Fix INACTIVITY_PENALTY_QUOTIENT description

[hwwhww]

Issue

It's a very old leftover from #949 (comment): when we didn't update the constant number description when we changed INACTIVITY_PENALTY_QUOTIENT from 2**24 to 2**25.

How to fix it

This PR updates corresponding INVERSE_SQRT_E_DROP_TIME to the right number. Alternatively, we can consider removing this paragraph as @JustinDrake suggested.

/cc @benjaminion for the annotated spec project.

[djrtwo]

Why was it changed in #949? It was listed as "cosmetic" in the PR -- CC @JustinDrake

I've been operating under the assumption of ~2.5 weeks. Not ~3.5 weeks

[JustinDrake]

Why was it changed in #949? It was listed as "cosmetic" in the PR -- CC @JustinDrake

The previous formula had a // 2 (see INACTIVITY_PENALTY_QUOTIENT // 2 here) which I removed and counter-balanced by changing the constant. The intent was to preserve functionality, i.e. make it a cosmetic change. It is entirely possible I messed up and made a substantive change 😂

[hwwhww]

@JustinDrake sorry, I didn't notice you removed // 2 in #949 when I read it for this PR!
So if the previous numbers were correct, this section should be:

The INACTIVITY_PENALTY_QUOTIENT // 2 equals INVERSE_SQRT_E_DROP_TIME**2 where INVERSE_SQRT_E_DROP_TIME := 2**12 epochs (about 18 days) is the time it takes the inactivity penalty to reduce the balance of non-participating validators to about 1/sqrt(e) ~= 60.6%. Indeed, the balance retained by offline validators after n epochs is about (1 - 1/INACTIVITY_PENALTY_QUOTIENT)**(n**2/2); so after INVERSE_SQRT_E_DROP_TIME epochs, it is roughly (1 - 1/INACTIVITY_PENALTY_QUOTIENT)**(INACTIVITY_PENALTY_QUOTIENT/2) ~= 1/sqrt(e).

However, I did some git log trace 🔎

1. The mysterious // 2 was added in 53dd491 (Changes to inactivity leak #347)

   • Adds a // 2 to the inactivity leak to compensate for it being applied twice

2. But, in d1d1b73 (Simplify justification and finalization accounting logic #826), changes, the twice penalties became just one.

   Inactivity leak penalty specifically on missing the target, not both the target and the source

Conclusion

Am I correct that we don't even need // 2 after #826, so the true fix should be simply changing INACTIVITY_PENALTY_QUOTIENT from 2**25 to 2**24 if we want INVERSE_SQRT_E_DROP_TIME to be 18 days?

/cc @djrtwo @vbuterin for more 👀 and better memory.

[vbuterin]

It does indeed seem like INACTIVITY_PENALTY_QUOTIENT should be changed to 2**24. The description that after n epochs the log-balance decreases by (n**2 / 2) / INACTIVITY_PENALTY_QUOTIENT, and so when n = INVERSE_SQRT_E_DROP_TIME = 2**12 the log-balance drops by 1/2, ie. a sqrt-e factor drop, is correct.

Though it doesn't break security at all if it's kept at 2**25; it would just mean the leak takes 41% longer, so if this ends up being the only change we need to do then not bothering with it is fine too.

[hwwhww]

closing by #1712