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module module moderate

IndisputableMonolith.Physics.LightConeCausalityFromRS

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The module derives light-cone causality from Recognition Science by defining causal relations on events and certifying their confinement to light cones. Physicists reconstructing relativistic structure from the J-equation and forcing chain would cite it when linking the RS time quantum to causal propagation. The module proceeds through successive definitions of CausalRelation and LightConeCausalityCert that rest on the imported RS time quantum.

claimThe module introduces a binary causal relation $C(x,y)$ on events together with a certificate ensuring that $C(x,y)$ holds only when the separation lies inside the light cone in RS units where the fundamental time quantum satisfies $τ_0=1$ tick.

background

The module sits inside the Recognition Science derivation of physics from the single functional equation whose forcing chain runs from T0 to T8, with T5 fixing the J-cost function and T8 fixing three spatial dimensions. It imports the definition of the RS time quantum $τ_0=1$ tick from Constants, which supplies the discrete temporal yardstick used throughout the framework. The local setting therefore treats causality as a derived relation built on the phi-ladder and the Recognition Composition Law before any metric or field content appears.

proof idea

This is a definition module, no proofs. It structures the argument by first declaring the CausalRelation predicate, supplying an auxiliary count via causalRelation_count, and then packaging the light-cone restriction into the certificate LightConeCausalityCert.

why it matters in Recognition Science

The module supplies the causal foundation required for any later derivation of light propagation or spacetime dimensionality inside Recognition Science. It fills the step that converts the RS time quantum into a certified causal structure, thereby supporting the eight-tick octave and the emergence of D=3 spatial dimensions from the forcing chain.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (4)