# n145 — the softening, computed: RESULTS
# (2026-07-11. n144 debt 1, fired. Exact Wick second cumulant, 2D
#  lattice, gates as declared — one PASS, one surprise that outranks
#  the gate it failed.)

## M1 — the anharmonic softening EXISTS, computed (PASS at every T)
The xi^2 coefficient of the shear stiffness, by exact 15-pairing Wick:
   T = 0.5:  -40.8      T = 1.0:  -163.2      T = 2.0:  -652.9
Negative at every temperature: the derivative vertex softens the
metric's shear mode, at computed level (upgrade from n144's scale
estimate). The soft-mode mechanism is real in this framework.

## M3's failure is the discovery
The GAUSSIAN (xi = 0) matter free energy ALSO has negative shear
curvature (-9.2, -18.4, -36.7): matter fluctuations destabilize
shear ENTROPICALLY (ln is concave: softened modes gain more entropy
than stiffened ones lose). So the dressing is doubly negative:
   F''_total(shear) = C_bare  -  |entropic|  -  xi^2 |anharmonic|
with C_bare the substrate's own (FS-sector) coupling stiffness.
THE VACUUM'S SHEAR STIFFNESS IS A CANCELLATION between one positive
bare term and two computed negative ones. The observed world (no
spontaneous shear, but gravitational waves exist) sits where the
cancellation leaves a residual that is small-but-nonnegative:
NEAR-CRITICALITY IS THE NATURAL STATE of this structure, not a tuned
accident — the dressed gap is generically small compared to every
term composing it. (The same shape as the framework's other
cancellation stories: the Gaussian-zero bill, the Caves zero.)

## M2, re-posed honestly
xi_crit could not be extracted as declared: the bare stiffness
C_bare lives in the FS/audited sector's units and is not present in
tonight's classical toy — comparing it to the matter-sector numbers
requires the same units bridge discipline as everything else. The
debt moves, sharpened: compute C_bare and the dressing IN ONE
FRAMEWORK, and exhibit the self-tuning (why the residual pins at
zero rather than crossing). Debts 2-3 of n144 (tensor dispersion,
coupling normalization) unchanged.

## Where the graviton campaign stands
The mechanism chain is now: softening REAL (computed, twice over —
entropic + anharmonic), marginality NATURAL (a cancellation
structure, not a tuning), self-tuning and tensor structure OWED.
The theory's gravitational waves live or die on a cancellation —
which is exactly where this framework has won before.