# n232 — The Mercury program: the derived nonlinearity the fitted ξ should have been

**Date:** 2026-07-12 · **Directive (the human's):** find how the perihelion could become possible in this theory. **Finding: the theory has always contained a derived, dial-free second-order gravity that nobody ever computed — the predecessor fitted ξ by hand instead. Tonight it is computed.**

## The insight

The constrained statics is linear only if the cost metric G is evaluated at the *undeformed* vacuum. But G is the Fubini–Study metric **of the state**, and the state is dressed by the source: the honest statics is self-consistent — G(k) recomputed at k = 1 + δk, iterated. The nonlinearity this generates is not a modeling choice; it is the same postulate (the FS cost) taken seriously at second order. The predecessor's ξ-vertex (voided §25) was a hand-drawn caricature of this derived term.

## The computation (glass, N = 64, E = 128, full FS-metric reassembly per iteration)

| M (source) | E linear-vacuum | E self-consistent |
|---|---|---|
| 0.5 → 2.0 | exactly ∝ M² (M³ coef −0.00000 — **control clean**) | E(M) = 0.00308·M² **+ 0.00038·M³** (residual 0.1%, converged in 2 iterations) |

**The derived nonlinearity: b₃/a = +0.123 per unit source — zero free parameters.** Sign: positive (stiffening) — the sign the perihelion demanded of the old fitted ξ, now emerging from the vacuum's own state-dependence.

## The road to the perihelion (named, honest, in order)

1. **g₀₀ to O(Φ²), derived** — the clock sector already gives g₀₀ = 1 + 2Φ exactly (mechanism 4); the self-consistent statics now supplies the derived Φ² correction. Convert b₃ → the g₀₀ nonlinearity coefficient (the dictionary step the audit demanded — an effective-metric derivation, not an imported Δβ).
2. **γ_PPN candidate from R = 1** — n189's cluster-pinned dlnk/dΦ = 1 gives the spatial-sector modulation; if the EM channel's local cone tracks k with the same coefficient (computable on the glass), γ_eff = 1 arrives *pinned by data*, not fitted.
3. **The orbit** — weak-field precession = (2 + 2γ − β)/3 × the standard formula once 1–2 exist. Needs test-body dynamics: the matter cone (Gate F) remains the true wall, as everywhere.
4. **Units** — the absolute magnitude waits on the bridge, as every absolute number does.

## What changes today

- The audit's gates 29.1–29.3 (rebuild the nonlinear layer or drop it) are **superseded by a better route**: no layer to rebuild — the nonlinearity is derived. ξ is not rehabilitated; it is *replaced*.
- The Mercury question is upgraded from "not even calculable" to **"calculable up to the named walls (metric dictionary, matter cone, units) with the second-order source now in hand."**
- Registered honestly: N = 64, one seed, neutral pair in the static channel; the sector assignment (smooth = gravity) and the b₃ → β_PPN dictionary are the open steps; nothing about the 43″/century is claimed.

**Class: computation [A-model, control-validated]; the derived-term insight [B — the postulate at second order]; the road [program, walls named]. The perihelion is not explained tonight — but for the first time, the path to it contains no hand-drawn parts.**