I have no idea if this is a really good time/score for a 20k or not, but it FELT pretty good. Comments appreciated.
Entry class: Open
Game status: Cultural 20K Victory for Persia
Game date: 1756 AD
Firaxis score: 4867
Jason score: 7193
Time played: 32:36:34
As I entered the Industrial Age in 1090 AD, drawing Medicine as my free tech, Egypt was on the ropes, falling in 1120 AD. That war yielded no more leaders. After building Bach's, Perseopolis started on a prebuild for a factory (later rushed for 428g), as I had no leaders, no prospects for getting any, and, sadly, no
immediate wonders worth building. After the factory Perseopolis started on Universal Suffrage (switched to Magellan's as I traded Germany Physics for Navigation in 1210 AD), completing Magellan's in 1255 AD. After that Perseopolis got a coal plant, hospital, and bank in rapid succession.
Research was Steam-Industrialization-Corporation-Electricity-Replaceable Parts (to get the fast workers)-Sanitation-Sci Method, all in 4 turns, at varying science rates. Sanitation netted me about 280 gpt while researching it at 50%. Got a couple of rushed stock exchanges in and Perseopolis built Wall Street in 1320 AD (followed by ToE). In 1315 I traded Germany into the industrial age (getting Military Tradition, gpt, and cash for ToG+Magnetism); they drew Medicine. I gifted Russia up, they drew Medicine. Phooey. Two turns later Germany broke the deal with a MI attacking a guerilla on the far north tundra island. Jerk.
As it was obvious that technology was not a major problem for me at this point, I looked for a target for leader-fishing. England was the obvious choice for a couple of reasons: they were isolated, weak, and more importantly had never met Egypt. So I started creating a few galleons and gathering my entire army (I was alone on the continent with a rail net) for a mass assault on England.
Perseopolis created ToE in 1365 AD, and I took the usual Electronics slingshot (having researched through Refining and Steel up top). I actually had Ergili (my replacement for the Iroquois capital, with the FP) finish Hoover a few turns after that. Perseopolis, for lack of anything better to do (and because armies make great prebuilds) finished the Military Acaedmy in 1395. It then went for a commercial dock and stock exchange as no culture was available (I could have built Battlefield Medicine here, I guess, but I didn't.)
England was reluctant to grant a right of passage to me, but Free Artistry and a world map convinced her.

So, I lined up my troops juuuuuust right.
The picture of England before...
... and after. (Hey, I got unlucky at Nottingham.

)
Took Nottingham the next turn; finally sunk an English caravel (a tracking transport and two privateers sunk before a rushed battleship did the job) in 1445. Russia was to be next.
In 1470, I made a ROP with Germany to be able to sail up to Russia quickly.
Went modern in 1490, and drew Fission as my free tech (yay). Set research to Computers, then Mini, then Genetics. That let Perseopolis switch from the army build (its second) to the UN (later switched to Manhattan for reasons soon to be obvious).
It took a little while to reposition for attack on Russia (my next target), but in 1500 I sneak-attacked them on the tundra island and made mass landings on their west coast. With tanks against a rail-less Russia, quick and brutal was the order of the day. Got a leader in 1520; he hopped a transport home to wait a few turns for Manhattan to finish in 1535, then rushed the UN in 1540, then rushed an offshore platform (because I could).
By 1545 Russia was reduced to it's new capital of Riga, on the one-square island off the German coast. And I still had five turns left on my ROP with Germany, and a whole lot of tanks.
My third ROP rape of the game started in 1560, with me razing everything in sight except one German city that I kept for roads and a rushed barracks. And was it ever fruitful.
Got a leader in 1565; he was ship-chained home to rush The Internet.
Got a leader in 1570, he was ship-chained home and rushed SETI.
Got ANOTHER leader in 1570; he made it home but had to wait a turn for Genetics to finish, then rushed Longevity in 1580.
Declared war on the wimpy Vikings also, because I could (Germany had relegated them to island duty), and got one last great leader with a cavalry unit; Perseopolis switched from Cure for Cancer to Apollo, finished that, and then the leader rushed Cure for Cancer in 1625. At this point, the Vikings had two cities, Germany and Russia each had one.
That wasn't the last wonder of the game though. In 1610 I made the most peculiar tech move I'd ever made: finished Space Flight, then did Economics in 4 at 10%.

Hand-built Smith's in 1675, then cash-rushed a couple more armies, then built Pentagon in 1705. Pushed Enter a lot until the game ended.
At game's end, Perseopolis had 20,023 culture, generating 149 cpt.