ACR X ON APCH HAD LTSS WITH ACR Y HOLDING IN POS. NMAC. SYS ERROR.

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ACR X ON FINAL FOR RWY 31 AT LGA. WE HAD PREVIOUSLY BEEN CLRED TO LAND SHORTLY AFTER INITIAL CONTACT WITH TWR; PASSING DIALS INTXN. VMC CONDITIONS AND WINDS OUT OF THE NW AT 18 KTS. I WAS FOCUSED ON THE 3 BAR VASI AND ON SPD AND GS. I XCHKED MY ALT AT AROUND 350 FT. AT APPROX 100 FT; I NOTICED AN AIRLINE ON THE RWY; IN POS AND HOLDING. I IMMEDIATELY EXECUTED A GAR; PASSING APPROX 50 FT OVER THE HOLDING ACFT. APPROX 4-6 SECONDS LATER; TWR INSTRUCTED US TO GAR. AFTER RETURNING TO THE ARPT AND COMPLETING A FULL STOP LNDG; I QUESTIONED TWR AS TO WHAT HAD HAPPENED. THE CTLR ADMITTED FAULT; ACKNOWLEDGING THAT HE HAD CLRED THE OTHER ACFT; CHALLENGER 601; ON TO HOLD AFTER GIVING US LNDG CLRNC. IT IS OF NOTE THAT I WAS COMPLETELY FOCUSED ON THE VASI'S AND RWY THROUGHOUT THE ENTIRE APCH AND DIDN'T SEE THE OTHER ACFT UNTIL 100 FT. ALSO; MY COPLT NEVER SAW THE OTHER ACFT UNTIL AFTER I HAD INITIATED THE GAR AND I HAD CALLED HIS ATTN TO THE SIT. DESPITE HIS BEACON AND NOSE GEAR LIGHTS ON; HE WAS VIRTUALLY INVISIBLE.