A B737-500 IS CITED BY DEP CTLR AS CLBING FROM 10000 FT TO 15000 FT WITHOUT AUTH; OR CLRNC N OF OAK; CA.

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DEPARTED OAK METRO ON THE SKYLINE 3 DEP OFF OF RWY 29. OUR INITIAL CLRNC WAS TO 10000 FT WITH A 2000 FT RESTR ON THE SID OF 4 DME. ON INITIAL CONTACT WITH BAY DEP; WE WERE TOLD TO CLB UNRESTR TO 150000 FT. THE CAPT CONFIRMED THE UNRESTR CLRNC TO 15000 FT AND READ BACK SUCH TO THE BAY CTLR. BAY ALSO ISSUED US A SPD RESTR OF 250 KIAS OR LESS; WHICH WE ACKNOWLEDGED. THE CAPT ACKNOWLEDGED 2 HDG CHANGES PRIOR TO INTERCEPTING THE 135 DEG RADIAL ON THE DEP. ON THE NEXT RADIO CALL; THE CTLR ASKED IF OUR SPD WAS 250 KTS OR LESS. THE CAPT ANSWERED WITH OUR SPD OF 240 KIAS. AS WE WERE LEVELING AT 15000 FT AND INTERCEPTING THE 135 DEG RADIAL; THE CTLR STATED 'ACR X; YOU WERE GIVEN 10000 FT; BUT THERE'S NO PROB.' THE CAPT AND I DISCUSSED WHAT WE HAD HEARD AND BELIEVED IT TO BE 15000 FT. WE SET THAT AND CONFIRMED THAT IN OUR ALT ALERT WINDOW ON THE INITIAL CONTACT WITH BAY DEP AS PER OUR PROCS. THE CTLR SEEMED FOCUSED ON OUR DEP SPD AND MAY NOT HAVE CAUGHT OUR READBACK OR OUR CLB TO 15000 FT. IF WE HEARD WRONG; WE WERE NOT CORRECTED; OR IF THE CTLR GAVE US 15000 FT INITIALLY AND THEN FORGOT; WE DON'T KNOW. SUPPLEMENTAL INFO FROM ACN 478687: AFTER A MILD SHOCK I REPEATED HE GAVE US CLRNC TO 15000 FT. MY FO AND I ARE AS SURE AS CAN BE THAT WE WERE GIVEN 15000 FT ON INITIAL CONTACT; AND I AM SURE THAT I REPEATED 'ROGER; CLRED UNRESTR TO 15000 FT.'