Papers · William Alexander Aldred

Propagation Is Not Enough: The Minimal Propagating-Torsion Extension Has No Vacuum Twist

by William Alexander Aldred — Independent Researcher

Abstract

The minimal propagating-torsion extension of Einstein–Cartan gravity — Einstein–Cartan gravity plus a kinetic term for the axial torsion, with one dimensionless coefficient κ geq 0 and κ = 0 recovering Einstein–Cartan gravity exactly — is executed against the two questions posed by the campaign's first-ranked re-opener. The re-opener asks for a structure beneath Einstein–Cartan gravity in which torsion propagates, and its deliverable is two-part: (a) a vacuum solution with background torsion 𝒯bg ≠ 0 at spin density σ = 0, and (b) then the count, against the specification fixed in GAP8. The minimal member is the front door of that re-opener: if propagation alone freed the vacuum twist, it would free it here first.

It does not. The extension is closed by a new forcing step, distinct from the algebraicity that closes Einstein–Cartan gravity itself. With the record conventions — torsion energy density ρ𝒯 = M̄_P²𝒯² and potential V(𝒯) = +M̄_P²𝒯² — the curvature of the potential at the origin is

V''(0) = +2M̄_P² > 0

at every κ, with the numerical value V''(0) = 3.046284×10⁶⁸ in the units of the computation. The unique minimum of the potential is at 𝒯bg/𝒯_A = 0.000000 for every κ tested, including κ = 0, κ = 1, κ = 8.397867×10³⁵, and κ = 10⁴⁰. The extension's vacuum twist is therefore nonexistent. The kinetic term gives the twist a way to travel; the potential — torsion as positive energy cost, which is the Aldred Limit's own content — holds it at zero. Deliverable (a) fails for the minimal member, by the sign.

The toll 3ΩLₐmbdₐ = 2.055 is untouched. Propagation at the Aldred scale costs κ* = (M̄_P/𝒯_A)² = 8.397867×10³⁵ = qpₒst/(2π), where qpₒst = 5.276535×10³⁶. That value is an admission price at elasticity 1 — a dial setting, not an output. Every apparent contact between the extension and the toll is of the same kind: a solved-for dial, exhibited as a match under the pre-registered kill K-dial, including the ratio of two such settings, (2.055/2)² = 1.055756. The extension's complete dimensionless output set is 0, 1, rationals, dials. No new pure number is produced.

The durable product is a sharpened specification. A deeper member of the propagating species must satisfy, as theorems with elasticity 0: (S) a sign mechanism, V''(0) < 0 at σ = 0 in vacuum, with the crossing identity ρ_A = M̄_P²𝒯_A² intact where spin density is high; (P) a pinning, the condensate 𝒯min/𝒯_A a pure number of the structure at elasticity 0 to all its couplings; and (b) then the count, per GAP8's specification, computed and never imported. Four wave-10 doors were specced against that specification and fired; their verdicts are folded into §8: the b(σ) door closed at the gate, the sign-mechanism class searched and empty, the parent-class census specced behind literature gates, and the scar-form decision delivered unadopted. The verdict of the computation is stated without qualification in §9: NOT SOLVED. The bar did not move. The run's inputs were ℏ, c, G, and the record 𝒯_A only.

Keywords: Einstein–Cartan gravity; torsion; propagating torsion; vacuum energy; Aldred Limit.

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 (this page)
• Axiom H
• One Flaw, Two Residues
• The ε_eff Turnover
• The Generation Map Has a Fixed Point
• Three Fences Any Λ Mechanism Must Pass