IndisputableMonolith.Mathematics.GodelTheoremsStructuralFromRS
This module derives structural analogues of Gödel's incompleteness theorems inside the Recognition Science framework. It organizes LimitativeResult and GodelTheoremsCert around the J-cost and phi-ladder to capture limitative phenomena. Researchers in foundations of physics and logic would cite it to link the forcing chain to incompleteness. The module contains no proofs and rests on the imported Constants declaration for its base time quantum.
claimThe module introduces $\text{LimitativeResult}$ and $\text{GodelTheoremsCert}$ as structural objects in the RS framework derived from the J-cost function and phi-ladder.
background
The module sits in the Mathematics domain and imports Mathlib together with IndisputableMonolith.Constants. The Constants module supplies the fundamental RS time quantum defined as $\tau_0 = 1$ tick. It establishes the setting for extracting limitative theorems from the Recognition Composition Law and the T0-T8 forcing chain.
proof idea
This is a definition module, no proofs. It structures the argument through the four sibling declarations LimitativeResult, limitativeResult_count, GodelTheoremsCert, and godelTheoremsCert.
why it matters in Recognition Science
The module supplies structural Gödel theorems that support the Recognition Science claim to derive physics from one functional equation. It aligns with T5 J-uniqueness and T7 eight-tick octave; no parent theorems appear in the used_by edges.
scope and limits
- Does not prove the classical Gödel theorems in Peano arithmetic.
- Does not connect to physical constants such as $\alpha$ or $G$.
- Does not address consistency statements beyond the RS structural setting.