# n129 — the tensor junction, opened
# (2026-07-11; n122 item #4, first engagement. Script: n129_junction_opened.py)

## J1 — the rotation fork, resolved (exact)
The audit reads budget violations A.J + dc/dt. For a stationary
axisymmetric rotator, dc/dt = 0 and the co-rotating maintenance flux
is divergence-free: the violation vanishes IDENTICALLY (lattice
check: max|A.J| = 0.0 for a loop current — machine zero, and it is
structural, not numerical). STATIONARY ROTATION IS AUDIT-DARK —
consistent with prediction 15 (the achiral audit) and n101 (the
resting proton), and now load-bearing:
FRAME DRAGGING CANNOT BE AN AUDIT RESPONSE. In this framework it
must be KINEMATIC — the advection of the emergent metric by the
substrate's maintenance flow: the acoustic-metric channel,
   g_0i = -v_i(maintenance flow).
THE JUNCTION'S TARGET EQUATION (LARES-2's 1e-3, inherited whole):
   v(r) around a rotating body  =  2 G J_ang / (c^2 r^3) x r_hat
The remaining half of the junction is the ADVECTION COEFFICIENT:
does the maintenance flow of a rotating budget co-rotate with
exactly the GR profile? Computing it needs the momentum sector
(how budget flux carries the source's angular momentum) — now a
single named calculation instead of a missing organ.

## J2 — where spin-2 lives (measured)
The emergent metric is BILINEAR in substrate correlations
(G_ef ~ Tr[Omega^-1 dOmega]^2), so graviton candidates are
two-phonon composites — the standard emergent-gravity route around
Weinberg-Witten. Measured on the 3D lattice vacuum:
  TT-projected fraction of the gradient-bilinear channel:
    0.281 / 0.288 / 0.296 at three q's — HELICITY-2 FLUCTUATIONS
    EXIST, carrying ~30% of the channel.
  Two-phonon spectral edge at momentum q: edge/(c q) = 1.000 at all
    three q's — THE HELICITY-2 CHANNEL IS LIGHTLIKE-EDGED. Composite
    gravitons ride the same cone as everything else (c_GW = c is
    structural at the composite level too).
Honest flags: an EDGE is not a POLE — a sharp graviton resonance
needs the interacting theory (the pump's stiffening is the natural
binder; unpriced). And ~30% TT weight is kinematics, not dynamics:
the coupling of the TT channel to sources with GR's coefficient is
exactly what the quadrupole-formula derivation must produce.

## The junction's remaining ledger (from four watchers to two calculations)
1. THE ADVECTION COEFFICIENT (J1's fork): v-field of a rotating
   budget vs 2GJ/c^2 r^3 — decides Lense-Thirring at 1e-3.
2. THE TT SOURCE COUPLING (J2's fork): the rate at which the audit's
   response feeds the TT bilinear channel — decides the quadrupole
   formula at 1.3e-4 and GW transparency.
gamma_PPN and beta are already held by locks and the derivative
layer; the junction is now two calculations wide, both named.