# n165 — the projection test: TT perfect, the leak localized, the
#         blocking computation identified
# (2026-07-11, mandate. The four-budget draft meets its own gate.)

## The measurement
Projection of source channels onto the physical dark space (q || z):
   '+' : 1.0000    'x' : 1.0000     [the TT pair: fully radiative]
   transverse trace (the eccentric-binary channel): 0.42-0.57
   h_zz: 0.82-0.88
The draft's dark space still admits ~25-30% of an O(1) scalar
channel: the four-budget FIRST DRAFT does not yet pass Hulse-Taylor.

## The gauge quotient (progress, and the survivor)
Physical modes = dark modes MODULO sym(grad u) (the substrate
relabelings - the quadrilemma's corner iii, now used as the gauge
group). At q || z the gauge span is {h_zz, h_xz, h_yz}: the vector
pair and the zz-content quotient away. THE SURVIVOR: the transverse
trace h_xx + h_yy is GAUGE-INVARIANT - it cannot be quotiented; it
must be WATCHED or it radiates.

## The diagnosis (this turn's result)
GR's Hamiltonian constraint at momentum q watches EXACTLY the
transverse trace: (delta_ij q^2 - q_i q_j) h_ij = q^2 (h_xx + h_yy)
at q || z. Our energy row (the unsigned incidence, 1 + e^{-iq.d})
watches the all-direction sum at q -> 0 and a LONGITUDINALLY-
weighted combination at O(q^2): THE WRONG TENSOR STRUCTURE at
radiative order. The founding budget row is correct for statics
(q -> 0 counting) and insufficient for radiation (O(q^2) structure).

## THE BLOCKING COMPUTATION (single, named)
Derive the constraint rows - energy AND momentum - from the Action's
own conservation laws at O(q^2), not as ansatze. The spec is now
exact: the derived energy row must reproduce the transverse-trace
watching of GR's Hamiltonian constraint, and then the radiative
dark space is {+, x} exactly: GR's radiation content, derived.
Everything else in the gravity checklist (normalization, Weinberg)
queues behind this one derivation.