APrioriPrediction
plain-language theorem explainer
Bundles an a priori ILG parameter prediction: predicted exponent α, amplitude C, a textual derivation source, and a Prop asserting no empirical input. Anyone citing the RS claim that α and C are fixed by self-similarity before SPARC comparison uses this record type. It is a plain structure definition, not a proved theorem.
Claim. An a priori prediction is a record of four data: a real predicted exponent $\alpha_{\mathrm{pred}}$, a real predicted amplitude $C_{\mathrm{pred}}$, a string naming the theoretical derivation source, and a proposition asserting that no empirical input entered the derivation. The intended RS values are $\alpha=(1-1/\varphi)/2$ from two-scale decomposition and $C=\varphi^{-2}$ from the three-channel factorization hypothesis.
background
The module addresses a gap flagged in the discrete informational framework paper: SPARC fits treated $(A,\alpha,r_0)$ as free, then noted post-hoc agreement with golden-ratio candidates. Recognition Science instead claims $\alpha$ and $C$ are forced a priori by self-similarity in the ledger.
The forcing chain runs RCL $\to$ unique $J(x)=\frac12(x+x^{-1})-1$ (T5) $\to$ self-similarity forcing the scale ratio $\varphi$ with $\varphi^2=\varphi+1$ (T6) $\to$ a memory kernel with $\varphi$-structure. From that kernel the fractional exponent is $\alpha=(1-1/\varphi)/2\approx 0.191$ via two-scale decomposition; the amplitude $C=\varphi^{-2}\approx 0.382$ needs an extra three-channel factorization hypothesis (paper Table I).
This structure is the data type that packages those predicted numbers together with an explicit "no empirical input" witness, so prediction and later SPARC validation stay logically separate.
proof idea
No proof: this is a structure declaration. Four fields are declared (two reals, a string source label, and a Prop for the no-empirical-input claim). Instantiation happens downstream in rs_a_priori_prediction, which fills $\alpha$ from the locked self-similarity value, $C=\varphi^{-2}$, source string "self-similarity in discrete ledger (T6)", and True for the empirical-input Prop.
why it matters
Closes the paper's post-hoc-agreement objection by giving a typed carrier for predictions made before any galaxy fit. Downstream, rs_a_priori_prediction is the concrete RS instance: $\alpha$ from two-scale self-similarity and $C=\varphi^{-2}$ under the three-channel hypothesis, with derivation source tied to T6. That instance feeds the ILG a priori certificate that separates prediction from SPARC validation. Framework landmarks: T5 $J$-uniqueness, T6 $\varphi$ fixed point, and the self-similarity $\to$ memory-kernel $\to$ fractional-exponent chain in the module doc. The $C$ leg remains explicitly conditional on the three-channel hypothesis listed as "Hypothesis" in Table I.
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