues.