Require a proof of work for each transaction - blocksize issue solution

[jonny1000]

I propose the following idea, which could help with Bitcoin scalability economics:

Miners are required to include a "mini proof of work" for each transaction in a block (excluding the coinbase transaction), also based on SHA256.  The difficulty of the mini proof of work could be a small fraction, say 10,000x less difficult, than the main block difficulty.

Advantages:
1. The system provides a variable marginal cost to the miner of including each additional transaction in a block
2. The system incentivizes miners to keep blocks smaller and therefore no maximum blocksize is needed
3. The total cost of mining or work done will not change as this extra work will be factored into the 10 minute target time
4. It makes sense for the Bitcoin miners to do the mini proof of work as there are economic synergies between the two proofs (This could always be enforced somehow if necessary)

Possible disadvantages:
1. The community will need to decide on the fraction (There could be a target fraction, that adjusts every two weeks, for example initially 10% of work is allocated to transactions and 90% to the block, these ratios can adjust as the block reward changes)
2. This increases complexity
3. Blocksizes will initially increase, as the extra hashes will take up space
4. This creates another economic use of SHA256 not directly related to Bitcoin security

EDIT:  Now I see miners would need to solve multiple problems, which would advantage large miners making this scheme unworkable.

[1715377185]

1715377185

[1715377185]

1715377185

[jl2012]

Do you mean we will all have a Bitcoin ASIC in our cell phone?

[jonny1000]

Do you mean we will all have a Bitcoin ASIC in our cell phone?

No I was thinking the miners who are trying to find valid blocks do this, this could be enforced by adding a hash of the coinbase transaction into each mini proof of work.