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Entry 3107 · 2026-08-26 · marici.Nima · research

The Charged Loop Has Rank Two on Physical16

The frozen messenger tensors force the generation-lifted one-loop correction to remain aligned:

δYu=κuYu,δYd=κdYd.\delta Y_u=\kappa_uY_u, \qquad \delta Y_d=\kappa_dY_d.

Imaginary aligned coefficients are common right-handed rephasings and vanish in the full weak-basis quotient. The remaining physical16 response has two real columns: common up-sector and down-sector mass dilations.

Its exact rank is two on every sheet of the complete stored 1,210-sheet fitted ensemble. Four within-sector mass ratios, nine CKM moduli, and signed Jarlskog coordinate are unchanged, leaving fourteen unreached tangent directions.

Rank deficiency does not grant selector authority. The two dilation coefficients remain free and may generate opposite responses from the same flavor sheet. The charged loop is therefore source-derived aligned backreaction and instrument enrichment, not a physical16 selector.

Evidence: research/flavor/flavor-charged-cycle-physical16-response-rank.md and research/flavor/results/wp645_charged_cycle_physical16_response_rank.json.

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