Physical premise (IDWT): Physical spacetime has infinitely many ordinary spatial dimensions plus time. Matter occupies up to ten spatial dimensions; all remaining spatial directions are unbound for every particle. Depth counts a pattern's bound spatial involvement within that space. “Observed” and “unobserved” describe an observer's access, not different kinds of dimension. Older projective and nested-geometry calculations below retain their additional hypotheses; they do not establish a separate physical manifold or compactified direction. See spatial meaning and mathematical scope.

Summary: Recoil does not cancel a neutral pair's relative electric dipole, while ordinary proton polarization gives a tiny fixed-radius cancellation benchmark rather than a universal V2 bound.

Recoil and polarization are different currents

For a hydrogen pair with electron charge −e, nuclear charge +e, positions x_e and R_N, and relative coordinate r = x_e−R_N,

dcharge=eRN−exe=−er. d_{\rm charge}=eR_N-ex_e=-er.

This identity is independent of the origin and the two masses. Nuclear recoil changes the relative dynamics and kinetic reduced mass, but is not an opposite dipole that cancels −er. In the center-of-mass frame the two particles move in opposite directions, so their oppositely signed charges produce current contributions in the same direction. This identity applies to arbitrary relative trajectories, not only circles. It is conditional on the ordinary point/centroid charge assignment, not the demo's raw detector map being physical position.

An induced internal nuclear dipole p_N is additional: d_total = −er+p_N. For a general extended V2 source, calculate the two charge-density first moments instead of assigning either centroid from an image. The total net-neutral dipole remains origin independent.

Combined radiation, not separate powers

At leading electric-dipole order in ordinary electromagnetism,

⟨Prad⟩=⟨∣d¨e+p¨N∣2⟩6πϵ0c3. \langle P_{\rm rad}\rangle =\frac{\langle|\ddot d_e+\ddot p_N|^2\rangle}{6\pi\epsilon_0c^3}.

The interference term matters. Adding electron-only and nucleus-only powers would miss it. The formula and approximation are derived in UT Austin's dipole-radiation notes. Cancellation of one harmonic requires the nuclear dipole to have the same amplitude and opposite phase in that channel. It does not eliminate other harmonics, magnetic dipole/electric quadrupole emission, or internal absorption. The source dimensions must also be small compared with the wavelengths retained in the dipole approximation.

The feedback simulation postprocesses this squared acceleration for the combined scalar dipole and compares it with the electron contribution along the same coupled trajectory. For κ = +0.7 the ratios are approximately 5.29, 5.42, and 5.48 for the two-, four-, and six-petal initial preparations; for κ = −0.7 they are 1.90, 1.86, and 1.84. These are dimensionless transient test results, not physical atomic power estimates. Initial nuclear relaxation was not assumed; the induced free oscillation contributes. Reversing the coupling sign changes interference without changing the electron state. The simulation does not include radiative backreaction itself.

A fixed-radius proton benchmark

For an illustrative ordinary electron at fixed distance R from a small proton, its quasistatic field at the proton is E_e = e r̂/(4πε₀R²), whereas its relative dipole is d_e = −eR r̂. Define the nuclear electric polarizability volume α_V by p_N = 4πε₀α_V E_e. In the static-response regime,

pN=−αVR3de,dtotal=(1−αVR3)de. p_N=-\frac{\alpha_V}{R^3}d_e,\qquad d_{\rm total}=\left(1-\frac{\alpha_V}{R^3}\right)d_e.

This is the favorable sign for partial electric-dipole cancellation. As a versioned benchmark, the PDG 2024 proton listing gives α_V = (11.2±0.4)×10⁻⁴ fm³. The NIST CODATA 2022 table gives a₀ = 5.29177210544×10⁴ fm. Their central values give

αVa03=7.56×10−18. \frac{\alpha_V}{a_0^3}=7.56\times10^{-18}.

Thus ordinary static proton polarization is much too small to cancel an ordinary fixed-radius Bohr-scale electron dipole in this benchmark. This is an amplitude ratio, not the size of every nuclear correction to atomic spectroscopy. It is not a prediction that the atomic electron follows a classical Bohr circle. The older versioned polarizability is used solely for reproducibility of an order-of-magnitude comparison, not as a claim of the latest recommended average.

Limits of that estimate

Do not average R^{-3} over the ideal displayed petal center crossings: the detector map has not been identified as electric charge position, and the point-source/nuclear-dipole approximations fail at nuclear overlap. A proper calculation uses the finite source, spatially varying nuclear response, physical frequency dependence, and the electromagnetic propagator. Near nuclear resonances, static polarizability is insufficient and absorption must be included. Magnetic and spin channels have not been bounded here.

If V2 predicts a much stronger response through its extra-dimensional projection, it must derive that enhancement and check it against nuclear response and atomic measurements. The existence of feedback is established within the candidate model; the enhancement and orbit stabilization are not.

nuclear_feedback_checks.py checks the neutral-pair dipole identity, interference algebra, and the versioned fixed-radius numerical ratio, separately from its dimensionless simulations.