So far the stories have given a time frame and mode of return for everybody that will come back. Because I'm a nerd, I have gone ahead and made a formula giving a general prediction of when people will return to see how well off those Returning will be. I doubt anybody is going to strictly follow this model since the Laws of Drama dictate that someone from the past can show up when needed, but I think it is interesting to see the numbers either way.

So, without further ado, here are some milestones for the number of Returned Persons:
Time for 1% Of the world's population to return: Approx. 6600-7000 years Post Event.
Time for 10% to Return: Approx. 8300-8500 years PE.
Time for 25% to Return: Approx. 9000-9100 years PE.
Time for 50% to Return: Approx. 9500 +/-50 years PE.
Time for 75% to Return: Approx 9800 +/- 10 years PE.
Time for 90% to Return: Approx 9925 +/- 5 years PE.

Time to reach 1 million Returned: Approx. 3400 to 4200 years PE.
Time to reach 1 billion Returned: Approx. 8500 to 8700 years PE.

I based my model off three assumptions:
1: The rate of population Return follows an exponential growth model. I.e. A*e^(k*t)=Pop. Returned, Where A=Initial population of Survivors (I.E. Lonely Day's Generation), k=Growth Constant, and t=time in years.
2: The total world population is roughly 7.3 billion at the time of the Event
3: The starting population of survivors is between 1400 and 10000.

My justifications for these are:
1: Luna said something to this effect, and this is a mercifully simple thing to model from what information is given in story.
2: This is the number I got when I googled the world's population. Granted this number was from July 2015 but I that was the closest date I got to May. The 300 million person difference evens out by the year 10000.
3: I got these values from looking at the various quotes on the number of those left behind, between 1/5000000 to 1/1000000. Even then, the time scale we are talking about here allows a lot of generous rounding.

For those interested, the range for the Growth Constant 'k' I used is between 0.00135 and 0.00155 for starting populations of 10000 and 1400 respectively.

I feel you have things mixed up a bit. There are two things to consider:

Descendents of the population already on Earth
People appearing from the Event in the future, in addition to natural population growth from descendents.

It appears to me the equation is not taking them both into account.

4647118 I should specify that this is only for the people that reappear. I.E. those that disappeared at the start of the first story. You can look at this as a prediction as to how long Lonely Day will have to wait to see her family again.

This doesn't take into account anything else. I don't have the know-how to predict anything else in any particular manner.

So, I've been summoned forth after my recent escape from hiatus to give a look at this.

First off, lets talk about modeling that exponential curve for what I referred to as 'Respawns,' or people simply returning after the effect of the spell has played its course and managed to (finally) match a soul to a body. Let me preface that besides 'exponential curve,' there was no other information on how exactly the rate of return worked I cannot say I am the best arithmetician, but with the help of a physicist and playing with numbers, we actually came up with the equation:
x = 7.125 * ((y / 10000) * 3.5) * e^((y / 10000) * 3.5) / (3.5 * e^(3.5))

You can see it plotted out here.

To get how many people have appeared in total up to a given year all one has to do is use said year as your Y value.

So lets take the years you gave roughly for when certain total values over time that people have appeared, 3,500 after event and 8,500 after event.

This provides us with the values of 0.25635 billion and 3.58261 billion total returned by those years.

Which brings us to having about 3.6% of the population returned by the year of 3500 and 50% by the year 8500

The model can have its curve adjusted, too, as you can alter the 3.5 up and down to alter things. 5 and above kinda breaks it, sadly, and I would probably have to go bother Hyper Atomic again to get it working again past that value.

If you want the total number of people returned in a given year OR a given span of years, model the number of the year you want to end in and subtract it by the value given by the year you want to start in.

Granted, keep in mind this only models the number of people returned. It does not model population growth by natural means at all.

I'll post more about population modeling later, as we do have a sheet that models this that I can pass to you all. ...Er, once I clean all the junk data out of it and all that, anyway.

EDIT: There we go, all clean and spiffy for everyone.
You can find the sheet here.
If you have any questions, feel free to ask.

4649325 Giving your numbers the 5 second glance, I am not sure where our numbers diverge really. I think I used e^kt where you used the more general exponential growth?

Granted the e^kt assumes that the rate of Respawn is based on the number already re-spawned, so your's might be more accurate. Though both illustrate that most Respawns will occur after the 6-7K year mark.

The timeline on the wiki gives an interesting reference point for that time period, though you can look it up yourself. I am honestly excited to try and write a story set in the millennia after the original stories, since that is when you can go crazy and speculate on things. You're not tied to the immediate post apocalypse. I really want to try and write a story about a Respawn that happens in a fairly Utopian society, though I feel the nature of the Utopian setting would make it difficult to have a conflict that isn't entirely internal. From their perspective, it might appear to be as if they landed on an alien planet, sort of like a normal HiE. You could even do a "Planet of the Apes" sort of reveal even, if it weren't for the fact that most readers would know the surprise already.

Granted, if I wanted to write a story set that far ahead and have it be relatively large scale (Nation, or even city scale), I'd have to deal with the fact that I don't know how far Starscribe is going to write stories in the setting. I don't know how many he has planned, though he might have mentioned it at some point.

4650290
Only 5 seconds? Maaan, I thought I was worth at least 7. =P

Part of why I did decided to poke in was not that you are 'wrong' in any way, and I'm sorry if I gave that impression. Rather, it was that this work has already been touched upon by our group. You had a good general theory for it. But you only had a theory when we had numbers, functions, spreadsheets, and other information that we could offer people.

Ok, so, the equation before we modified it to show a scale from 0-10000 was 7.125 * y * e^(y / (3.5 * e^(3.5)). It's just there to get a curve. Y was converted to ((y / 10000) * 3.5) so that from points one to 10000 would actually show their corresponding values rather then just having a curve. With the equation chopped back a bit without those bulky sections, you can see there's a basis built from e^kt and expanded on.

Yes, you're right, inputting a given year will only show how many have respawned up to that year. We have been deriving how many have respawned in a given time period by calculating the value for the end year and subtracting for the value of the beginning year.

>>The timeline on the wiki gives an interesting reference point for that time period, though you can look it up yourself.
Yes, I've seen the timeline. In fact, when I finally finished cleaning up my work I provided a link in the above post to a spreadsheet that not only models how many of these respawns occur within 100 year blocks, but also calculates for natural growth as well as modifying the population on certain years based on some of the events in the timeline (plague and war).

It includes explanations for most of the variables and such in the sheet and anyone can make a copy of the file and try to fiddle with it themselves.

As for writing in the Utopian eras? I'd still say go for it. Besides information available in the timeline, you can always do what some of the rest of us did when we were afraid we were getting too far and go poke Starscribe. Otherwise, you have an entire globe to work with that is at least 5000 to 8000 years out from what everyone else is working on. Pick a spot and have fun!

4650660 Yeah, I figure I might as well write something set further down the line. 50-50 chance it will be taken as cannon. Heck, it might give others a jumping off point.

Then again I have at least one idea I KNOW probably won't be canon unless I end up puling a Harper Lee and make it my one good story. Still might write it for fun.