# n157 — the polarization audit: the graviton count, exact
#         transversality for '+', and the breather in the chamber
# (2026-07-11, loop tick. The junction's penultimate calculation.)

## The wins (both exact)
1. THE GRAVITON COUNT IS STRUCTURAL: dim ker A(q) = d - 1 = 2 at
   every momentum (one unsigned-incidence constraint on d edge
   polarizations). The framework produces exactly TWO dark metric
   polarizations in 3D - the graviton's count, from constraint
   counting alone.
2. EXACT TRANSVERSALITY FOR '+': the mode h_xx - h_yy (q || z) has
   |A.v| = 0.0 at EVERY q - identically dark, identically marginal
   (the thermostat applies), identically transparent. One of GR's
   two tensor polarizations comes out perfect. (The 'x' polarization
   needs off-diagonal h_xy - absent on the square lattice without
   diagonal edges: a truncation artifact, named, not physics.)

## The loaded chamber: the breather
The second dark mode is a traceless-at-q->0 BREATHER
(h_xx = h_yy, h_zz growing with q). It is exactly dark (|A.v| ~ 1e-17),
so the thermostat makes it marginal and massless TOO - and stress
conservation does NOT automatically decouple it from sources
(checked: its source overlap ~ 0.37(T_xx+T_yy) - 0.75 T_zz-mix does
not vanish for generic compact sources). Dynamic blindness also
holds (linearity: an A-dark mode's time derivative is A-dark).
CONSEQUENCE, stated at full volume: as it stands, the framework
predicts a SCALAR-LIKE GW POLARIZATION alongside the tensor one -
in direct tension with its own prediction 17 (pure tensor, forever)
and with LIGO-Virgo-KAGRA polarization fits. THE JUNCTION'S ENDGAME
NOW HAS ONE QUESTION: find the breather's decoupling mechanism
(candidates: a projection hidden in the source coupling's derivation;
mixing with the audited trace at finite omega; the h_xy completion
restoring the proper TT projector), or the breather kills the
framework with its own registered kill condition. Either way, the
next computation is FORCED and named: THE BREATHER'S COUPLING.

## The junction scoreboard after n157
count: DELIVERED (2, structural) · transversality('+'): EXACT ·
masslessness: DERIVED (n156) · transparency: EXACT (n154) ·
speed: selected (n149) + inherited (universal part) ·
normalization + Weinberg: pending · THE BREATHER: loaded, chambered,
aimed at prediction 17. The theory's gravitational-wave sector is
one decoupling away from complete - or one polarization measurement
away from dead.