track1ForallDispStationarityEndpointProjectionCount_eq_one
plain-language theorem explainer
The audit projection count for the direct uniform seven-displacement stationarity handoff endpoint equals one. Gravity Track 7 integrators cite it as the Session 563/568 receipt that the forall-displacement stationarity leaf is a single closed projection, not a multi-leaf residual. The proof is reflexivity: the count is defined to be 1.
Claim. The natural-number audit count attached to the Track 1 uniform (forall-displacement) stationarity handoff endpoint equals $1$.
background
This module is the Track 7 integration-lane receipt for parallel gravity fork handoffs (Tracks 1.B stationarity reduction, physical residual/Bianchi, many-body amplitude lift, Page-capacity, dark-energy $w(z)$, and falsifier sensitivity). It records what the new endpoints prove without upgrading the discovery claim; remaining Track 1 displacement-class leaves stay as open dependencies.
The counted object is the Session 563 audit projection for the direct uniform-stationarity handoff: a $\mathbb{N}$-valued flag that the forall-displacement stationarity target has been reduced to a single closed projection. Upstream gravity structure (Regge TT hinge-aware zero modes, $J$-Ehrhart span and posting-layer floor gaps, ledger total as conjugate to imbalance, and uniform Shannon distributions) supplies the stationarity and displacement-symmetry language that the endpoint packages, but this declaration only freezes the count.
proof idea
One-line term proof by rfl. The definition track1ForallDispStationarityEndpointProjectionCount is the literal natural number $1$, so equality to $1$ is definitional. No lemmas are applied.
why it matters
In the Track 7 fork-handoff ledger this is the Session 568 receipt that total stationarity plus displacement symmetry closes the uniform seven-displacement stationarity target as a single projection. Sibling endpoints in the same module cover Schläfli reduction, disp0 base-vertex and stationary reductions, seven-stationarity, and the Track 2 many-body lift; this one freezes the forall-disp stationarity audit count so integrators can treat that leaf as discharged rather than multi-way open.
It does not itself prove stationarity or the Recognition forcing chain (T5 $J$-uniqueness, T7 eight-tick octave, etc.). It is bookkeeping that the handoff projection multiplicity is one, keeping the remaining displacement-class leaves as the next dependency. No downstream theorems currently consume it.
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