The Shell-Radius Exponent Corrected (T267): Restoring the Body-Area Normalization in the SP-4 Heat-Flux Fit Moves rₛhell from M⁰. 31 to M⁰. 66, Confirming the Internal-Consistency Note from the Full Eight-Body Data, with the Structural Reading rₛhell ~ M^ (2/3) and the Downstream Papers Flagged

Photonic Universe Hypothesis (PUH) — T267 — CORRECTION / EMPIRICAL RESULT. The SP-4 programme inferred the Planck-shell radius scaling rₛhell ~ M⁰. 31 by HALVING the fitted heat-flux exponent (F ~ M⁰. 619 => rₛhell ~ F^ (1/2) ~ M⁰. 31). The Internal-Consistency Note (10. 5281/zenodo. 20434894) flagged that this halving is valid only if F is proportional to shell area alone, and argued the correct exponent is nearer M⁰. 66. This note settles it quantitatively from the full eight-body data, confirms M⁰. 66, gives its structural reading, and flags the downstream papers. THE OMITTED NORMALIZATION: the dimensionally complete Equal-Rate relation (T213) for a SURFACE FLUX is F = Rₛub (rₛhell/Rbody) ². The measured flux constrains the RATIO rₛhell/Rbody, never rₛhell alone. Extracting rₛhell from F requires the body radius Rbody as an explicit input. Solving: rₛhell ~ Rbody F^ (1/2) ~ M^ (q + p/2), with p the flux exponent (F ~ Mᵖ) and q the body mass-radius exponent (Rbody ~ Mq). The omitted route set q=0 (body radius mass-independent) — which is false. THE FIT (eight bodies: Pluto, Moon, Mercury, Venus, Earth, Neptune, Saturn, Jupiter): - Flux exponent p = 0. 59 (R² = 0. 95; consistent with published 0. 62 on five bodies). - Body mass-radius exponent q = 0. 37 (R² = 0. 98) — bodies grow with mass, q near 1/3 not 0. - CORRECTED shell-radius exponent s = q + p/2 = 0. 37 + 0. 29 = 0. 66, vs omitted p/2 = 0. 29. Restoring the body-area normalization moves the exponent by MORE THAN A FACTOR OF TWO, from 0. 31 to 0. 66 — reproducing the Internal-Consistency Note's M⁰. 66 INDEPENDENTLY from the full eight-body fit. STRUCTURAL READING: if bodies are roughly constant mean density (Rbody ~ M^ (1/3), q=1/3) and the flux exponent is p=2/3, then s = 1/3 + 1/3 = 2/3 EXACTLY => rₛhell ~ M^ (2/3). Fitted q=0. 37, p=0. 59 are close to 1/3, 2/3, making M^ (2/3) the natural target — stated as a reading, not a derivation (small sample; gas giants pull q above 1/3; p below 2/3). The corrected 0. 66 matches neither the volumetric law (M¹/3=0. 33) nor the surface law (M¹/2=0. 50): it is the composite q+p/2 of a body-area-normalised flux. DOWNSTREAM CONSEQUENCE (flagged, not recomputed): any result using rₛhell ~ M⁰. 31 should be re-evaluated at M⁰. 66 — specifically the SP-4d inner-core density-deficit estimate and the SP-4g gravitational-wave-echo magnitude, both of which depend on the shell radius. SCOPE: revises an EXPONENT, not a mechanism. The Equal-Rate relation, universal-shell-density assumption, Planck-core heat-source picture, and measured-anchor structure are unchanged. Found via full-corpus search + an eight-body log-log fit.