Papers · William Alexander Aldred

One Flaw, Two Residues: The Exhaustion of the Single-Imperfection Conjecture in Einstein–Cartan Cosmology

by William Alexander Aldred — Independent Researcher

Abstract

Einstein–Cartan cosmology with a Henneaux–Teitelboim unimodular sector — Route E, as developed in Two Bounds — contains two numbers it does not explain. At the non-singular bounce known as the Aldred pin sits the baryon asymmetry, η = 6.1×10⁻¹⁰. At the infrared end sits the vacuum ratio, ρ_Λ/ρ_Pl = 1.13×10⁻¹²³, carried as the integration constant Λ_int. This paper states at full strength the framework's most attractive conjecture — Conjecture C: a single dimensionless imperfection ε, seated at the pin, generates both residues by derivation — and reports its complete exhaustion.

The power-law bridge class was already dead: in a 50,000-draw solve the pin drew 1 hit in 200,000 at underived exponents, the signature of numerology. Iteration 1 enumerated every named mechanism with a forced functional form. Gravitational baryogenesis misses by −39.98 dex at the Planck scale and by −2.66 dex at the only nominated non-Planck scale. The Nieh–Yan / axial class is dead in both forms: its coherent form by the pin's incoherent branch, ⟨𝒮^μ⟩ ≡ 0; its anomaly form by ≥18.8 dex, coefficient non-universality, and sphaleron erasure. The flux classes miss the floor by +44.27 dex, are vacuous as a boundary condition, absent as a stepping sector, or miss by +83.91 dex while restating ε_pin in disguise. Exponential suppression undershoots by ~10³⁸ dex. The Hehl–Datta asymmetry overshoots by +8.2 to +9.2 dex behind a conversion sector the framework does not contain, and gives η = 0 in-framework. Coleman / Baum–Hawking quantum selection is killed: its forced output is Λ → 0, not a finite Λℓ_P² = 2.85×10⁻¹²²; it supplies no η; and it imports an ensemble foreign to EC+HT.

Iteration 2 ran the two computations left open, under thresholds registered before either ran. Attack 1 derives the baryogenesis cutoff: integrating out algebraic EC torsion yields only κ²-built contact terms, no derivable (∂_μ𝒯)J^μB−L operator at any non-Planckian scale. The nominated scale ħc𝒯_A = 2.657 GeV is a κ²-dressed background value, 𝒯_A = κ²cs_A, not a coupling. The derived scale, 2.44×10¹⁸–1.22×10¹⁹ GeV, exceeds the pre-registered 0.4 GeV threshold by +18.78 dex; η misses by −37.5 to −38.9 dex even with the true bounce profile, whose peak |Ṙ| = 43.85 GeV³ is 11.7× the estimate it replaces. The η side is empty. Attack 2 tests all eight matching conditions (M1–M8) for the conjugate pair (Λ_int, V₄) across H = 0. All eight are Λ-blind, centred on the exact cancellation of ρ_C in ρₑff + pₑff and on Λ_int being the momentum conjugate to a cyclic coordinate. Matched bounces exist for the whole open interval ρ_C ∈ (−ρ_A/4, +∞), unselected throughout. The floor side is empty.

Conjecture C is dead by exhaustion, at its own kill line, in a stronger form than the line contemplated: no derivation in the framework produces either residue from the pin. The two residues return to being two separate open problems that happen to share a framework. Nothing here touches Tier-1 Route E decoupling, the pin, or any claim in Two Bounds, where the link closed here was labelled open. The fourteen-entry kill log is the deliverable: a conjecture killed by exhaustion is a map of where the answer is not.

Keywords: Einstein–Cartan gravity; Henneaux–Teitelboim gravity; cosmological constant; baryon asymmetry; gravitational baryogenesis; torsion; negative results

The program

• The Aldred Limit
• 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 (this page)
• The ε_eff Turnover
• The Generation Map Has a Fixed Point
• Three Fences Any Λ Mechanism Must Pass