We determine the initial mass function ( IMF ) of the “ thin disk ” by means of a direct comparison between synthetic stellar samples ( for different matching choices of IMF , star formation rate SFR and depletion ) and a complete ( volume-limited ) sample of single stars near the galactic plane ( |z| < 25 pc ) , selected from the Hipparcos catalogue ( d < 100 pc , M _ { V } < +4.0 ) .
Our synthetic samples are computed from first principles : stars are created with a random distribution of mass M _ { * } and age t _ { * } which follow a given ( genuine ) IMF and SFR ( t _ { * } ) .
They are then placed in the HR diagram by means of a grid of empirically well-tested evolution tracks .
The quality of the match ( synthetic versus observed sample ) is assessed by means of star counts in specific regions in the HR diagram .
7 regions are located along the MS ( main sequence , mass sensitive ) , while 4 regions represent different evolved ( age-sensitive ) stages of the stars .

We find a bent slope of the IMF ( using the Scalo notation , i.e. , power law on a logarithmic mass scale ) , with \Gamma _ { 1 } = -1.70 \pm 0.1 ( for 1.1 M _ { \odot } < M _ { * } < 1.6 M _ { \odot } ) and \Gamma _ { 2 } = -2.1 \pm 0.1 ( for \approx 4 M _ { \odot } > M _ { * } > 1.6 M _ { \odot } ) .
In addition , comparison of the observed MS star counts with those of synthetic samples with a different prescription of the MS core overshooting reveals sensitively that the right overshoot onset is at M _ { * } = 1.50 M _ { \odot } .

The counts of evolved stars , in particular , give valuable evidence of the history of the “ thin disk ” ( apparent ) star formation and lift the ambiguities in models restricted to MS star counts .
A match of the evolved star counts yields a stellar depletion in the sample volume which increases with age ( i.e. , by apparent SFR ( age ) / SFR _ { 0 } ) .
A very good match is achieved with a simplistic diffusion approximation , with an age-independent diffusion time-scale of \tau _ { dif } = 6.3 \cdot 10 ^ { 9 } yrs and a ( local ) SFR _ { 0 } = 2.0 \pm 0.1 stars ( with M _ { * } > 0.9 M _ { \odot } ) formed per 1000 years and ( kpc ) ^ { 3 } .
We also discuss this “ thin disk ” depletion in terms of a geometrical dilution of the expanding stellar “ gas ” , with H _ { z } ( t _ { * } ) \propto \sigma _ { W } ( t _ { * } ) .
This model applies to all stars old enough to have reached thermalization , i.e .
for t _ { * } > 7 \cdot 10 ^ { 8 } yrs and H _ { z } > 230 pc .
It yields a column-integrated ( non-local ) “ thin-disk ” SFR _ { col } which has not changed much over time ( < 30 % ) , SFR _ { col } \approx 0.82 * pc ^ { -2 } Gyr ^ { -1 } ( i.e. , stars with M _ { * } > 0.9 M _ { \odot } ) .