Instead of having a halving every 4 years or something, wouldn't it be better to increase the time between each halving according to the Fibonacci numbers?
Number of blocks: reward
524284: 4096
524284: 2048
1048568: 1024
1572852: 512
2621420: 256
4194272: 128
6815692: 64
11009964: 32
17825656: 16
28835620: 8
46661276: 4
75496896: 2
122158172: 1
197655068: 0.5
319813240: 0.25
517468308: 0.125
837281548: 0.0625
1354749856: 0.03125
2192031404: 0.015625
3546781260: 0.0078125
5738812664: 0.00390625
9285593924: 0.001953125 (now after 28655 years at least 9 decimals will be needed).
It continues like that forever resulting in a total supply of 8589869056 which is the sixth perfect number. 25% is mined before the first halving, 37.5% is mined until the second halving and 50% is mined before the third halving. The numbers above are for a blocktime of 60 seconds resulting in halvings after 1,2,4,7,12,20,33,54,88,143,232,,, years and i believe this is the ideal distribution(25% mined after 1 years, 50% mined after 4 years).
This is just a suggestion in the case someone plan to start a new coin, for a
PoA coin the block reward would be split into one PoW reward and one PoS reward after 1572852 blocks.
Marketcap(including future coins) needed for secure network assuming a 10x in price is needed for the same security after halving
1 years: 100000$
2 years: 1 million $
4 year: 10 million $
7 years: 100 million $
12 years: 1 billion $
20 years: 10 billion $
33 years: 100 billion $
If the new coin is successful the price will increase enough for the network to remain secure after each halving, of course most coins fail and then it does not matter how good the distribution model is. This distribution model can be applied to any new coin but it is most suitable for pure PoW and i actually think pure PoW is the best solution when implemented properly.
Number of blocks: reward
2097136·1: 1024
2097136·1: 512
2097136·2: 256
2097136·3: 128
2097136·5: 64
2097136·8: 32
2097136·13: 16
2097136·21: 8
2097136·34: 4
2097136·55: 2
2097136·89: 1
2097136·144: 0.5
2097136·233: 0.25
2097136·377: 0.125
2097136·610: 0.0625
2097136·987: 0.03125
1048568·1: 2048
1048568·1: 1024
1048568·2: 512
1048568·3: 256
1048568·5: 128
1048568·8: 64
1048568·13: 32
1048568·21: 16
1048568·34: 8
1048568·55: 4
1048568·89: 2
1048568·144: 1
1048568·233: 0.5
1048568·377: 0.25
1048568·610: 0.125
1048568·987: 0.0625
524284·1: 4096
524284·1: 2048
524284·2: 1024
524284·3: 512
524284·5: 256
524284·8: 128
524284·13: 64
524284·21: 32
524284·34: 16
524284·55: 8
524284·89: 4
524284·144: 2
524284·233: 1
524284·477: 0.5
524284·610: 0.25
524284·987: 0.125
262142·1: 8192
262142·1: 4096
262142·2: 2048
262142·3: 1024
262142·5: 512
262142·8: 256
262142·13: 128
262142·21: 64
262142·34: 32
262142·55: 16
262142·89: 8
262142·144: 4
262142·233: 2
262142·377: 1
262142·610: 0.5
262142·987: 0.25
131071·1: 16384
131071·1: 8192
131071·2: 4096
131071·3: 2048
131071·5: 1024
131071·8: 512
131071·13: 256
131071·21: 128
131071·34: 64
131071·55: 32
131071·89: 16
131071·144: 8
131071·233: 4
131071·377: 2
131071·610: 1
131071·987: 0.5