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Top 100 trophy should be permanent (should not appear and disappear)

For now top 100 trophy depends on current rating. So while my current rating changes, chess 960 top 100 trophy appears and disappears. It is annoying and contradicts the nature of trophy (I can not give link to my profile and say "look, I has a trophy" --- it may easily disappear after 15 minutes). Also it needs costly recalculation each 15 minutes.

What can be done? May be like this:

1. Trophy is bound to some month, say, "Chess 960 top 100 for November 2015"

2. Trophy is calculated once per month (that is, 1 Dec 2015) on the *maximum* player rating during November 2015.
May be to calculate trophy some time later, to give some time to detect cheaters (and remove them from list). (As for me, 960 chess seems to me to free from cheaters on lichess.org. But I see many complaints on forum.)
When I think about a trophy like the Stanley Cup, it isn't something that the winning team gets and then keeps. If the team doesn't win the next year then they hand the cup over to the newly won team. The problem I presume with permanent trophies is that it encourages people to make new accounts to try and very quickly attain very high ratings. Then when they can't maintain them they still get to keep the trophy.
No. It is disappearing trophies that encourage people to make new accounts.

Say, now I have a top 100 trophy. I know that my rating naturally oscillates (say, +50...-50), so I inclined to stop to play at this account and create another one.
From our findings, players in the 1800-2000 range are far more likely to be multiaccounters, not top 100. Either way you don't keep your trophy or position in the rankings unless you play at least one game in that category each fortnight.
1. 2000 is enough to be top100 in c960 and even top 50 in horde.

2. OK, to keep my trophy I need to play some games each fortnight to make my oscillation fully oscillate to nearly same value (that is near to my maximum).

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