alphaInvGenesis_from_selfSimilar
plain-language theorem explainer
Every self-similar dressing recovers the forward inverse-fine-structure object: channel budget times the dressing at spectral load equals α⁻¹_genesis. Cite this for the M5 calibration-forcing closure (zero normalization input to the α seed). Proof is a one-line unfold-and-rewrite using that every such dressing equals the forced continuous weight on nonnegative loads.
Claim. For every self-similar dressing $D$ (survival fraction $g$ that factorizes on independent loads, is antitone on nonnegative loads, and obeys the self-similar balance $g(1)=1/(1+g(1))$), one has $\alpha^{-1}_{\mathrm{genesis}}=S\cdot g(w_8/S)$, where $S$ is the EM channel budget and $w_8/S$ is the spectral load.
background
Alpha Genesis M5 eliminates unit-linear-response calibration from the dressing. A self-similar dressing is a survival fraction $g$ under gap load with three premises only: factorization over independent nonnegative loads, antitonicity on $[0,\infty)$, and the self-similar balance $g(1)=1/(1+g(1))$ — the same fixed-point equation that forces the T9 measure step. No derivative condition and no unit convention appear.
The forward inverse-$\alpha$ object is defined as channel budget $S$ (geometric seed of the EM recognition loop, $4\pi\cdot 11$) times the T9 forced continuous weight at spectral load $w_8/S$. Upstream, every self-similar dressing is already forced to that measure: $g(t)=\varphi^{-t}$ on nonnegative loads (response_forced). The spectral load is positive, so the evaluation point is admissible.
proof idea
Unfold the definition of the forward $\alpha^{-1}$ object (channel budget times continuous weight at spectral load). Rewrite the dressing evaluation via response_forced at the spectral load, using positivity of the load to meet the nonnegative hypothesis. Both sides become identical. Pure term-mode unfold-and-rewrite; no further algebra.
why it matters
Clause 4 of the Calibration Forcing Certificate (M5 closure): the forward $\alpha$ object follows from every self-similar dressing. With step forced to $\varphi^{-1}$ from balance alone and the full response forced to $\varphi^{-t}$, this discharges the residual normalization worry — the dressing of the $\alpha$ seed carries zero calibration input. Form, rate, and step are forced by the same two structural facts (factorization, self-similar balance) that force the recognition measure itself. No CODATA reference. Demotes the older calibrated dressing response to a natural-units display of this object.
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