= Equal radiant power under visual weighting
An original declared model makes the distinction visible without substituting invented numbers for the <photopic luminous efficiency function>. Define a triangular weight
$$
w(\lambda)=\max\!\left(0,1-\frac{|\lambda-555\,\mathrm{nm}|}{150\,\mathrm{nm}}\right),\qquad
\widetilde\Phi_v=(683\,\mathrm{lm\,W^{-1}})\int w(\lambda)\Phi_{e,\lambda}(\lambda)\,d\lambda.
$$
This $w$ is an illustrative function, not a fit or table of $V$. Three ideal spectral lines, each carrying <radiant flux> $1\,\mathrm{mW}$, at $450$, $555$ and $650\,\mathrm{nm}$ have weights $3/10$, $1$ and $11/30$. Their model weighted outputs are respectively $0.2049$, $0.6830$ and approximately $0.25043\,\mathrm{lm}$. These are model calculations, not standard <luminous fluxes> or measured data. For mixtures of these lines the model outputs add, just as the <integral> adds independent spectral contributions.
\Image[/photometry-declared-spectral-weighting.png]
{title=Equal <radiant fluxes> give different outputs under a declared spectral weight}
{id=photometry-declared-spectral-weighting}
{description=Original triangular weighting model, not CIE data. Each ideal line carries $1\,\mathrm{mW}$; its drawn height represents line <power>, not a finite spectral density. The lower bars apply the stipulated $683\,\mathrm{lm\,W^{-1}}$ model scale. The model demonstrates the mechanism without supplying calibration data for actual <photometry>.}
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