IndisputableMonolith.URCAdapters.ELProp
The module supplies adapter definitions for the energy level property in the Recognition Science URC framework. It introduces the energy level proposition and establishes that the property holds, building directly on cost function definitions. The module structure is minimal, serving as a bridge to incorporate the property into larger chain arguments with only Mathlib and Cost imports.
claimThe energy level proposition $P_{EL}$ together with the assertion that $P_{EL}$ holds, both derived from the cost function $J$ and the recognition composition law.
background
The module operates inside the Recognition Science setting imported from the Cost module, which supplies the J-cost function, defect distance, and related structures on the phi-ladder. No new foundational definitions appear here; the module simply packages the energy level property for adapter use. The local theoretical context is the unified forcing chain (T0 to T8) with its eight-tick octave and three-dimensional spatial outcome.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds the energy level consistency requirement into the main URC theorems and the overall forcing chain. It supplies the adapter needed to close the step from cost definitions to the phi-ladder mass formula and the alpha band constraint.
scope and limits
- Does not introduce new axioms or hypotheses beyond those in the Cost module.
- Does not contain any proofs or tactic scripts.
- Does not depend on any modules other than Mathlib and Cost.
- Does not appear in any downstream used-by relations.