Oracle 18c

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WITH t( written_1, writer, inrunningdelay_1 ) AS
(
 SELECT to_timestamp('03/17/2020 08:02:56.303398','mm/dd/yyyy hh:mi:ssxff'), 1078, 5000 FROM dual UNION ALL
 SELECT to_timestamp('03/17/2020 08:02:53.227820','mm/dd/yyyy hh:mi:ssxff'), 1078, 5000 FROM dual UNION ALL
 SELECT to_timestamp('03/17/2020 08:02:43.999741','mm/dd/yyyy hh:mi:ssxff'), 1078, 5000 FROM dual UNION ALL    
 SELECT to_timestamp('03/17/2020 08:02:28.756472','mm/dd/yyyy hh:mi:ssxff'), 1078, 6000 FROM dual UNION ALL
 SELECT to_timestamp('03/17/2020 08:02:20.430255','mm/dd/yyyy hh:mi:ssxff'), 1078, 5000 FROM dual UNION ALL  
 SELECT to_timestamp('03/17/2020 08:02:11.458479','mm/dd/yyyy hh:mi:ssxff'), 1078, 2000 FROM dual UNION ALL 
 SELECT to_timestamp('03/17/2020 08:02:00.490496','mm/dd/yyyy hh:mi:ssxff'), 1078, 3000 FROM dual UNION ALL 
 SELECT to_timestamp('03/17/2020 08:01:46.095546','mm/dd/yyyy hh:mi:ssxff'), 1078, 5000 FROM dual UNION ALL 
 SELECT to_timestamp('03/17/2020 08:02:00.490496','mm/dd/yyyy hh:mi:ssxff'), 1079, 3000 FROM dual UNION ALL 
 SELECT to_timestamp('03/17/2020 08:01:46.095546','mm/dd/yyyy hh:mi:ssxff'), 1079, 4000 FROM dual UNION ALL 
 SELECT to_timestamp('03/17/2020 08:02:00.490496','mm/dd/yyyy hh:mi:ssxff'), 1079, 4000 FROM dual 
), t2 AS
(
  SELECT t.*, 
         ABS( inrunningdelay_1 - LEAD(inrunningdelay_1) 
             OVER ( PARTITION BY writer ORDER BY written_1 ) ) as ld            
    FROM t      
   ORDER BY writer, ld, written_1   
)
SELECT written_1, writer, inrunningdelay_1  
  FROM t2  
 ORDER BY ROW_NUMBER() OVER  ( PARTITION BY writer ORDER BY ld )
 FETCH FIRST 1 ROW WITH TIES

WRITTEN_1	WRITER	INRUNNINGDELAY_1
17-MAR-20 08.02.43.999741000	1078	5000
17-MAR-20 08.01.46.095546000	1079	4000