λEnter Calculus CompanionRegistered manuscripts, kept distinct

Manuscript V@1 · V.tex · figure · e7ddf37d

Cubic witness away from transfers

Contrast: the Newton–wave cubic form › A fully symmetrized regular-region witness · lines 3718–3754

V@1#fig:cubic-degree-witness

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metricscalarrepresented quantumdefect / unresolvedsupport / scope
Regular three-creation region
p1=p2=p3=p∗≠0\mathbf p_1=\mathbf p_2=\mathbf p_3=\mathbf p_*\neq 0Every pair transfer is 2p∗≠02\mathbf p_*\neq 0. A small symmetric compact neighborhood avoids all three transfer sets.
χ3=βKf+++∥βKf+++∥2\chi_3=\frac{\beta K_f^{+++}}{\|\beta K_f^{+++}\|_2}Cf(3)(χ3,Ω)>0\mathcal C_f^{(3)}(\chi_3,\Omega)>0
Sector separation
Ψ±=(Ω±εχ3)/1+ε2\Psi_\pm=(\Omega\pm\varepsilon\chi_3)/\sqrt{1+\varepsilon^2}
No vacuum-to-three-particle connection for degree at most two.
cubic connectionΔ⟨Cf(3)⟩=4ε1+ε2Cf(3)(χ3,Ω)>0\Delta\langle\mathcal C_f^{(3)}\rangle=\frac{4\varepsilon}{1+\varepsilon^2}\mathcal C_f^{(3)}(\chi_3,\Omega)>0for ε>0\varepsilon>0

Analytic form witness away from transfers. Not a record experiment.

Cubic witness away from transfer singularities. A compact symmetric three-particle wavefunction is selected in a regular region where the three-creation kernel is nonzero. The relative sign in the vacuum–three-particle superpositions is invisible to defined polynomial forms of degree at most two, but produces a nonzero cubic expectation difference.

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