LXXVIII-A: Numerical Evaluation of the Sunset–Tadpole Ratio in the Extended TT Truncation (Bridge-Stage Evidence Bundle)

# LXXVIII-A: Numerical Evaluation of the Sunset–Tadpole Ratio in the Extended TT Truncation (Bridge-Stage Evidence Bundle) This repository contains the complete, cryptographically verified computational evidence bundle for the LXXVIII-A bridge-stage of the History-Dependent Gravity (HDG) research program. It establishes numerical reproducibility, measures the first Level-2 truncation effect, maps method stability boundaries, and quantifies regulator dependence without post-hoc tuning. ## Key Scientific Results1. **Reproducibility**: Machine-precision replay of the LXXV Q11C baseline and algebraic/numerical recovery of the $K_2 \equiv K_0$ limit.2. **Level-2 Truncation Effect**: Controlled substitution $K_0 \rightarrow K_2$ yields a measurable truncation effect of $\delta R_{TS} = +22.775\%$ (Litim scheme, $p/k=0.05$).3. **Numerical Stability Boundary**: Finite-difference extraction of 3rd and 4th order vertices amplifies roundoff as $\mathcal{O}(\epsilon^{-3})$ and $\mathcal{O}(\epsilon^{-4})$. The working point $\epsilon_{fd}=10^{-4}$ is established as a practical floor; refinements to $10^{-5}$ are numerically unreliable.4. **Scheme Dependence**: The diagnostic ratio $R_{TS}$ exhibits substantial regulator dependence ($\Delta_{reg} \approx +25.6\%$) when comparing Litim and Exponential regulators within the finite integration domain ($x_{max}=1$). ## Honest Limitations- Full convergence at $\epsilon_{fd}=10^{-4}$ is not strictly proven (isolated quadrature test was halted).- Regulator comparison is restricted to the finite domain $x_{max}=1$; full UV-tail comparison is deferred.- The default extended-range JSON output from A.3 was overwritten during F3 ablation runs; combined A.3 $R_{TS}$ values are preserved and verified via `a3_comparison.json`.- Scheme independence is not established in the current truncation and requires further extensions (e.g., vertex dressing, scope of LXXVIII-B). ## Evidence Chain IntegrityThe principal computational stages were defined in the LXXVIII-00 acceptance contract. Completed evidence artifacts are hash-verified, and incomplete branches are explicitly identified. See `LXXVIII_A_master_manifest.json` for the complete cryptographic manifest, environment fingerprint, and cross-references. ## Directory Structure- `A.1/` – Frozen provenance replay- `A.2/` – Algebraic and numerical recovery- `A.3/` – Finite Level-2 evaluation and forensics- `A.4/` – Convergence limits and FD sensitivity diagnostics- `A.5/` – Regulator diagnostic (Exponential vs Litim)- `A.6/` – Stop-gate assessment and frozen configuration- `LXXVIII_A_master_manifest.json` – Master cryptographic manifest of all artifacts