Universal Comb–Fourier Coherence Does Not Fix Null Events
Hostile carrier
The degree-twelve Gaussian-polynomial carrier constructed in the existing falsifier is:
- exactly Fourier-fixed;
- vacuum-null;
- positive on every nonzero integer sample;
- assembled through the same integer-comb dilation orbit;
- equipped with off-critical Mellin-window zeros.
Its integer-labelled summands inherit the same dilation relation that produces prime-filtered recursion. The integer and reciprocal labels also share the same adelic-height cutoff.
Thus it possesses the universal structures currently under consideration:
- Fourier self-duality;
- conjugation reality;
- comb sampling;
- dilation-labelled prime recursion;
- reciprocal adelic-height synchronization;
- complementary Fourier homogeneity.
Yet its Mellin readout has off-seam zeros.
No-go theorem
No zero-selection theorem depending only on those six structures can imply critical-line confinement.
The proof is by the explicit degree-twelve witness. Any such theorem would apply to that carrier and contradict its exact off-line Mellin zeros.
In particular, the proposed equalizer cannot be formed merely from:
- Fourier transport;
- source self-duality;
- the scalar zero section;
- common adelic height.
Those data are still universal across a larger carrier class than the actual theta current.
What the hostile carrier does not preserve
The actual archimedean current is the unique minimal even Gaussian-polynomial Fourier fixed point satisfying the source nullity and differential-order constraints. Its Mellin factor is zero-free in the open critical strip apart from the arithmetic zeta section.
The degree-twelve witness changes that archimedean carrier and introduces its own Mellin divisor. It is therefore rejected by minimal carrier provenance.
This rejection protects the separation between the authorized archimedean carrier and the arithmetic Euler section.
It does not constrain hypothetical off-line zeros of the actual Euler section.
Consequence for the equalizer programme
A valid fixed-event theorem must be applied after the archimedean carrier has been rigidly factored out. Otherwise it confuses:
- zeros inserted by changing the carrier;
- zeros belonging to the arithmetic section.
After that factorization, the hostile degree-twelve example disappears, but the RH problem remains intact. A hypothetical off-line zeta zero is still compatible with all universal reciprocal symmetries.
Therefore carrier rigidity is a typing gate, not the missing arithmetic orientation law.
Revised target
The next comparison object must act on the arithmetic determinant line relative to the fixed carrier. It must distinguish the actual multiplicative Euler source from a divisor-bearing symmetric modification without relying on the scalar divisor itself.
Plausible non-universal inputs are:
- the full prime-power Fock grading;
- completion-sensitive primitive and square currents;
- an arithmetic Green current coupling those grades;
- a determinant-line connection derived before scalar compression.
The earlier positive-Fock theorem controls which arithmetic contributions exist. The missing theorem must control how their relative boundary event is fixed under reciprocal sewing.
Falsifier
Any proposed equalizer should first be run against two independent hostile classes:
- a changed archimedean carrier, represented by the degree-twelve witness;
- a fixed carrier multiplied by a symmetric divisor-bearing arithmetic factor.
Passing only the first test proves carrier provenance. RH force requires passing the second.
Explanatory gain
We now know where the additional wall must sit. It is not between Fourier transport and the completed scalar source; that wall is universal.
It lies between the fixed archimedean carrier and the multiplicative arithmetic section. The relevant null event must be fixed because of how prime grades compose, not merely because the ambient source is self-dual.