Papers · William Alexander Aldred

Two Bounds and an Integration Constant: The Kopczyński–Trautman pin, the de Sitter floor, and the open value problem

by William Alexander Aldred — Independent Researcher

Abstract

Einstein–Cartan (EC) gravity contains a spin-sourced correction to the effective energy density that can halt collapse at a finite density, and a positive cosmological constant imposes a late-time floor on the expansion. This note places those two bounds in a single framework alongside a Henneaux–Teitelboim unimodular sector transplanted into EC, in which the cosmological constant is demoted to an integration constant and, at the classical level, constant vacuum shifts decouple from the traceless field equations. This note does not solve the cosmological constant problem.

For the radiative-instability tier it claims only that decoupling, within this framework and at that level; it organizes the value tier into a three-link chain in which one link is a known result inside a labeled model, one is an identification by construction, and one is open with no calculation yet in existence; and it makes no claim on the coincidence tier. The ultraviolet bound discussed here is the Kopczyński–Trautman bound of 1972–73, not a new result; its sub-Planckian pin is a property of the dust spin-fluid reading used in that literature, and under the self-consistent relativistic ε(n) evaluation the balance retreats to ∼the Planck density. The infrared floor is standard de Sitter asymptotics. No derivation of the floor's value from the bounce state currently exists, and this note makes no empirical prediction distinct from ΛCDM plus the cited EC literature. A numerical near-equality sometimes presented as a two-clock coincidence is shown to be bookkeeping — the same combination of constants up to an exact factor of 8π/3. What remains is a research program with stated kill conditions, not a result.

Program note

This note is the second paper in a three-paper program on the vacuum-energy problem. Its ceiling is the Kopczyński–Trautman pin of “The Aldred Limit” (DOI 10.5281/zenodo.23485325); its supplementary memos (pin calibration, Route E design, two-clock stress test) are deposited at DOI 10.5281/zenodo.23485410; the program's third paper is “The Constant Changes Address” (DOI 10.5281/zenodo.23610897). This note does not solve the cosmological constant problem.

The program

• The Aldred Limit
• Two Bounds and an Integration Constant (this page)
• 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