I think that the issue here is not so much that anyone disagrees with the principle of a more efficient engine. What you are hoping to do is laudable. I think a quote from every maths and statistics teacher I've ever had sums up the general level of scepticism: "show your work"... that is, don't just give us your results, show us how you got there.
You don't need to give us pages of calculations. If you want a constructive discussion, your claims of a 25% efficiency gain need to be backed up by some validated (i.e. published by someone else preferably in a scientific or trade journal) numbers like:
- the residual exhaust gasses that are leading to incomplete combustion at idle/low revs in the average engine (pick one injection, aspiration and displacement type and do all calculations on that basis)
- the proportion of incomplete combustion at the engine speeds you're talking about for your exemplar engine (puts a limit on what gain you can achieve)
- the pressure the compressor will have to work against at TDC to purge residual gasses
- actual fuel use numbers for your exemplar engine at idle and at city driving speeds
- actual CO2, CO, N2 etc for your exemplar engine at idle and speed
From numbers like these (and I'm sure there are more to consider), you can give us calculations to back up you efficiency gain claims. If you can't produce these numbers to back up some pretty extraordinary claims, very few people will take you and your system seriously.