What question did this study set out to answer?

The aim is to correct the shell-radius exponent and analyze its implications on selection hypotheses and mass dependence.

June 29, 2026Open 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

Key Points

The aim is to correct the shell-radius exponent and analyze its implications on selection hypotheses and mass dependence.
Corrected the shell-radius exponent from r_shell ~ M^0.31 to r_shell ~ M^0.66.
Explored three hypothesis scalings: H1 (linear), H2 (volume), and H3 (Yukawa-screened).
Assessed implications for the SP-4d/SP-4g compatibility window based on the corrected exponent.
H2 volume hypothesis is excluded by a factor of two when compared to the corrected exponent, indicating a preference for a steeper scaling.
The shell-to-body ratio becomes mass-dependent, growing significantly from smaller bodies like Earth to larger bodies like Jupiter.
The SP-4d/SP-4g compatibility window no longer remains fixed, requiring specific calculations for mass-scaled adjustments.

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.

Read Full Paperexternally

Perguntar à IA

Bookmark

View Full Paper