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Manuscript I@2 · I.tex · figure · 85631fa7

Continuation residual test

Born laws and destructive projective residuals › Residual identification by future tests · lines 1845–1870

I@2#fig:residual-test

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ψ=∑j∣j⟩S∣ξj⟩B,pκ=∥ξκ∥2>0,φκ=ξκ/pκ\psi=\sum_j|j\rangle_S|\xi_j\rangle_B,\quad p_\kappa=\|\xi_\kappa\|^2>0,\quad \varphi_\kappa=\xi_\kappa/\sqrt{p_\kappa}
Source
Enter on SS
κ\kappa
unknown residual uκu_\kappa on BB
fixed VV on BB
Enter
λ\lambda
pκ PVuκB(λ)p_\kappa\,\mathsf P^B_{Vu_\kappa}(\lambda)
Deferred
copy SS to fresh RR
same VV on BB
read BB, then RR
return SS
∣⟨λ∣V∣ξκ⟩∣2|\langle\lambda|V|\xi_\kappa\rangle|^2
The record equation equates the joint weights. VV is not controlled by κ\kappa.
Vφκ=∣0∣B∣⟩,∣⟨0∣B∣∣V∣uκ⟩∣2=1⟹uκ≐φκV\varphi_\kappa=|0^{|B|}\rangle,\qquad |\langle 0^{|B|}|V|u_\kappa\rangle|^2=1\Longrightarrow u_\kappa\doteq\varphi_\kappa

A separately chosen experiment for each fixed positive branch.

Residual identification uses the outcome theorem already proved, not the concrete update rule. The branch-specific choice of test is external to the experiment's record-independent continuation.

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