Explain the Lean theorem `cone_bound_export` in module `IndisputableMonolith.ConeExport.Theorem`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

1. Plain English Statement

The theorem cone_bound_export states that if a causal system enforces a strict light-cone speed limit across single discrete steps, then any event $y$ reachable from an event $x$ over any number of steps $n$ obeys the exact same macroscopic bound. The difference in spatial radius is bounded by the speed of light $c$ multiplied by the elapsed time, completely independent of the intermediate step count $n$.

2. Relevance to Recognition Science

Recognition Science models reality fundamentally as a discrete sequence of ledger events (Universal Forcing). However, macroscopic physics (like special relativity) formulates causality continuously, without referring to granular discrete step counts. This THEOREM-grade result bridges that gap. By formally stripping the discrete step parameter $n$ from the causal inequality, it demonstrates how macroscopic, path-independent light cones reliably emerge from discrete sequential bounds.

3. Reading the Formal Statement

• H : LightCone.StepBounds K U time rad: The assumption that single-step causal bounds hold given the underlying kinematics K, units U, and coordinate functions time and rad.
• {n x y}: Implicit parameters defining the step count $n$ and the initial and final events $x$ and $y$.
• h : Causality.ReachN K n x y: The hypothesis that event $y$ is causally reachable from $x$ in exactly $n$ steps.
• rad y - rad x ≤ U.c * (time y - time x): The physical conclusion. The spatial displacement is less than or equal to the speed of light $U.c$ times the elapsed time. The integer $n$ drops out entirely.

4. Visible Dependencies

The proof is a single tactic: simpa using (LightCone.StepBounds.cone_bound ... H h). This indicates that the mathematical heavy lifting—an inductive proof over $n$ steps—is performed by an upstream theorem (cone_bound) imported from the LightCone module. The cone_bound_export declaration acts strictly as a verification-level interface layer, adapting the signature for downstream continuous physics by hiding the explicit dependence on $n$.

5. What it Does Not Prove

This theorem does not prove that the single-step bounds natively hold for any given system; it takes LightCone.StepBounds purely as an input hypothesis H. It does not derive the magnitude of $c$ (which the framework establishes as exactly 1 in structural units elsewhere). Finally, it strictly concerns kinematics and makes no claims about holographic entropy or information capacity, which are handled independently in the same module via the OPEN/MODEL axiom cone_entropy_bound.