IndisputableMonolith.Causality.ConeBound
Causality.ConeBound supplies cardinality bounds for finite causal cones constructed via successive steps in a discrete kinematic setting. Researchers working on light-cone structures derived from the J-uniqueness and phi fixed-point steps of the forcing chain would cite these results. The module assembles its content from basic finite-set cardinality lemmas applied to ball constructions.
claimUpper bounds on the cardinality of successor balls in a discrete kinematic graph are established, yielding finite growth rates for causal cones under bounded-step propagation.
background
Recognition Science models causality via the J-cost functional and the self-similar fixed point phi. The module introduces supporting definitions for bounded propagation steps and kinematic relations that enable cone-size arguments. It imports only Mathlib and relies on standard results for finite sets, unions, and neighbor cardinalities.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies supporting cardinality controls that feed into parent results on causal structure within the unified forcing chain, particularly those leading to D = 3. It closes discrete-cone gaps before application to higher-level kinematics and dimension derivation.
scope and limits
- Does not derive cone bounds directly from the J-functional equation.
- Does not treat continuous or relativistic limits.
- Does not connect to mass ladder or fine-structure results.
- Does not address quantum or Berry-threshold effects.