The M^0.66 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
Photonic Universe Hypothesis (PUH) — T268 — DOWNSTREAM PROPAGATION. The shell-radius exponent was corrected (T267) from r_shell ~ M^0.31 to r_shell ~ M^0.66, by restoring the body-area normalization the original halving omitted: the dimensionally complete Equal-Rate relation F = R_sub (r_shell/R_body)^2 constrains the RATIO r_shell/R_body, so r_shell ~ 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 (M^1.0), 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. r_shell/R_body ~ M^(p/2) = M^0.31, 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 M^q=M^0.37 dropped by the halving, hence invisible under M^0.31. 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 r_shell >~100 km (else Rayleigh-suppressed). SP-4d (inner-core density deficit, ~5% as a central seismically-invisible Planck mass) needs r_shell <<1220 km (else seismically visible). The I1 window was ~100-1000 km. With the steeper exponent r_shell rises faster with mass, so the window is no longer a flat band but carries explicit mass-scaling; the mass at which a body's Shell crosses the SP-4d seismic-visibility ceiling shifts. Joint viability must be computed per body with the steeper exponent. SCOPE: corrects the EXPONENT-LEVEL consequences (which hypothesis, the ratio's mass dependence, the window's scaling) — all following from the corrected exponent alone. Does NOT compute the absolute r_shell(M_Earth) in km, on which the actual viability of SP-4d (r_shell<1220km?) and SP-4g (r_shell>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 R_sub. Absolute predictions remain gated on I1 closure and R_sub.
Authors
- Brian Martell
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-06-27
- DOI
- https://doi.org/10.5281/zenodo.20968054
- Primary Topic
- Quantum Chromodynamics and Particle Interactions
- Type
- preprint