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June 29, 20260 citationsOpen Access

The M⁰. 66 Shell-Radius Correction Propagated Downstream (T268): The Steeper Exponent Excludes the Volume Hypothesis H2 in the I1 Selection, Makes the Shell-to-Body Ratio Mass-Dependent, and Rescales the SP-4d/SP-4g Compatibility Window

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BMBrian Martell

Key Points

  • The aim is to correct the shell-radius exponent in the Photonic Universe Hypothesis and analyze its implications.
  • Corrected the shell-radius exponent from 0.31 to 0.66.
  • Evaluated implications for the I1 Working Note's hypothesis selection.
  • Analyzed the shell-to-body ratio and compatibility windows in relation to mass.
  • The corrected exponent excludes the volume hypothesis (H2) which was previously favored.
  • The shell-to-body ratio showed a significant mass dependence, growing fifty-fold from Earth to Jupiter.
  • The SP-4d/SP-4g compatibility window now scales with mass, indicating a shift in joint viability.

Abstract

Photonic Universe Hypothesis (PUH) — T268 — DOWNSTREAM PROPAGATION. The shell-radius exponent was corrected (T267) from rₛhell ~ M⁰. 31 to rₛhell ~ M⁰. 66, by restoring the body-area normalization the original halving omitted: the dimensionally complete Equal-Rate relation F = Rₛub (rₛhell/Rbody) ² constrains the RATIO rₛhell/Rbody, so rₛhell ~ M^ (q+p/2) with q=0. 37 (body mass-radius exponent) and p=0. 62 (flux exponent), giving 0. 66 not 0. 31. This note propagates that correction into the three programmes the I1 Working Note flagged as dependent, and finds the consequences are NOT cosmetic. 1. I1 HYPOTHESIS SELECTION CHANGES. The I1 Working Note tested three scalings: H1 linear (M¹. 0), H2 volume (M^ (1/3) =0. 33), H3 Yukawa-screened (flexible). Against old 0. 31, H2 was reported closest (within ~7%) and volume favoured. Against corrected 0. 66, H2 is off by a FACTOR OF TWO (98%), EXCLUDED on exponent grounds. The corrected 0. 66 is closer to H1 linear (1. 0) than to H2 volume; the data favour a STEEPER-than-volume scaling (linear-leaning or screened H3). The qualitative I1 conclusion flips. 2. SHELL-TO-BODY RATIO BECOMES MASS-DEPENDENT. rₛhell/Rbody ~ M^ (p/2) = M⁰. 31, so the Planck Shell occupies a GROWING fraction of more massive bodies — about FIFTY-FOLD growth in the ratio from Earth-core mass (~5e21 kg) to Jupiter (~1. 9e27 kg). This was the factor Mq=M⁰. 37 dropped by the halving, hence invisible under M⁰. 31. Restored, it means the Shell fraction is not universal but scales with mass. 3. SP-4d/SP-4g COMPATIBILITY WINDOW RESCALES. SP-4g (GW echo, archival LIGO/Virgo/KAGRA) needs rₛhell >~100 km (else Rayleigh-suppressed). SP-4d (inner-core density deficit, ~5% as a central seismically-invisible Planck mass) needs rₛhell 100km? ) depends. That requires the I1 field-equation closure (Euler-Lagrange from the T175 Lagrangian, spherical solve, degree-30 Casimir profile) not yet in the archive, plus Rₛub. Absolute predictions remain gated on I1 closure and Rₛub.

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Cite This Study

Brian Martell (2026) studied this question.

synapsesocial.com/papers/6a420ba8f91bb43ea9192a36https://doi.org/10.5281/zenodo.20968055
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