Internal audit: cyclic transport and meridian boundary

8 September 2026. Self-audit only; no independent specialist or peer review.

Exact structural checks

• The map Psi(W(u))=B^(sum u_w)W(-u_w,u_z-u_w) is integral, symplectic and order three on full roots. The coefficient character is additive, and its three cyclic exponents sum to zero.
• Psi(f_j)=-w_j^-2 f_j is an exact left-unit normalization. This is the correct side for S f_j. Edge and filling generators retain arbitrary right multipliers after transport.
• Every actual scalar transforms with its raw row. Both edge scalars become -A² and both edge characters become one; the filling and complementary longitude scalars become one. They are not discarded by a discretionary renormalization.
• Lambda’=C Lambda is the original unsaturated image under an integral automorphism. The map transports the named vacuum itself to 1-(l’)². Odd root inputs and their native imaginary phases are included in the verification.
• The transformed graph has Q’=(x1+x2)²+(2q/d)(x1-x2)², d=2q-p. Its exact cone condition is 1+2q/d>0 when d is nonzero. The graph degenerates at d=0, where a vertical moment ray prevents all-input convergence.
• Under that cone condition and |d|>2, the linear degree coefficients 2±4/d are positive and the longitude defect (-2/d,2/d) is nonintegral. The zero-coordinate endpoint is explicitly excluded. The two-polarization coverage proof is symbolic: use the prior result for p/q≥0 and the transported result for p/q<0, when |d|≥3.
• All-input convergence precedes image reindexing. Each series cutoff in the actual controls has a coercive quadratic bound; no cancellation by a chosen summation order is used.

Meridian result: two distinct proofs and the projection limit

The meridian average has an exactly symmetric pair of double sums for unit and longitude square. Reindexing proves their equality. Euler summation proves the unit is nevertheless nonzero, with leading term -mathfrak-q².

The stronger vacuum-zero claim is proved separately by eight recurrence relations. The integral moment normal form is complete, and the recurrence certificate is lifted to a full quantum Laurent identity with explicit right edge and filling multipliers. The verifier checks this identity before and after inverse cyclic transport. This is a genuine algebraic certificate in the actual all-plus sector, not an inference from a zero detector value.

The most important scope restriction is directional: nonzero sector image implies nonzero preimage in the original six-root quotient; zero sector image does not imply zero preimage. No injectivity of the central specialization has been proved or used. The full six-root meridian vacuum is therefore unresolved. The all-plus sector and the native meridian cokernel are nonzero, so no nonzero-target conjecture is refuted here.

The certificate addresses the specified vacuum. We do not rely on an unproved classification of every solution of the symmetric recurrence or all odd classes. The next question is the vacuum before central specialization, not another all-plus seed.

Evidence level and limitations

The exact verifier uses standard-library Gaussian integers, rational exponents, and Laurent polynomial dictionaries. One control (-5,1) verifies transport where the old seed has a negative recession ray; the meridian control checks the distinct boundary behavior. These are tests of specific uncertainties, not a census.

The named six-root trace and filling identification remain retained AI-assisted proof dependencies. The direct algebra in this note does not externally validate them. The original-source raw rows are retained from the previous source-checked packet; fresh web access was unavailable. No later-priority search is claimed.

This remains a supporting research note. The unrestricted Panitch–Romo conjecture, triangulation independence, a new invariant, and the full-six-root meridian vacuum are not resolved. No new Publication or researcher outreach is warranted.