Track1MixedAxisCoeffSoundnessToExplicitFiberEndpoint
plain-language theorem explainer
Packaging endpoint for Session 213 Track 1.B: if the real explicit-fiber residual matches the rational coefficient expansion at N=5, the corrected mixed axis-stencil target follows. Track 7 fork-handoff integration cites it as a coefficient-soundness bridge, not a discovery claim. Defined as a pure implication Prop; a companion theorem discharges it by an existing packaging lemma.
Claim. The proposition that coefficient soundness of the explicit-fiber axis stencil at $N=5$ (for every vertex potential, the real residual equals its unordered rational monomial expansion) implies the canonical periodic mixed-hinge deficit explicit-fiber axis-stencil target at $N=5$.
background
This module is the Track 7 integration-lane receipt for parallel fork handoffs in the gravity master theorem. It records what new endpoints prove without upgrading the discovery claim, and keeps remaining Track 1 displacement-class leaves as open dependencies.
The hypothesis side is coefficient soundness at $N=5$: for every five-vertex potential, the real explicit-fiber axis-stencil residual equals the unordered monomial expansion of the rational residual coefficients. Upstream docs call this the remaining algebraic packaging surface after Session 212 closed every coefficient.
The conclusion is the global explicit-fiber coefficient-table target specialized to $N=5$ (with the three size witnesses decided). Its closure is exactly the corrected mixed axis-stencil target used by the Track 1.B stationarity reduction path.
proof idea
Pure definitional packaging: the declaration is the implication Prop itself, not a proof. The companion theorem track1_mixed_axis_coeff_soundness_to_explicit_fiber_endpoint_holds discharges it in one step by applying canonicalPeriodicMixedHingeDeficitExplicitFiberAxisStencilTargetAtN5_of_coeffSoundness, which turns coefficient soundness into the corrected $N=5$ mixed axis-stencil target.
why it matters
Session 213 Track 1.B packaging endpoint consumed by Track 7. It feeds the fork handoff integration certificate as part of the Track 1 reduction/interface package (not a closure of open Schläfli leaves) and is witnessed by the companion ..._holds theorem.
In the Recognition gravity stack this sits on Fork A (Track 1.B stationarity reduction at $N=5$): once residual coefficients are identified with the rational model, the corrected explicit-fiber axis-stencil target is available to downstream stationarity and mixed-hinge deficit arguments. It does not finish the master theorem; it only tightens the coefficient bridge the structural witnesses still rely on.
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