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Evaluate whether compact stars can be modeled as horizon-scale Planck cores beneath a thin film of matter by comparing theoretical radius predictions to astrophysical measurements, and examine how core processing capacity scales with mass.

August 14, 2026Open Access

PUH Theorem 328 (Two Mechanisms Reversed by One Scaling) — A Mass-Carrying Core Predicts 4.5 km Where NICER Measures 11–13, So the Thin-Film Reading Fails; and Shell Capacity Grows as M² While Demand Grows as M, So the Absorption Criterion Inverts

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Evaluate whether compact stars can be modeled as horizon-scale Planck cores beneath a thin film of matter by comparing theoretical radius predictions to astrophysical measurements, and examine how core processing capacity scales with mass.
Calculated theoretical shell radii for thin-film mass-carrying Planck cores at the accretion floor ($r_{\text{shell}} = 1.077 r_s$) across various compact star masses.
Compared predicted radii directly against pulse-profile X-ray radius measurements for PSR J0030+0451 (1.44 $M_\odot$), PSR J0740+6620 (2.08 $M_\odot$), PSR J0437−4715 (1.42 $M_\odot$), and a standard 1.40 $M_\odot$ neutron star.
Evaluated horizon-scale surface area growth ($A_{\text{shell}} \propto M^2$) versus linear mass demand ($M$) across a 1 to 100 $M_\odot$ range to test absorption-dominated implosion conditions.
Predicted radii ranged from 4.45 to 6.62 km compared to measured values of 11.4 to 12.7 km (PSR J0030+0451 predicted 4.58 km vs. 12.7 km measured; PSR J0740+6620 predicted 6.62 km vs. 12.4 km measured), missing observations by nearly a factor of three.
For a 1.40 $M_\odot$ star, the intervening matter between the 4.45 km shell and 11.5 km surface constitutes 94.2% of the star's volume, refuting the thin-film envelope hypothesis.
Planck core surface area scaled quadratically from $1.10 \times 10^8\text{ m}^2$ at 1 $M_\odot$ to $1.10 \times 10^{12}\text{ m}^2$ at 100 $M_\odot$, causing core capacity to outpace linear infall demand by a factor of 100 and inverting the absorption mechanism.

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Implication

Theoretical scaling analysis demonstrates that thin-film Planck cores underestimate neutron star radii by threefold, indicating that core capacity scales quadratically rather than linearly.

Cite This Study

Brian Martell (2026) studied this question.

synapsesocial.com/papers/6a7ec78db70b84ec8b913fef https://doi.org/10.5281/zenodo.21905928

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Implication

Theoretical scaling analysis demonstrates that thin-film Planck cores underestimate neutron star radii by threefold, indicating that core capacity scales quadratically rather than linearly.

PUH Theorem 328 (Two Mechanisms Reversed by One Scaling) — A Mass-Carrying Core Predicts 4.5 km Where NICER Measures 11–13, So the Thin-Film Reading Fails; and Shell Capacity Grows as M² While Demand Grows as M, So the Absorption Criterion Inverts

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Discussion

Implication

Cite This Study

PUH Theorem 328 (Two Mechanisms Reversed by One Scaling) — A Mass-Carrying Core Predicts 4.5 km Where NICER Measures 11–13, So the Thin-Film Reading Fails; and Shell Capacity Grows as M² While Demand Grows as M, So the Absorption Criterion Inverts

Key Points

Discussion

Implication

Cite This Study

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