>[!warning]
>This content has not been peer reviewed.
The Resource Allocation Equation is the single law that governs how the [[Format]] distributes its resources between [[Signal]] and [[Noise Floor|noise]].
$I = \Omega \cdot \mu\!\left(\frac{\Omega}{N}\right)$
In plain language: **the source equals the output times the rendering quality**.
This one equation contains Newton's gravity, Einstein's general relativity, MOND, the cosmological constant, and the transition between all of them. It is the "E = mc$^2
quot; of the [[Relational Substrate Theory (RST)|Relational Substrate Theory]].
**Axiom source:** Derives from [[Relational Resolution Theory (RRT)]] (Landauer floor, Relational Landauer Principle) via [[Relational Substrate Theory (RST)]].
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## RST Formalization
**Symbol:** $I = \Omega \cdot \mu(\eta, n)$
**Components:**
- $I$ = [[Signal]] (the source/request)
- $\Omega$ = [[Workload]] (the measured output)
- $\mu$ = [[Fidelity]] (rendering quality)
- $\eta = \Omega/N$ = [[Signal-to-Noise Ratio]]
- $n$ = [[Transition Sharpness]]
**Equivalence:** This equation is algebraically identical to the [[Resource Triangle]] $W^n = \Omega^n + N^n$ (see [[RST Super-Relational Mapping]]). The two formulations are the same identity viewed from different angles. **Verifiable:** [[Super-Relational Mapping Verification]]; calculation: [[Super-Relational Mapping - Code]].
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## In the Equation
**"The Law"**
Everything in the [[Relational Substrate Theory (RST)|Relational Substrate Theory]] derives from this single line. The covariant action, the Horndeski mapping, the PPN constraints, the SPARC evaluation — all of it is the translation of this equation into the mathematical language required by modern physics.
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## The Two Limits
**High [[Fidelity]]** ($\mu \to 1$): $I = \Omega$. Newton's law. Maxwell's equations. The [[Format]] renders perfectly.
**Low [[Fidelity]]** ($\mu \to \eta$): $I = \Omega^2/N$, so $\Omega = \sqrt{I \cdot N}$. The geometric mean of source and noise. Flat rotation curves. The Baryonic Tully-Fisher Relation (Famaey & McGaugh 2012; [[SPARC Evaluation Verification]]). No dark matter needed.