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Glamorgan 273 (Carlson 64, Revis 5-50) and 401 for 5 dec (Northeast 166, Byrom 101, Carlson 52) drew with Yorkshire 500 (Masood 192, Bean 93, Hill 71)
Northeast ended the day unbeaten on 166, while Byrom was out for 101 and captain Kiran Carlson contributed 52 to pass the landmark of 1,000 runs in a season for the first time in his career.
For the Welsh county, who produced similar backs-against-the-wall defensive efforts against Sussex and Durham in the Spring, it was an 11th draw in 13 matches this season and officially killed off any lingering promotion hopes.
Yorkshire started the day with an outside chance of an innings victory, but they remain bottom of the table, despite picking up 13 points to Glamorgan's eight, following their 48-point deduction earlier in the season for their handling of the Azeem Rafiq racism scandal. With a first-innings deficit of 227 runs, the home side, following on, resumed on 120 for 2 - still 107 runs behind - and with the aim of batting all day.
Blue skies and bright sun made for perfect conditions for the batters, while the placid pitch was also in their favour - offering the Yorkshire bowlers very little encouragement. Northeast, unbeaten on 45 overnight, made it to 50 in the fourth over of the morning and his partnership with Byrom, who resumed on 52 not out, quickly ticked over into three figures.
Northeast got away with a moment of recklessness in the 56th over when he chased a wide delivery from Matthew Revis and saw a thick inside edge cannon into his boot. But, with few other signs of a breakthrough, Yorkshire opted to give wicketkeeper Jonathan Tattersall the ball and his unthreatening leg breaks allowed Byrom and Northeast to make serene progress.
Finlay Bean took the gloves and he had little to do as Revis, who claimed five wickets in the first innings, also struggled to make anything happen. Byrom completed his century with a sweep off Dom Bess, but his fine innings came to an end soon afterwards as he tried one reverse sweep too many and was bowled by Bess for 101 off 199 balls having put on 178 with Northeast.
The home side reached 230 for 3 at lunch, a lead of three runs, with Northeast on 88 and Carlson 11. Northeast survived an LBW appeal from Adam Lyth on 93 and then an attempted caught and bowled as he drove the ball into the foot of James Wharton at silly point and it shot off towards Bess, who got fingertips to it.
But he claimed his hundred in the 80th over with a stylish cut to the boundary off Lyth, just before Yorkshire got their hands on the new ball with Glamorgan 254 for 3 - a lead of 27.
Ben Coad and Jordan Thompson replaced Bess and Lyth, but they couldn't stem the flow of runs and Carlson passed his thousand-run milestone in the 82nd over. The Glamorgan skipper reached his half-century before being caught behind by Tattersall for 52 off the very next ball as debutant Ben Cliff claimed his maiden first-class wicket to leave the hosts on 305 for 4.
Glamorgan progressed to 354 for 4 at tea, and, though Wharton bowled Billy Root for 45, the teams shook hands on the draw at 4.20pm with the hosts on 401 for 5 and leading by 174.
Northeast and Byrom earn Glamorgan valiant stalemate with Yorkshire
Welsh county's 11th draw of the season kills off lingering promotion hopes
Matthew Revis takes five as Yorkshire sniff innings victory over Glamorgan
21-year-old registers maiden five-wicket haul as Yorkshire to enforce the follow-on
Shan Masood's 192 puts Yorkshire in total command against Glamorgan
Carlson half-century resists but huge deficit remains on cards