I. Possibility of 'Cheating Nature'
1. It was thought as late as the 2010's that there was nothing more efficient than a permutation or a turning wheel. However, if an exception presented itself, it would mean something important. However, no concept really existed to explain the possibility. The closest analogy was a perpetual motion machine, but perpetual motion machines were thought not to work.
2. In Feb and Nov 2013 Nathan Coppedge invented the theoretical concept of exponential efficiency in the process of finding examples of the same. Even without referring to the examples, the general idea of making an efficiency that is exponentially efficient suggests improving at least some kinds of efficiency to a point where there could be something more efficient than a wheel or permutation. All that were needed were examples, and this is what Nathan found in 2013. But dismissing great examples without understanding them is not a fair argument, the burden of proof now rested on the opposing scientists. And, in a way, that was all that needed to initially be proved as perpetual motion was thought to be impossible by the scientists.
II. Necessity of Proportionality
2. Given the existence of other combinable cheating methods such as leverage, balances, difference of mass, and pulleys, it follows from 1/2 mass X distance that since a larger mass csn be moved by a smaller mass and motion takes place from rest, perpetual motion can be created if proportionality can be overcome. This is in part because a working proportionality could be built physically and could incorporate multiple overlapping 'cheating' methods.
3. However, proportionality CAN be overcome by analogy to a circle. Completing a cycle of motion is clearly physically possible, even more so in three-dimensionality than two-.
III. Energy in Some Cases
1. Proving energy is as simple as proving two-directional natural momentum (from rest). However, this is not necessarily easy. I have found it can be done (https://www.youtube.com/watch?v=ao0pIBVKjDo&list=PLcttXCrYoAgP88CiJ3ibPqVl1FjlAAIdi&index=9&app=desktop).
2. Consider a 3X lever counterweighted on the short end may have 1X additional structural mass on the long end. If the leverage applied on the long end to a ball by the mass on the short end is greater than 2.5X and less than 4X the mass of ball being moved, and the long end has the additional 1X structural mass, the 1X ball will begin to move by the force of the mass on the short end at 3X leverage distance if the 1X ball is positioned on a slotted track operated by the lever that is mostly horizontal but slightly upwards sloped (although under some conditions this is hard to prove). For example, 3 X leverage X 1 mass for ball / 2 for support is 1.5X mass + 1 for additional weight is 2.5 X effective mass. If counterweight is greater than 2.5X it may move ball under some conditions.
3. However, if ball is unsupported at the same amount of leverage, it has higher effective mass. 3 X leverage X 1X mass = 3X effective leversge + 1 additional structursl mass of lever means that if counterweight on short end is less than 4X mass of ball, then ball can lift counterweight when ball is supported by lever without the slotted track support (under some conditions).
4. Now we have proven there is two-directional motion in at least one case. And since the weight of the lever is accounted for and motion takes place from rest, it does not assume absolutely ideal physics, just fairly good conditions. Actual operation may depend on the size of the mass window and whether friction can be overcome in a case similar to a low-friction balance, which I suggest IS possible, although the practical window may be smaller than stated, and my example is one of the better cases.
Perpetual Motion Links
