And a whitepaper before end of October is the must need and appreciated, I am curious to know which POS model will you use.

Each block has "generationSignature" parameter.  An active account signs "generationSignature" of the previous block with its private key.  This gives 64 bytes which are hashed with SHA256.  The first 8 bytes of the hash gives a number (I call it a "hit").  The hit is compared to the current "target" (64bit number).  If the hit is lower than the target then next block can be generated.

The target for each account is proportional to the balance.  Someone holding 1000 coins gets a 50 times bigger target than someone with 20 coins. Thus the owner of 1000 coins will generate 50 times more blocks than the owner of 20 coins (in the long run).

The target is not constant, it grows each second passed since the timestamp of the previous block.  If noone generated a block on the first second then the target becomes 2 times bigger and so on.  The base target is the target on the 60 second mark.  If there is only a few active accounts then after a long time someone will generate a block because the target will become very big.  If you open the client and log with any funded account you can see a ticking timer in BLOCKS widget.  It shows when the target will become greater than your hit.