Published June 5, 2026 | Version v1

Paper 67B: Neutral Support Spacing in the Dimensionless Gravity Hierarchy Why the Neutron Mass May Set the Holosphere Gravity-Cell Scale

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Paper 67B continues the 67-series by asking why the dimensionless gravity hierarchy uses the neutron mass cubed. Paper 67A identified the dimensionless hierarchy number n_G = 2 M_p pi^3 h c / (G M_n^3) as the proper first target, while keeping clear that the series has not yet derived G. Paper 67B narrows the question: why does M_n^3 appear in the denominator?

The main proposal is the neutral support-spacing hypothesis. In this interpretation, the neutron mass is not chosen merely as a convenient particle scale. It is treated as the candidate mass of the first neutral closed VROS support unit. Its Compton wavelength, lambda_n = h / (M_n c), is then interpreted as the candidate neutral Holosphere support-spacing scale relevant to gravitational source loading.

The hierarchy formula can be factored as G = (h c / M_n^2)(2 pi^3 / n_G)(M_p / M_n). This separates three roles. The factor h c / M_n^2 supplies a natural dimensional coupling at the neutral hadronic scale. The factor 2 pi^3 / n_G supplies the large structural hierarchy suppression. The ratio M_p / M_n supplies a matter-sector or charged-baryon offset relative to the neutral support scale.

Paper 67B also introduces the charged-envelope hypothesis. Neutral closed states may define compact support spacing, while charged states may require extended Compton coherence envelopes because charge is field-bearing. In this exploratory mapping, proton-like and electron-like states may be 6-vacancy charged/open VROS candidates, while the neutron-like state may be a 12-vacancy neutral/closed VROS candidate. This is not claimed as a proven particle derivation. It is a mechanism hypothesis for why the neutron scale, rather than the electron scale or proton scale alone, appears in the gravity hierarchy denominator.

A key local result is that the one-neutron-equivalent gravitational source length can be written as G M_n / c^2 = lambda_n (2 pi^3 / n_G)(M_p / M_n). This gives n_G a physical interpretation: it may be the structural dilution factor between local neutral support spacing and the much smaller gravitational source length associated with one neutron-equivalent mass.

The result is bounded. Paper 67B does not derive the neutron mass, proton mass, electron mass, VROS particle identity, S_9, n_G, or G. Its contribution is a neutral-spacing mechanism audit. It gives the neutron mass a structural role inside the dimensionless hierarchy and prepares the next step: testing whether the large count S_9 can be generated by Holosphere structural recursion.

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