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IndisputableMonolith.Verification.ILGAPrioriPredictionCert

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Certification module for the a priori ILG prediction: self-similarity of the recognition memory kernel forces the fractional exponent α and the prefactor C from the φ-structure alone. Galaxy-rotation and SPARC-fit consumers cite the resulting numerical band. The argument chains φ-forcing through a two-scale decomposition of the fractional integral kernel and checks the prediction against SPARC best-fit windows.

claimIn a self-similar recognition memory kernel $\rho_{\mathrm{rec}}(t)=I_t^{\alpha}[\rho_{\mathrm{baryon}}](t)$, scale consistency under $\varphi$ forces the fractional exponent $\alpha$ and the ILG weight $w(k,a)=1+C\,(a/(k\tau_0))^{\alpha}$. The module records the resulting a priori pair $(\alpha,C)$ and certifies that it lies inside the SPARC best-fit $n\sigma$ window.

background

Infra-Luminous Gravity (ILG) replaces a dark-matter halo by a recognition weight on baryonic density. The kernel is written $w(k,a)=1+C\cdot(a/(k\tau_0))^\alpha$, with $\tau_0$ the RS time quantum (one tick). The memory side is a fractional integral $\rho_{\mathrm{rec}}(t)=I_t^\alpha\rho_{\mathrm{baryon}}$.

PhiForcing shows that a discrete ledger with J-cost that can reference itself at different scales is forced to the golden ratio $\varphi$. The present module imports that forcing together with the ILG kernel formalization and asks what values of $\alpha$ and $C$ are compatible with self-similarity under scale $\varphi$.

Sibling material introduces a SelfSimilarMemory predicate, derives $\alpha$ from a two-scale decomposition, packages the pair as an APrioriPrediction, and compares it to SPARCBestFit via a within-$n\sigma$ predicate, using elementary bounds $1/\varphi\in(0.6,0.7)$.

proof idea

The module is organized as a short forcing-plus-certification chain rather than a single theorem. Self-similarity of the memory kernel under the $\varphi$-rescaling is stated first. That hypothesis is fed to a two-scale decomposition lemma that isolates the only fractional exponent compatible with the ledger's $\varphi$-structure, yielding an explicit $\alpha$ (classically near $1/\varphi$). The prefactor $C$ is then read off from the same scale-matching, producing the a priori prediction record. Finally the predicted $(\alpha,C)$ is compared componentwise to the SPARC best-fit window by a within-$n\sigma$ checker; elementary inequalities on $1/\varphi$ discharge the numerical side conditions.

why it matters in Recognition Science

Recognition Science claims that the ILG modification to gravity is not a free phenomenological fit but is fixed once the ledger is required to be self-similar at scale $\varphi$ (the T6 landmark of the forcing chain). This module is the verification certificate for that claim: it turns the PhiForcing and ILG.Kernel imports into a concrete, checkable $(\alpha,C)$ prediction and records that the prediction sits inside the SPARC band.

No downstream modules currently import it (used_by is empty); it sits at the verification leaf of the ILG stack. Its value is archival and audit-facing: a working astrophysicist or referee can see exactly which RS-native constants and which self-similarity hypothesis produce the published a priori ILG numbers, without opening the phenomenological fitting pipeline.

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