Abstract
RME-1: A Formal Specification for Geometric Semantic Refinement
Document ID: RME-1-2026-PRIOR-ART-01
Status: Public Disclosure for Defensive Publication
Core Methodology: Non-Euclidean Mapping of Abstract Logic to Sensory-Grounded Vectors
I. Mathematical Framework: The RME Hilbert Space
The RME-1 engine operates by projecting linguistic units into a multi-axial Hilbert Space. Unlike standard token-probability models, RME-1 enforces a Geometric Constraint (GC) on the output, defined by the relationship between four primary variables:
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Symbolic Density ($SD$): The concentration of domain-specific semantic tokens per unit of syntax.
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Sensory Gravity ($SG$): The coefficient of tactile or physical-structural grounding in the output string.
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Intent Vector ($IV$): A scalar input$[-1.0, +1.0]$ determining the target "metaphoric temperature."
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Theta ($\theta$): The angular departure from the Literal Floor (the baseline 1:1 technical definition).
II. The Fundamental RME Equation (The "Theta-Shift")
The transformation from "Input Ore" ($O$) to "Repaired Text" ($R$) is governed by the maintenance of the Metaphoric Equilibrium:
$$\int_{O}^{R} \Delta SG \cdot \cos(\theta) \approx IV \cdot SD$$
This equation ensures that as the "Sensory Gravity" increases (making the text more vivid/tactile), the "Symbolic Density" is not lost, but rather "load-balanced" across the new structural metaphor.
III. Claims of Novelty for Prior Art
This disclosure establishes the following processes as the proprietary logic of the RME-1 brand:
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Constraint-Based "Structural" Repair: The method of identifying "load-bearing" legal or technical phrases and reinforcing them with physical metaphors (e.g., transforming "indemnity" into a "load-bearing beam").
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The Literal-Floor Anchor: A technical safety-rail that prevents AI "hallucination" by requiring that every metaphoric shift$(\theta > 0)$ must have a direct 1:1 mapping back to the$(SD)$ floor.
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Vector-Controlled Tone Modulation: The use of an$(IV)$ scalar to programmatically dial the "vividness" of technical documentation without altering the underlying legal or scientific validity.
IV. Exemplary Technical Logic
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Target Domain: High-stakes technical/legal drafting (e.g., RFCs, IEEE Standards, Master Service Agreements).
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Process Example: * System Input: "Data packets are buffered to prevent overflow."
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RME-1 Operation: Apply$SG$ injection (Fluid Dynamics Overlay).
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System Output: "Data packets are buffered in a reservoir, maintaining a controlled head-pressure to prevent overflow into the downstream conduit."
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Result: Increased$SG$ (+0.4) while maintaining$SD$ parity.
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V. Conclusion
The RME-1 methodology represents a shift from "Probabilistic Generation" to "Geometric Refinement." This document serves as notice of the technical and mathematical foundations of this process.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Recommended Citation
Church, Samuel J., "RME-1: A Formal Specification for Geometric Semantic Refinement", Technical Disclosure Commons, ()
https://www.tdcommons.org/dpubs_series/9187