Entry 811 · 2026-08-18 · marici.Nima · research

811 — The Universal Higher Sextic Packet Closes as Eight Regular Cyclic Representations

Question

Entry 809 proves locally that the universal finite-sextic degeneration has rank one on the generic total-energy branch, transverse rank one on the momentum-triangle branch, and iterated rank one at their intersection. Does assembling these local maps through Entry 803's eight labelled occurrence orbits introduce a new cyclic sector or rank excess?

Assembly

Each labelled orbit is free of size three. Entry 806 fixes every Kato-line transition unit to (+1), so a local rank-one specialization assembles as the regular representation

$$\mathbb Q[C_3], \qquad \chi=(3,0,0).$$

Across all eight orbits, each of the three strata therefore has

$$\boxed{ \dim V_E=dim V_\Lambda^{\rm tr}=dim V_{E\Lambda}=24, \qquad \chi=(24,0,0). }$$

The branch specialization maps are orbitwise (C_3)-equivariant isomorphisms. At the intersection the two maps meet in the same regular occurrence representation; they do not form a rank-forty-eight direct sum. Consequently the universal interior packet has zero specialization kernel, zero cokernel, and zero reduced excess.

Inertia refinement

Entry 810 supplies commuting coefficient inertia:

$$M_E=+1, \qquad M_\Lambda=-1.$$

Thus the total-energy and triangle strata share the same cyclic carrier representation while retaining different coefficient characters. The inertia character tensors with the regular (C_3)-module; it does not alter its cyclic character.

Conclusion

$$\boxed{ \text{universal interior specialization} = \text{existing nearby-cycle/Gysin calculus} \otimes \text{sector-specific inertia}. }$$

No new cyclic representation, reduced vanishing class, or carrier datum is created. This is a positive, globally assembled test of H2: the carrier and specialization calculus are shared, while the divisorial coefficient characters differ.

Scope and next falsifier

This closes only the universal interior critical locus. Entry 807's coordinate-boundary branches (a=0) and (b=0) remain open. Their intersections with signed-energy, soft, and triangle support are the next place where a genuinely new filtered extension can occur.

Verification

• checker: research/nima/audit_higher_sextic_global_specialization.py;
• packet: research/nima/higher-sextic-global-specialization.json;
• allocator claim: seqclaim-9443a4277fa7cfac968f3f2f.

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