We actually see this in the Cultural HOF table where Quick speed has for many months been used nearly exclusively, since it was perceived to have an advantage over the other speeds due to its proportionally more valuable Great Work.
This is wrong. And it is a point that affects the article somewhat. The Great Works are not more valuable in Quick Speed. Normal * 0.67 = Quick. 4000c *0,67 = 2680, just as it should. The Great Work is perfectly balanced with other game speeds.
Sorry, my point as stated is at best vague and at worst as you pointed out above wrong (based on an insufficient definition of balanced). To say that The Great Work is balanced with respect to game speed simply because it satisfies a linear ratio of speed to Cultural value (as you noted above) is naive. To be mathematically correct, you must analyze how Culture is accumulated over time (in years) in a Culture game at each speed. The amount of Culture in each game turn is a monotonically increasing function. The Total Culture accumulated by a particular turn is the Integral of that function. The Integral of a function can be approximated by integrating over a finite delta time. It is a well known fact that each such approximate Integral value will be less than the true Integral value at any given point. The smaller the delta used, the larger the approximate Integral value will be. Therefore, all other things being equal, the Marathon game will always accumulate more Culture that the Epic game; the Epic more than the Normal game; the Normal game more than the Quick game. The value of the The Great Work is not visibly balanced to account for this difference between the game speeds.
Let's compare Culture accumulation with a Settler settled (Palace is only source of Culture at 2 Cpt) at turn 0 for each speed:
3985 BC: Marathon 02; Epic 00; Normal 00; Quick 00
3970 BC: Marathon 04; Epic 02; Normal 00; Quick 00
3955 BC: Marathon 06; Epic 02; Normal 02; Quick 00
3940 BC: Marathon 08; Epic 04; Normal 02; Quick 02
3925 BC: Marathon 10; Epic 06; Normal 02; Quick 02
3910 BC: Marathon 12; Epic 06; Normal 04; Quick 02
3895 BC: Marathon 14; Epic 08; Normal 04; Quick 02
3880 BC: Marathon 16; Epic 08; Normal 06; Quick 04
3865 BC: Marathon 18; Epic 10; Normal 06; Quick 04
3850 BC: Marathon 20; Epic 12; Normal 06; Quick 04
3835 BC: Marathon 22; Epic 12; Normal 08; Quick 04
3820 BC: Marathon 24; Epic 14; Normal 08; Quick 06
3805 BC: Marathon 26; Epic 14; Normal 08; Quick 06
3790 BC: Marathon 28; Epic 16; Normal 10; Quick 06
3775 BC: Marathon 30; Epic 18; Normal 10; Quick 06
3760 BC: Marathon 32; Epic 18; Normal 12; Quick 08
3745 BC: Marathon 34; Epic 20; Normal 12; Quick 08
3730 BC: Marathon 36; Epic 20; Normal 12; Quick 08
3715 BC: Marathon 38; Epic 22; Normal 14; Quick 08
3700 BC: Marathon 40; Epic 24; Normal 14; Quick 10
See how Marathon speed leads the Culture pack with Epic, Normal and Quick mostly catching up and only momentarily doing so, if ever?
This effect is repeated every time the Cpt increases. How many times is the Cpt increased in a Culture City in the course of a complete Culture game? It's like having your tax rate increased by .02% 100 times without compounding; effectively 2%. Each such Culture advantage is insignificant, but adding many together may leade to a significant advantage. If your winning Culture game could be improved by 2% by using Marathon versus Quick, how much sooner would that be?
Again, The Great Work is not balanced with respect to game speed simply because it satisfies a linear ratio of speed to Cultural value, because it must be measured against other elements of the game that also change with game speed like the Legendary Culture value (as you did actually do as quoted below).
What is an advantage for Quick is the total amount of culture needed. Normal * 0,67 = Quick. 50000c * 0.67 = 33500c >> 25000c
Your biggest mistake is saying The Great Work is in balance simply because it satisfies a simple linear formula that is somehow reassuring, but we all know that that is not enough for a balanced Game. It ignores the fact that The Great Work must be balanced with all other game elements at all speeds and doing so doesn't necessarily result in a nice linear formula for The Great Work with respect to game speeds.
Sorry, I just don't see how any particular game element can be considered in balance in isolation from the game. As a corollary, only the whole Game with respect to each game speed can be measured as balanced through exhaustive whole game testing. However, as a practical manner, each Victory Condition for the Player can be tested in isolation for balance between the game speeds, so long as none of the AIs have their VC restricted.
Sun Tzu Wu