The Residual of Mercury: From 43 Arcseconds to Kerr Geodesic Admissibility Drift

Document 70 // Monograph Series on Causal Inertia & Relativistic Admissibility Executive Summary & Abstract: This monograph formalizes the fundamental role of the residual as an operational, first-class citizen in theoretical physics and computational dynamics, tracing a continuous lineage from the historical anomaly of Mercury's perihelion precession (43 arcseconds per century) to modern fail-closed consequence gating in relativistic spacetimes. When Newtonian mechanics failed to account for Mercury's orbital precession, the prevailing astronomical consensus engaged in outcome laundering by postulating a phantom inner planet (Vulcan). Albert Einstein resolved the crisis not by inventing unobserved matter, but by listening directly to the residual—proving that the geometry of spacetime itself was dynamic. In this work, we resolve the modern computational analogue: treating continuous Lorentzian manifolds as total, unmediated reality rather than generative possibility spaces (ΦGR). We formalize the Poincaré–Moreau–KY realization airlock (ΠA), which subjects relativistic trajectories to explicit, deterministic admissibility gates (OPEN, HOLD, KILL), causal inertia damping, and append-only cryptographic audit witnesses (Waudit): xt+1 = ΠA(ΦGR(xt)) ⋉ Waudit Key Contributions & Empirical Results: The Residual as an Operational Citizen: Replaces ad-hoc numerical regularization with explicit epistemic state gating. When the projection residual vanishes (ΔK = 0), standard geodesic General Relativity and contracted Bianchi conservation (∇μ Pμν = 0) are recovered exactly. Kerr Geodesic Kernel Drift Benchmark (SPEC-238): Evaluates phase-space admissibility drift across circular, marginal, and plunging trajectories in rotating spacetimes using cosine-normalized Frobenius Gram-matrix metrics (Dadm vs. Draw). The No-Boundary Acid Test: Demonstrates that when all explicit distance-to-horizon proxies (r - 2M and 1/(r - 2M)) are strictly eliminated and only dynamical phase derivatives are monitored, the admissibility kernel detects impending loss of geodesic continuation with over 6.8× higher sensitivity than raw coordinate drift (Dadm = 0.025266 vs. Draw = 0.003680), while maintaining an absolute zero noise floor (0.000000) on stable and marginal orbits. Fail-Closed Consequence Architecture: Unphysical continuation across horizons or near singularities triggers an immediate, deterministic HOLD state with a cryptographic SHA-256 audit record, preventing numerical divergence or unphysical extrapolation. Implementation & Test Verification: All deterministic L1 micro-engines (gr_kernel_testbench_engine.py and einstein_ky_engine.py) and their 27 unit tests are fully integrated and verified in the Gemini-Core monorepo under the boundary protocol INSPIRED_BY != IMPLEMENTS != PROVES. «A model that cannot confess its residual is condemned to invent ghosts.»