canonical
plain-language theorem explainer
Non-vacuity witness: the continuous weight forced by the recognition measure is itself a self-similar dressing (factorizes, antitone, step balance). Anyone citing calibration-free α genesis needs this object as the concrete inhabitant. Construction packages MeasureForcing.contWeight and checks the step identity via φ² = φ + 1.
Claim. The continuous weight $g$ forced by the recognition measure is a self-similar dressing: it factorizes over independent nonnegative loads, is antitone on $[0,\infty)$, and satisfies the single-step balance $g(1)=1/(1+g(1))$.
background
Module M5 (Calibration Forcing) eliminates the unit-linear-response normalization that earlier α-genesis stages carried as an input. A self-similar dressing is a survival fraction $g:\mathbb{R}\to\mathbb{R}$ with three structural premises only: factorization over independent nonnegative loads, antitonicity on $[0,\infty)$ (more load never helps), and the fixed-point balance $g(1)=1/(1+g(1))$ on the unit step. No derivative condition and no unit convention appear.
Those three premises are exactly the ledger and balance facts that force the T9 recognition measure. Upstream, contWeight is the continuous weight of that forced measure, already known to factorize and to be antitone, with value at $1$ equal to the measure step $\rho$. The golden-ratio identity $\varphi^2=\varphi+1$ (from $x^2-x-1=0$) converts the balance equation into the unique admissible positive root $g(1)=\varphi^{-1}$.
proof idea
Definitional package of SelfSimilarDressing with $g:=$ continuous weight from MeasureForcing. Factorization and antitonicity are the first two conjuncts of contWeight_satisfies_premises. For the step balance: rewrite $g(1)$ as $\rho$, unfold $\rho$, then use positivity of $\varphi$ and $\varphi^2=\varphi+1$ with field_simp and nlinarith to obtain $g(1)=1/(1+g(1))$.
why it matters
Closes the residual normalization worry of Alpha Genesis: the dressing of the α seed carries zero calibration input. Form, rate, and step are forced by the same factorization-plus-self-similar-balance pair that forces the recognition measure itself (T9 / W2 step). Downstream, every self-similar dressing yields the forward α object (alphaInvGenesis_from_selfSimilar), and the older (D1)+(D2) dressing response demotes to the natural-units display of this object (natural_display). The certificate CalibrationForcingCert packages the non-vacuity. No CODATA reference enters.
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