dimensionlessPredictions
plain-language theorem explainer
Catalog of standard dimensionless RS outputs: inverse fine-structure sketch, golden ratio and its square, coherence energy ratio φ⁻⁵, and the eight-tick cycle from D=3. Calibration and verification authors cite it to separate zero-parameter φ-only claims from SI-anchored numerics. The body is a fixed five-entry list of value/formula/verified triples.
Claim. The standard dimensionless Recognition Science predictions are the finite list of triples $(v, f, b)$ with $v \in \mathbb{R}$ a pure number from $\varphi$, $f$ a formula string, and $b$ a Lean-verification flag: $\alpha^{-1} \approx 137.036$ (unverified), $\varphi = (1+\sqrt{5})/2$ (verified), $\varphi^2 = \varphi+1$ (verified), $E_{\mathrm{coh}}/E_{\mathrm{ref}} = \varphi^{-5}$ (verified), and $\tau$-cycle $= 2^3 = 8$ for $D=3$ (verified).
background
The CalibrationPolicy module separates two classes of RS claims. Dimensionless predictions are ratios, exponents, and discrete periods fixed by $\varphi = (1+\sqrt{5})/2$ alone; they need no external SI input. SI-anchored predictions require at least one external scale (for example CODATA $\hbar$) before absolute units make sense.
A DimensionlessPrediction is a structure with a real value, a formula string describing the $\varphi$-derivation, and a Boolean recording whether Lean has checked the identity. Upstream forcing fixes spatial dimension $D = 3$ (T8/T9) and the hypercube period $2^D = 8$; the $\varphi$-ladder supplies powers such as $\varphi^{-5}$ used for the coherence-to-reference energy ratio. Constants currently sit in placeholder units ($c=1$, $\hbar=1$, $G=1$), so the live policy is dimensionless-only mode.
proof idea
Definitional list literal, not a proof. Five structure values are written out: an approximate $\alpha^{-1}$ entry marked unverified; three algebraic $\varphi$ identities and the eight-tick period marked verified. No lemmas are applied; the list is the data.
why it matters
This list is the concrete inventory behind the module's dimensionless-only claim: what RS may assert without accepting an external anchor. It records the framework landmarks $\varphi$, $\varphi^2=\varphi+1$, the $\varphi^{-5}$ energy ratio (matching RS-native $\hbar = \varphi^{-5}$), and the eight-tick octave forced by $D=3$ (T7/T8). The $\alpha^{-1}$ row sits in the reported band near $137.03$–$137.04$ but is flagged unverified, so SI fine-structure claims stay outside the zero-parameter core until a certified derivation lands. No downstream consumers are wired yet; the entry exists so calibration-mode checks and compliance reports can enumerate the $\varphi$-only surface.
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