# n162 — the breather's true executioner (and a correction to n157)
# (2026-07-11. The continuous-refinement mandate's first act: sharpen
#  the loaded chamber into a quantitative bound.)

## The correction (n157 was wrong in detail, at full volume)
n157 said "one polarization measurement away from dead" via LVK.
WRONG IN DETAIL: the breather's source is the transverse trace
I_xx + I_yy = m r^2 - CONSTANT for circular orbits. Quasi-circular
mergers emit NO breather radiation at leading order; LVK polarization
fits on binaries are structurally BLIND to this mode. The danger was
real, the executioner misidentified.

## The true executioner: eccentric-binary decay
An eccentric orbit breathes: r(t) varies. Computed on the Hulse-
Taylor eccentricity (e = 0.617):
   <(I_trace''')^2> / <(I_+''')^2> = 0.055
An O(1)-coupled breather adds ~5% to the orbital decay; PSR B1913+16
matches GR at 1.3e-4. BOUND:
   (g_breather / g_tensor)^2  <  2.4e-3
THE BREATHER MUST COUPLE BELOW ~5% AMPLITUDE OF THE TENSOR, or the
framework died in 1982 without knowing it. The chamber is no longer
merely loaded - it has a trigger pressure, measured.

## What can supply the suppression (the candidates, ranked)
1. The h_xy completion: the square lattice's missing off-diagonal
   components distort the kernel; the full complex may rotate the
   dark space toward pure TT (the n159 hint, option b).
2. Dynamic mixing: the breather's h_zz component grows with q
   (n157) - at finite omega it may mix into the WATCHED trace and
   inherit a width (partial cooling -> stiffening -> not marginal).
3. Nothing - and the framework carries a scalar GW mode at < 5%
   coupling as a PREDICTION: eccentric systems radiate slightly
   more than GR says, just below current precision. (A live,
   falsifiable remainder: improved timing of eccentric pulsars
   would see it - or kill it.)
Next computation of the mandate: candidate 2 (the dynamic mixing is
computable with the n147 machinery at finite omega).

## The mandate's ledger (gravity-complete checklist, standing)
statics+PN: done · masslessness: derived · '+' polarization: exact ·
transparency: exact · speed: conditional theorem · breather: bounded
at 2.4e-3, mechanism pending · 'x' mode: truncation, pending ·
coupling normalization (G): pending · EIH+quadrupole via Weinberg:
pending the above. THE STOP CONDITION IS NOT YET MET.