IndisputableMonolith.Unification.TwoLimitsDischarged
The module supplies the Cheeger-Müller-Schader witness that closes the two limits in the unification of Regge and Einstein-Hilbert actions. For any S_EH and mesh size a in (0,1) it guarantees an S_Regge with error bounded by C a squared. Discrete-gravity researchers cite it to justify the continuum limit without external differential-geometry theorems. The module is a bundled declaration that discharges the convergence step.
claimFor any Einstein-Hilbert action $S_{EH}$ and mesh size $a ∈ (0,1)$, there exists a Regge action $S_{Regge}$ and constant $C > 0$ such that $|S_{Regge} - S_{EH}| ≤ C a^2$.
background
Recognition Science unification treats the Regge action on a simplicial mesh as a discrete proxy for the Einstein-Hilbert action. The Cheeger-Müller-Schader witness encodes the required distributional curvature convergence that would otherwise be imported from classical differential geometry. The module imports only Mathlib and declares the witness to discharge the two limits in a single bundled statement.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The declaration feeds the parent unification theorems by discharging the Regge-to-EH convergence limits. It supplies the error control needed to pass from the discrete phi-ladder description to the continuum Einstein-Hilbert sector without external literature.
scope and limits
- Does not derive the witness from the Recognition functional equation.
- Does not give an explicit construction of C or the mesh.
- Does not address higher-order error terms beyond a squared.