AFTER SOME UNEXPECTED SPD ADJUSTMENTS; UNPLANNED ALTS; AND OFF COURSE VECTORS; A B737 CREW REFUSED HOLDING AND DECLARED LOW FUEL. CTLR IGNORED LOW FUEL UNLESS CREW DECLARED AN EMER.

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CRUISE PHASE TO ZZZ WAS PLAGUED WITH SPD ADJUSTMENTS; UNPLANNED ALTS AND OFF-COURSE VECTORS. PROJECTED FUEL ON BOARD SLOWLY WENT FROM 7.0 EARLY IN CRUISE TO 5.0 AT TOP OF DSCNT. AT ABOUT 12000 FT ON DSCNT ATC GAVE US A HOLD. (FUEL ON BOARD WAS NOW 4.8.) WE TOLD ATC WE COULD NOT HOLD BECAUSE WE WERE AT MINIMUM FUEL. HE ASKED IF WE WERE DECLARING AN EMER. WE SAID WE WERE DECLARING MINIMUM FUEL AND ANY DELAY WOULD CAUSE US TO HAVE AN EMER. HE SAID WE COULD NOT CONTINUE UNLESS WE DECLARED AN EMER; SO WE DECLARED A LOW FUEL EMER. WE WERE CLRED ON TO ZZZ WITH LITTLE DELAY. WE BLOCKED IN WITH 4100 LBS OF FUEL. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED HIS FLT PLAN WAS FROM ZZZ1 TO ZZZ. WHEN THE CREW RPTED MINIMUM FUEL; THE CTR CTLR ADVISED THAT THE TRACON WOULD NOT ACCEPT THEM UNLESS AN EMER WAS DECLARED. THEY DECLARED EMER AND WERE TAKEN DIRECT TO ZZZ. HE SAID THEY HAD TAKEN ON 2000 LBS OF EXTRA FUEL AT THEIR DEP ARPT BUT THAT WAS USED UP QUICKLY WITH A NUMBER OF UNPLANNED ALT CHANGES; SPD ADJUSTMENTS; AND SEVERAL OFF-COURSE VECTORS FOR SPACING BY THE CTR BEFORE HDOF TO TRACON. NO ONE CONTACTED THEM AFTER LNDG. SUPPLEMENTAL INFO FROM ACN 636525: DURING THE ARR INTO ZZZ; WE WERE GIVEN A HOLD JUST PRIOR TO XXX INTXN. AS A RESULT OF AN UNPLANNED ALT AND OFF-COURSE VECTORS FOR SPACING; WE INSTRUCTED ATC WE WERE UNABLE TO HOLD BECAUSE WE WERE AT MINIMUM FUEL (4.3 LBS ARR). ATC ASKED IF WE WERE DECLARING AN EMER. WE RESPONDED; 'NO; BUT WE CANNOT ACCEPT A DELAY; AND THEREFORE; UNABLE TO HOLD.' ATC SAID; 'ADVISE WHEN READY TO COPY HOLDING INSTRUCTIONS.' AT THAT POINT WE HAD NO CHOICE BUT TO DECLARE AN EMER. WE ARRIVED AT THE GATE WITH 4.1 LBS. WE TERMINATED THE FLT WITHOUT FURTHER INCIDENT.