IndisputableMonolith.Causality.Basic
The Causality.Basic module supplies core definitions for discrete reachability and ball predicates that model causality in the Recognition Science framework. Researchers developing ledger uniqueness and potential lemmas cite these primitives as the starting layer for T4 arguments on reach sets. The module contains only definitions and imports from Mathlib, with no internal proofs or higher chain steps.
claimThe module introduces the reachability predicate $Reaches(x,y)$ and ball predicate $inBall(r,x,y)$ together with the auxiliary $ReachN$ and monotonicity properties such as $inBall_mono$.
background
In the Recognition Science setting, causality is expressed through discrete reach sets rather than continuous light cones. This module defines the basic kinematics layer via ReachN for n-step reachability, the inBall predicate for finite-radius neighborhoods, and the Reaches relation that composes them. It imports Mathlib for foundational logic and sets the notation used by all downstream causality modules without referencing the forcing chain or phi-ladder.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds the BallP, LedgerUniqueness, and Potential modules, supplying the discrete reach sets required for dependency-light T4 uniqueness lemmas on reach sets. It occupies the initial causality layer before any uniqueness or potential arguments are developed.
scope and limits
- Does not prove any uniqueness statements.
- Does not reference the J-function or phi fixed point.
- Does not address continuous limits or higher-dimensional extensions.
- Does not contain mass formulas or physical constants.