A genuine high-energy (UV) completion of the framework requires that the one-loop quantum corrections of the frozen 13D graviton-plus-ghost spectrum be finite and well-behaved. The single named object that this turns on is the sixth Seeley–DeWitt heat-kernel coefficient, tr[a₆], of the de-Donder graviton operator on the frozen geometry M₄×K₆×S²×S¹_Y, projected onto the cubic-curvature (mass-dimension-6) basis. This gate asks whether that coefficient can be computed from the frozen spectrum and whether a finite, positive value would actually constitute a UV completion.
The frozen 13D geometry fixes the operator whose heat kernel is being expanded: it supplies the graviton and ghost bundles, their holonomy decomposition under K₆×S²×S¹_Y, and the background curvature invariants that feed the a₆ functional. So the geometry makes the question well-posed and pins the clean, scale-free content — in particular an exact dimensionless ratio (the color factor) that has been dual-validated against independent sphere cross-checks. What the geometry does not do is supply a UV completion: it sets up the coefficient, it does not certify that the coefficient closes the high-energy problem. Given the spectrum is not the same as deriving the spectrum, and a single coefficient is one term in an unbounded tower.
Badge: OPEN (the magnitude is scheme/scale-anchored). No status was ever upgraded.
This is a serious candidate / partial-unification gate — not validated. It touches none of the famous walls: it is a finite-matching question, not a route across the Yang–Mills mass gap or the cosmological constant.
A concrete (heavy, but in-principle finite) path exists for the bulk; the no-go sits at the total and the sufficiency. Closing the gate requires, in order: (1) fix the shared one-loop scheme object so the magnitude stops riding an injected scale; (2) correct the curvature input feeding the engine; (3) obtain the Z₂ orbifold-defect coefficient — currently blocked pending an order-6 mixed-boundary heat-kernel result that does not yet exist in the literature — and assemble the total; (4) construct the positivity test and its adjudication rule (MO-10/MO-11); and (5) settle the field-level question (MO-12) of whether a finite, positive a₆ earns the words "UV completion" at all. Step (5) is shared with quantum gravity broadly and has no known short route here.
Status: OPEN. The scale-free content is genuinely derived and cross-checked; the dimensionful magnitude, the total coefficient, its positivity, and its sufficiency for a UV completion all remain open.
This gate asks a single well-posed question: take the frozen 13-dimensional geometry, read off the graviton-plus-ghost operator it fixes, and compute one named term in its short-distance (heat-kernel) expansion — the sixth Seeley–DeWitt coefficient, tr[a₆], projected onto the cubic-curvature basis.
It rests on: the frozen 13-dimensional invariant geometry; the graviton-plus-ghost spectral operator that geometry fixes; and standard heat-kernel quantum field theory. From these the geometry genuinely delivers the scale-free content: an exact dimensionless color factor and four exact-rational cross-checks on test geometries (spheres), reproduced by two structurally independent calculations, together with the signs of the corrections. That is recovered physics. It is not, and does not pretend to be, a UV completion.
Established (given the observed inputs and the frozen geometry): the scale-free sector — the exact color factor, the four exact-rational sphere cross-checks reproduced two independent ways, and the geometric signs — is a genuine theorem of the underlying invariant theory plus standard quantum field theory. For the reflection-symmetric fixed locus, the governing object is the equivariant (fixed-point) heat-trace contribution, which exists to all orders; the apparent literature wall over a missing boundary-coefficient does not obstruct the construction.
Precisely open: (1) the dimensionful magnitude rides an injected scale and terminates on no measured invariant — in an odd number of dimensions the sixth coefficient sits at a power divergence, not a logarithm, so no scheme-independent finite magnitude exists, and the dimensionful number is admissible only as a labeled, scheme-anchored consistency coefficient, never as a closing result; (2) the numeric boundary-defect coefficient is not yet emitted — the one needed cross-check disagreed and is unverified, so no total coefficient may be formed; (3) the positivity test is unbuilt and no sign is asserted — the relevant background is off-shell where the coefficient is gauge-dependent, and a single local coefficient cannot certify a property of the whole spectrum; and (4) whether a finite, positive coefficient would constitute a UV completion is a question shared with quantum gravity at large, with no short route here. This is a serious candidate and an honest finite-matching diagnostic — not a validated UV completion. It touches none of the famous walls: it is not a route across the Yang–Mills mass gap or the cosmological-constant problem.
GAPS_AND_WALLS_REGISTER.md.gap_01_uv_quantum_gravity/.GAP01_A6_RECONCILIATION_2026-06-24.md.dcc66f1b2685 / a5b1e6f9d951, READ-ONLY) — referenced in the register and reconciliation record.(Linked from the public theory register; no external DOIs are asserted for this gate, as the closing computation does not yet exist.)