>[!warning] >This content has not been peer reviewed. ## **A Meta-Ontological Formalism for Informational Systems** ### I. The Foundational Axioms 1. **The [[Format]] ($f$):** The independent, dynamic substrate of reality. It exists regardless of observation and determines the physical constants ($k_B$, $T$) that set the cost of [[Translation]]. 2. **[[Information]] & Resolution ($\sigma$):** A [[You|Reference Frame]] distinguishes $N$ states within the Format. **Resolution ($\sigma$)** is the effective bit-count required to maintain those distinctions: $\sigma = -\sum p_j \log_2 p_j$, where the sum runs over the states distinguished by [[You]]. 3. **[[Proper Time]] ($\tau$):** The local refresh **interval** of any system’s relations. Time is not a background; it is the duration between discrete translations. 4. **[[Translation]] ($\rightarrow$):** The irreversible mechanism of change. Every change in format or state is an **[[Event]]**. Because the Format is in constant flux, maintaining a state requires active error correction; therefore, identity is a dissipative process. **Note (RST alignment):** In [[Relational Substrate Theory (RST)]], these four appear as A1–A4. **Relational Distance** ($d$) — the number of Translation steps to relate one system to another — is treated there as a fifth foundational concept (A5), so that RST axioms A1–A5 align with the full RRT picture. In this draft, $d$ appears in the Landauer section below rather than as a separate axiom. ### II. The Relational Landauer Principle Persistence in a thermal environment ($T > 0$) is an active expenditure of energy. The minimum power required to maintain a system's resolution against the noise of the substrate is governed by the **Systemic Bit-Rate**, summed over all $n$ actively maintained [[Relating|relations]]: **Foundational citation:** Landauer, R. (1961). *Irreversibility and heat generation in the computing process.* IBM J. Res. Dev. 5, 183. — establishes $k_B T \ln 2$ per erased bit; RRT extends this to relational maintenance across $d$ steps. Where [[Relational Distance]] ($d$) is the number of [[Translation]] steps required for one [[System]] to [[Relating|relate]] to another. **The Physical Minimum ($\Phi_{\min}$):** $\Phi_{\min} = k_B \ln 2 \sum_{i=1}^{n} \frac{\sigma_i \cdot T_i}{\tau_i}$ This is the local case, where all relations are at $d = 1$. **The Relational Efficiency Index ($K_R$):** $K_R = \frac{\Phi_{measured}}{\Phi_{\min}}$ > [!IMPORTANT] > **The Landauer Floor:** No physical, biological, or technological system can persist below its calculated $\Phi_{\min}$. $K_R \ge 1$ is a universal boundary. $\Phi_{\min}$ is a **local invariant**: evaluated in each [[System]]'s own [[Proper Time]], it is the same regardless of gravitational potential. Gravity does not change the local cost of [[Existence]]; it changes the cost of [[Relating]] across locations with mismatched $\tau$. **Relational Friction:** [[Relating|Relations]] across $d$ [[Translation]] steps cost $d$ times the local Landauer rate. The general form becomes: $\Phi_{\min} = k_B \ln 2 \sum_{i=1}^{n} \frac{d_i \cdot \sigma_i \cdot T_i}{\tau_i}$ When $T$ varies along the chain, each step is a separate term in the summation with its own local $T_j$ and $\tau_j$. The $d \cdot T$ form assumes uniform conditions along the path. > [!NOTE] > **Scope:** This principle applies to [[System|Systems]] maintaining resolved [[Information]] ($\sigma > 0$) in a thermal environment ($T > 0$). Unitary quantum evolution (coherent states before decoherence) is a property of the [[Format]] itself, not a [[Translation]] in this framework. The Landauer cost begins where [[Information]] is resolved against thermal noise. ### III. Inherent Principles 1. **The [[Local Arrow]]:** For any persisting system, the experienced direction of Time is the emergent result of the energy expenditure required for active error correction (maintenance). 2. **Thermodynamic Scaling:** [[Zoom Logic|Coarse-graining]] (Collapsing Resolution) reduces the aggregate Systemic Bit-Rate. This is a thermodynamic strategy to lower the energy cost of existence. ### IV. Conjectures **Emergent Space:** We postulate that each discrete [[Translation]] step corresponds to a quantum of physical space. If so, spatial distance is an emergent count of relational [[Event|Events]], not a background void. See also: [[Open Questions]] --- ### V. Physical Formalization These axioms have been formalized into a covariant field theory and unified framework: **[[Relational Substrate Theory (RST)]]** — applies RRT to the physical universe, identifying the [[Format]] with spacetime, noise with cosmic expansion ($\theta = 3H$), and the [[Energy Floor]] with gravitational workload. The theory reproduces Newton, MOND, and $\Lambda$ as three regimes of a single Resource Allocation Equation, and maps all four fundamental forces as projections of a Resource Triangle. | RRT Concept | RST Identification | |:---|:---| | [[Format]] ($f$) | Spacetime + aether field $A^\mu$ | | [[Information\|Resolution]] ($\sigma$) | [[Signal]] — the structure being maintained | | Noise ($T$) | [[Noise Floor]] — expansion scalar $\theta = 3H$ (FLRW); gravitational threshold $a_0 = c\theta/(6\pi) = cH/(2\pi)$ (acceleration, derived from $\theta$) | | [[Energy Floor]] ($\Phi_{\min}$) | [[Workload]] — gravitational maintenance effort | | [[Translation]] | The refresh cycle (each discrete update) | | [[Proper Time]] ($\tau$) | Local refresh interval → [[Refresh Burden]] | | [[Relational Distance]] ($d$) | [[Relational Friction]] — cost scaling with distance | | [[Zoom Logic]] | Resolution shedding → strong force confinement | **Symbol index:** For a short cross-document list of symbols ($I$, $N$, $\Omega$, $W$, $\mu$, $\nu$, $\eta$, $n$, $\tau$, $\theta$, $\sigma$, $a_0$, etc.), see [[Symbol Index]] (in expanded theory). **Interaction ontology:** For relations *between* Systems (inter-System stances, inherent sign partition, 3×3×μ matrix), see [[Interaction Meta-Ontology (RRT)]].