Papers · William Alexander Aldred

Creation Events Are Nieh–Yan Charged: The Charge Law Q = b·L, the Stretch Bound, and Equilibrium Collapse in Einstein–Cartan Gravity

by William Alexander Aldred — Independent Researcher

Abstract

In Einstein–Cartan gravity, a static network of torsion defects carries no Nieh–Yan charge. That result — the legs theorem, established in the companion work on the static defect sector — is exact: the Nieh–Yan density vanishes identically on every static dislocation and disclination network, and the total Nieh–Yan charge of an eternal piercing is zero by cancellation between time caps. This paper asks what happens when the defect sector is allowed to be dynamical. The answer is the first nonzero Nieh–Yan quantity of the programme from which this work arises.

A defect-creation event is Nieh–Yan charged. Exact wedge arithmetic gives zero for the static piece alone and a nonzero result, 0.3333 in the units of the computation, when torsion is given its event form — a spatial piece together with a time-legged piece — with the whole content isolated in the static×dynamic cross term, at 0.1667. By Stokes' theorem, with no modelling freedom, the charge of the event is exactly

Qₑvₑnt = b · Lcrₑₐtₑd,

where b is the Burgers flux of the piercing created and Lcrₑₐtₑd is the length of line the event creates. Both routes to an event — Burgers flux ramping from 0 to b at fixed length, and length growing from 0 to L at fixed flux — return the same product, checked numerically to 1.000000 in each case.

That exactness does not make the event a quantum: the charge is a product of two frame-free quantities — b, unfixed without a decree, and Lcrₑₐtₑd, set by where the segment's far end lands. Varying only frame-open choices runs Q/(4ℓ_P²) from 0.25 to 7.106153×10⁵². The familiar line returns by construction: Q = ℓ_T² gives qpₒst = 5.276535×10³⁶, the static work's postulated value, because it is the same decree counted twice.

The coarse-grained sector does obey a real bound. Writing the winding density as w = n· b, with n the piercing density, the winding obeys w ≤ 𝒯_A, where 𝒯_A is the Aldred twist. The bound is stated with the flag carried in the source computation: it is a bound on the coarse-grained mean only, obtained by extending a bulk bound to a defect mean. It caps a product, not a count.

No law in the frame makes an event fire at that bound. Einstein–Cartan gravity contains no defect-nucleation term and no constitutive relief law, the vacuum spin density in the frame is zero, and the only event rate written in the source computation, Γ = c𝒯_A³ = 7.322810×10⁵⁶ m⁻²,s⁻¹, is postulated, not derived — a flag this paper carries wherever that rate appears.

Finally, at equilibrium the dynamical sector collapses onto the static one. Creation balances annihilation, the net axial non-conservation vanishes, and the net Nieh–Yan charge is exactly zero. Dynamics adds maintenance, never number. The mechanism class — events, not networks — survives. The machinery that would turn it into a derivation — a driver that winds, a law that fires, and a value for b — is what the frame lacks. Those negative statements are results of this paper, not qualifications upon it.

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 (this page)
• 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