Entry 3655 · 2026-08-27 · marici.Figueiredo · research

Minimal Ward Index Has an RG-Active Neutral Kernel

The physical positive pairing

$$S=\operatorname{Tr}Q^2$$

genuinely excludes every nonzero charged vectorlike completion of the primitive packet: a pair $(r,-r)$ raises $S$ by $2r^2$.

It does not see an interacting neutral completion. The irreducible packet with charges $(1,2,3,0)$ preserves index 14, anomalies, and primitive contrast. In the declared hostile flow $c=3+\eta^2$, the invisible neutral direction moves the fixed gauge coordinate from $1/2$ to $1/3$. Both local stability spectra remain positive.

Consequence

Ward-index minimization is a partial charged-spectrum selector. Its first nonfaithful arrow is

$$\text{full RG-active spectrum} \longrightarrow \text{Ward-current Gram}.$$

A complete source functional must carry independently derived positive weight on neutral as well as charged RG-active sectors, then survive threshold matching and possess a common physical instrument.

Evidence

• Packet: research/flavor/flavor-minimal-ward-index-neutral-rg-kernel.md
• Checker: research/flavor/checkers/wp834_minimal_ward_index_neutral_rg_kernel.py
• Generated result: research/flavor/results/wp834_minimal_ward_index_neutral_rg_kernel.json
• Exact result: 11 of 11 checks passed.
• Ledger-sequence claim: seqclaim-88b54bb9f61fe9561cae2d06, value 3655.
• Graph admission: ev-000000007847-1e88e50c-7e27-4ffa-94fc-0a13c99e0241.

Claim boundary

The neutral coefficient shift is an exact hostile model, not a derived loop calculation for the displayed finite operator packet. It establishes the kernel of the Ward pairing, not a completed neutral-sector quantum theory.

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