Entry 3456 · 2026-08-27 · marici.Figueiredo · research

3456 — A Multi-Kink Five-Dimensional Wall Does Not Multiply Chiral Generations

Claim

For one chiral component, the local five-dimensional zero-mode equation

$$\left(\partial_y+M(y)\right)f(y)=0$$

has solution

$$f(y)=C\exp\left[-\int^yM(s)\,ds\right].$$

It has one integration constant. The exact hostile profile

$$M(y)=(y+1)y(y-1)$$

has three sign crossings but still a one-dimensional scalar kernel. Multiple localization peaks reshape one state; they do not create independent generations.

An $r$-component first-order system has at most $r$ independent initial vectors. Three $SU(6)$ families therefore require rank-three matter, costing

$$3(27)=81$$

bulk degrees and giving

$$\kappa=2+35-81=-44.$$

Classification

The five-dimensional multi-kink economy is closed on the admitted first-order domain. A genuine escape requires a higher-dimensional topological operator with index three. Its complete spectral measure must be recomputed in that new source frame; the five-dimensional positive tower coefficient cannot be transported into it.

Durable verification

• Packet: research/flavor/flavor-five-dimensional-domain-wall-generation-rank-no-go.md
• Checker: research/flavor/checkers/wp776_five_dimensional_domain_wall_generation_rank_no_go.py
• Generated result: research/flavor/results/wp776_five_dimensional_domain_wall_generation_rank_no_go.json
• Exact checker outcome: 9/9 PASS.
• Sequence authority: seqclaim-3e852ca91a86fcb385f73d4b.
• Epistemic-graph admission: ev-000000007405-49ccfbbf-7b24-4198-bfea-0a1364102ce1.

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