v0.440.0 — FRONT 4 RE-SPECIFIED AND MEASURED SHIP

B286 (PAPER_2281): front 4 of the Navier-Stokes proof set - caught
mis-specified before any CPU, re-posed on the right observable, and then
MEASURED the same day with a simulation written from scratch. One band
since v0.439.0.

- THE DEFECT (the program's own; Rule 7): PAPER_2276 sec 6.4 asked the MD
  run to compare "the transverse current integrated over omega" with
  exp(-0.344 (k/k_c)^2). That integral is C_T(k,0) = N k_B T/m at EVERY
  wavenumber in any classical fluid at equilibrium - the equipartition
  identity, flat in k. A run would have "falsified" the roll-off while
  testing nothing.
- THE OBSERVABLE: the wavevector-dependent shear viscosity eta(k) from the
  transverse-current autocorrelation (Palmer 1994; Hess 2002; gmx tcaf) -
  the fluid's transverse-momentum TRANSFER at k. PREDICTION: eta(k)/eta_0
  = exp(-0.344 (k/k_c)^2), k_c = 5.31 nm^-1 (c_0) or 2.45 nm^-1 (c_inf);
  gmx-tcaf coefficient a = 0.344/k_c^2 = 0.0122 / 0.0570 nm^2. Falsifier
  stated before measurement.
- THE INSTRUMENT: the package index being unreachable, md_grade/
  md_engine.py - a rigid TIP4P/2005 water MD in numpy (RATTLE, virtual M
  site, O-O LJ + reaction-field Coulomb, site-based 0.9 nm cutoff) -
  validated on force/energy consistency (machine precision), energy
  conservation (-0.006 kJ/mol per molecule over 2 ps) and the model's
  potential energy (-47.5 vs -47.4 published). Every line ships in
  md_grade/ with the run script, analysis, log, NVE check and CSV.
- THE MEASUREMENT: 512 molecules, 240 ps, 26 k-shells to 13.8 nm^-1,
  eta(k) by the Green-Kubo integral with block errors. eta_0 1.05 mPa s.
  eta/eta_0 flat to k ~ 6 nm^-1, then rolling off to 1/e at 13.3 nm^-1 -
  MEASURED k_c = 7.8 nm^-1.
- THE READING: c_0 (5.31) - SAME SCALE, factor 1.47, NOT a precision
  match. c_inf (2.45) - EXCLUDED by a factor 3.2: the first fluid-side
  evidence on Q-247, and it points to c_0 = 1480 m/s. Shape (Gaussian vs
  Lorentzian) undecided at this quality; the second estimator gives k_c
  4.4, so c_0 sits between the estimators. Per the pre-stated falsifier
  this is NOT a pass of the 0.344 coefficient: the roll-off exists, on
  the sound-cone scale; the exact coefficient is not confirmed.
- Q-250 OPENED (is eta(k) the canonical reading of transfer). PAPER_2276
  carries a dated correction. Registry rows front4_specification,
  front4_eta_k_grade (GRADED), front4_measured_roll_off (FINDING).

Not claimed: front 4 passed or closed; one run, one box, one seed,
reaction field; the diffusion coefficient. Record run (8 nm, 1-2 ns,
PME) is the next instrument.

Gate 6,113/0. Dispatch 2,332 keys. Registry 7,132 rows. Acceptance
109/109 (simulator untouched).
