Photonic Universe Hypothesis (PUH) — Computation and Verdict. THE QUESTION T305 LEFT OPEN. T305 corrected the echo-delay corollary, removing a refractive factor that double-counted an effect the tortoise coordinate already contains. The corrected delay (704–718 tM) lies inside the range scanned by the most recent collaboration echo search, which reports no evidence for echoes. But whether a null result is a CONSTRAINT or a CONFLICT depends on the amplitude the framework predicts, and none had been computed. T237 (the Impedance Theorem) had flagged this exact gap when deriving perfect reflection: its own text records that a quantitative reflection coefficient for the partially-saturated near-core region, and the absolute echo amplitude, remained open. THIS NOTE COMPUTES THE AMPLITUDE. THE TRANSMISSIVITY. Integrating the Regge–Wheeler equation d²ψ/dr*² + (ω² − V) ψ = 0, with V = (1 − 2M/r) l (l+1) /r² − 6M/r³, for quadrupole gravitational perturbations at the fundamental quasi-normal frequency ωM = 0. 3737, with a purely transmitted wave on the inner side: |T|² = 0. 468. INTERNAL VALIDATION: the barrier maximum is ≈ 0. 151 in geometric units while ω² = 0. 140, so the wave sits marginally BELOW the barrier top — precisely the quasi-normal condition — and transmission exactly at a barrier top is one half by the standard parabolic result. Obtaining 0. 468 where 0. 5 is expected confirms the integration is behaving. Across the band the transmissivity rises steeply: 0. 055 at ωM = 0. 30, 0. 92 at ωM = 0. 45. THEOREM 306. 1. With reflection coefficient R at the Shell, the first echo arrives at ≈ |T|²R relative to the ringdown. For R = 1 — which T237 derives from the vanishing of residual degrees of freedom established in T175 — that is FORTY-SEVEN PERCENT. For the loudest catalogue events at ringdown SNR 10–30, the echo carries SNR ≈ 5–14, above the threshold at which a matched-template search reports a detection. THE PREDICTION IS NOT MARGINAL. THE OBSERVATION AND THE VERDICT. No such echoes were found. Taking a detection threshold of SNR 5 and the loudest analysed event at ringdown SNR 30, escaping detection requires R < 0. 36 — roughly a factor of three below the derived value. THE ESTIMATE ERRS IN THE FRAMEWORK'S FAVOUR: the single-bounce calculation neglects the resonant build-up of the full echo train, which would increase the predicted amplitude. Threshold and SNR are order-of-magnitude and the transmissivity varies across the band; none of this moves the result by the required factor. VERDICT: THE NULL ECHO SEARCH IS A CONFLICT with the framework as presently formulated, not merely a constraint upon it. T305 left this open; it is now closed, unfavourably. TWO RESOLUTIONS, NAMED AND NOT CHOSEN. (1) IMPERFECT REFLECTION — T237's perfect reflection is derived at the fully-saturated core where residual degrees of freedom vanish; just outside, in the partially-saturated transition region, they do not, and the reflection coefficient is finite. That is precisely the gap T237 flagged. If the transition returns less than 0. 36 the observations are satisfied; the cost is that the framework must stop describing the Shell as a perfect reflector of gravitational waves and must compute what the transition returns. (2) ABSORPTION — the Shell may absorb gravitational waves rather than reflect them, in which case there are no echoes at all and the null result is explained rather than survived. A mechanism is already in the archive: the lattice at the Shell sits at the snap threshold, so an incoming tension oscillation would carry it over that threshold and be converted into folding rather than returned — T287's photon-absorption growth channel arriving by a different route, and adding a gravitational-wave contribution to core growth the framework does not presently have. NEITHER IS ADOPTED HERE: choosing requires re-reading the reflection results in full and would change more than one filed paper. WHAT IS NOT AT RISK. The non-evaporation result is untouched, structurally rather than fortunately. Evaporation concerns whether a core EMITS; reflection concerns whether it ABSORBS — opposite questions. T172's theorem states that two Casimir leaves may merge into one while one may not spontaneously split into two: MERGING IS ABSORPTION, SPLITTING IS EMISSION. It therefore forbids emission and PERMITS absorption. The amalgamation-only picture, T289's mass-floor dividend, and T297's armed prediction of an identically vanishing primordial explosion rate all rest on emission and are unaffected. Further: the second resolution above is not merely permitted by that theorem but POINTED AT by it, absorption being the topologically allowed channel. WHAT IS AT RISK is the reflection side: T237's perfect reflection; T292's assignment of gravitational waves to a reflected bulk channel while photons are absorbed as surface modes; and the echo prediction in its entirety rather than merely its amplitude. If absorption is adopted, that assignment inverts for gravitational waves and T292 requires revision alongside T237. KILL-CONDITIONS: (i) the transmissivity is a numerical integration of a standard equation, falsified by any independent computation returning a materially different value at the quasi-normal frequency — the barrier-top consistency is the check to reproduce first; (ii) if the relation between echo amplitude and barrier transmissivity carries a suppression not accounted for here, the bound on R weakens, though the neglected resonant build-up pushes the other way; (iii) if a future search reports a detection at the corrected delay with amplitude near half the ringdown, perfect reflection is confirmed and this verdict overturned. NOT CLAIMED: that the framework is refuted (two resolutions restore consistency) ; that the transition-region reflection coefficient has been computed (it has not — that remains T237's open calculation) ; that absorption is established (a named candidate, whose adoption would require revising T292) ; that non-evaporation is affected; or that the null search favours any competing framework, since an absence of echoes is equally consistent with there being no reflecting surface at all.
Brian Martell (Mon,) studied this question.