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FRC-700-001 · v0.1

The Two-Face Threshold: Inward Realization, Selective Interface, and Outward Participation v0.1

H. Servat2026-07-177 minFRC 700 seriesSpeculativeμ4 Logical / conceptual
thresholdsinterfaceinward-outwardnon-reconstructionledgermu-levels

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A bounded unit has an inward realization and an outward participation only relative to a declared boundary. Between them lies a selective interface, not an identity. This paper represents a threshold by an inward space X, environment E, boundary, outward description L, and map ell:X→L. It proves that a noninjective interface cannot support unique inward reconstruction and gives a finite fiber example. FRC 830 strong morphisms then provide a stricter commuting-square test for proposed transformations. The result constrains the FRC μ lens without deriving the 830 mathematics from it.

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Philosophical / formal framework note

preprint

Declared μ register

μ4 · Logical / conceptual

Logic, formal models, language as explicit reasoning, and computational design.

Open boundary

Review the paper’s declared scope, controls, limitations, and kill conditions.

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v0.1 · Current release

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A bounded unit has an inward realization and an outward participation only relative to a declared boundary. Between them lies a selective interface, not an identity. This paper represents a threshold by an inward space X, environment E, boundary, outward description L, and map ell:X→L. It proves that a noninjective interface cannot support unique inward reconstruction and gives a finite fiber example. FRC 830 strong morphisms then provide a stricter commuting-square test for proposed transformations. The result constrains the FRC μ lens without deriving the 830 mathematics from it.

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