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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.

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confidence: high in recognition cached

Explanation of cone_bound_export in IndisputableMonolith.ConeExport.Theorem

(1) In plain English, the declaration states: given an assumption H that per-step radial and temporal bounds hold for a light cone (under kinematics K and units U), then for any points x and y reachable from each other in n steps, the radial separation satisfies rad y - rad x ≤ U.c * (time y - time x). The step count n disappears from the final inequality.

(2) In Recognition Science this matters because it exports the discrete light-cone bound at verification level without retaining the step parameter, enabling direct use of causal inequalities in the RS framework while preserving the underlying voxel/tick structure (c = 1 voxel/tick).

(3) The formal statement is read as: theorem cone_bound_export (H : LightCone.StepBounds K U time rad) {n x y} (h : Causality.ReachN K n x y) : rad y - rad x ≤ U.c * (time y - time x). Here H supplies the step-wise bound hypothesis, h witnesses finite-step reachability, and the conclusion is the integrated cone inequality. The proof reduces via simpa to the underlying cone_bound lemma.

(4) Visible dependencies in the supplied source are the imports IndisputableMonolith.Causality.Reach, IndisputableMonolith.LightCone, and IndisputableMonolith.Constants; the theorem itself; and the sibling declaration cone_entropy_bound (which relies on the ConeEntropyFacts class). No other declarations from the supplied modules are referenced.

(5) This declaration does not prove the step bounds H (they are an input), the definitions of LightCone or ReachN (imported), or the entropy bound (left as a class axiom). It also does not address the broader forcing chain or constant derivations present in other supplied modules.

See cone_bound_export and cone_entropy_bound.

cited recognition theorems

outside recognition

Aspects Recognition does not yet address:

  • Definitions and proofs of LightCone.StepBounds, Causality.ReachN, and the underlying LightCone module (only imported, not supplied).
  • Any connection to the forcing chain, Alexander duality, or constant derivations in other supplied modules.

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.