# n112 — the Nordtvedt run: RESULTS
# (2026-07-10; the gun pre-registered in n111 attack 6, fired same day.
#  Scripts: n112_nordtvedt_run.py (1D), n112b_nordtvedt_3d.py (3D probe),
#  n112c_nordtvedt_charge.py (final method), n113_derivative_mercury.py,
#  n114_pump_bill_derivative.py)

QUESTION: does interaction/self energy re-enter the gravitational
SOURCE at order xi with one universal coefficient (eta_N = 0), or is
the coefficient composition/structure/separation dependent (killed by
LLR at 1e-4, MICROSCOPE at ~1e-12)?

## The method fought back twice (recorded, per the n61/n87b tradition)
1. 1D ring: gate N4 (monopole cleanliness) FAILED 64% — on a ring the
   order-xi effective source phi_A*phi_B is global; no far-field
   monopole exists. The pre-declared 1D IR caveat triggered; verdict
   deferred to 3D. (The N2/N3 failures in 1D are therefore VOID.)
2. 3D point-probe readings: all gates failed including the one that is
   an exact identity — diagnosis: periodic-image + zero-mode background
   contamination (E_int itself was not box-converged). Method replaced
   by TOTAL EFFECTIVE CHARGE extraction (for a localized effective
   source, the far-field monopole shift IS -xi*Q_eff; no probe).

## RESULT 1 — the Nordtvedt identity (theorem on the lattice)
For DERIVATIVE anharmonic coupling (effective source (grad eps)^2),
with compatible discrete operators (forward differences, L = D^T D):
   Q_cross = sum 2 grad(phiA).grad(phiB) = 2 phiA(B) = 2 E_int
   Q_self  = sum   grad(phiA).grad(phiA) =   phiA(A) = 2 E_self
EXACT — residuals 1e-14..1e-16, every separation, every box:
   k_self = k_cross = 2.000000000000.
Self energy and interaction energy source with the SAME coefficient
by discrete integration by parts: ETA_N = 0 AS AN IDENTITY, for every
composition, structure, separation. LLR (eta = (-0.2+/-1.1)e-4) and
MICROSCOPE (1e-15 UFF) become structural passes; any CONFIRMED
Nordtvedt-type violation is now a clean kill. Promoted to
prediction 23.

## RESULT 2 — the cubic layer is dead (headstone 29)
For the CUBIC potential vertex (n87b's layer, effective source eps^2),
the effective charge DIVERGES LINEARLY with the box:
   Q_A(d=6): 0.148 (n=24) -> 0.289 (32) -> 0.442 (40) -> 0.600 (48)
(int of phiA*phiB ~ int dr: linear, as dimensional analysis says).
The cubic anharmonicity cannot define a far-field Nordtvedt
coefficient AT ALL in 3D — it fails as the post-Newtonian layer, not
by a wrong number but by having none. The Nordtvedt gate SELECTS
derivative coupling — the same selection GR itself makes (its
nonlinear source is field energy, (grad phi)^2, not phi^2).
Cause of death: IR-divergent second-order charge. Buried 2026-07-10.

## RESULT 3 — the chain re-closed the same day
The Mercury calibration and the Lambda-sign chain were cubic-layer
results — suspended at RESULT 2, re-run with the derivative vertex:
- n113 (exact first-order perturbation; the n87b solver lesson
  applied after the Newton iteration diverged — recorded):
     Delta-beta = (+2.163)*xi   [cubic pipeline check: +542.8*xi,
     sign reproduced]. Mercury (Delta-beta = +1/2) demands xi > 0:
     SAME sign demand. Mercury re-delivered; in-situ xi = +0.231
     (this convention).
- n114 (n87c rerun, every eps_a^2 vertex -> (eps_{a+1}-eps_a)^2;
  gates L1-L4 re-declared): bill = +1315*xi^2, L1 machine-zero,
  L2 even, L4 sign stable over N in {6,8}, g in {0.1,0.2},
  kappa in {2,3}. LAMBDA > 0 SURVIVES THE LAYER SWAP.
  Observation: the bill is branch-independent (active = passive to
  all digits) — Lambda's sign does not depend on the branch; the
  attraction/repulsion dichotomy lives in the mediated force, not
  in the idle metabolism.

## Balance
The refutation hunt's third sweep produced: one headstone (29: the
cubic layer, killed by our own pre-registered gate), one lattice
theorem (eta_N = 0 exact for the derivative layer), one new
prediction (23), and a same-day re-closure of the Mercury-Lambda
chain on the surviving layer (+2.163*xi, +1315*xi^2). The theory is
harder to vary than it was this morning: the anharmonic layer is no
longer a choice — the Nordtvedt gate forces the derivative form,
and GR agrees about why.