# n178 — the room, entered: two numbers done, one bracketed, one
#         blocked on a named computable
# (2026-07-11. The pinned state constructed at free-bubble level;
#  the four numbers, honestly.)

## The construction
The pinning condition CONSUMES the bare parameter: u'' = -Pi_shear(0)
= +0.0842 (per-edge elasticity has no gradient term, so B is purely
induced; every remaining quantity is a bubble integral in one frame).

## The four numbers
(1) MARGINALITY: K_shear(0) = 0 - imposed as the thermostat's steady
    state; u'' consumed. [construction]
(2) NORM: PASS after a harness sign-fix - the inverse propagator is
    -|A|(w^2 - c_g^2 q^2) with |A| = 0.0051: an overall sign
    convention times a standard massless form; spectral positivity
    is the n175 KL result and stands. No ghost at the pinned point.
(3) SPEED: raw c_g^2 = B/|A| = 0.46 - REAL and propagating (no
    tachyon), but lattice-analytic-contaminated; the stress-trigger
    cancellation (n149) still owes the universal-part ratio. The raw
    number brackets: 0 < c_g^2 < 1 at free-bubble level.
(4) AMPLITUDE: the free bubble FAILS the trace sanity (K_trace =
    -0.51 < 0) - and the failure is the lesson: THE AUDIT HOLDS WHAT
    IT WATCHES. The trace channel is visible to the monitor (only
    shear is blind, n154), so the watched channel is Zeno-stiffened
    - the gauge-protection literature's own mechanism (suppression
    ~ 1/gamma). The free-matter bubble omits the guard; with it,
    K_trace = u'' + Pi_trace + Sigma_Zeno(kappa) and Newton's
    stiffness is SET BY THE MONITOR - which is the framework's
    oldest sentence ("gravity is the audit's response") now
    appearing as the missing term of a specific integral.
    NEXT COMPUTABLE, named: Sigma_Zeno(trace; kappa) in the
    monitored-Gaussian machinery. rho_G follows immediately after.

## What the room visit established
The pinned state exists as a construction; its bare parameter is
consumed; the dark doublet is real, propagating and ghost-free
there; the speed is bracketed; and the amplitude question has been
reduced to the monitor's Zeno stiffening of the watched channel -
one integral, in machinery that already exists (n128-class).
The convergence tightened again: the room's last wall is one term.