Is this the Smith/Kapanadze secret ?

[verpies]

Just remembered that inductance of caduceus coil is zero

If by "caduceus" you mean two layer bucking coils, then the schematic should be adjusted as shown below.
If you mean two layer aiding coils then the former schematics and arguments still apply.
The coil configuration is denoted by the dot convention.

...this means that mutual inductance between W1 and W2 is also zero in your picture. When connected like this it is possible to tune system so there are hot and cold coils as I have explained, and testing confirmed it. So yes, I do think this has some merit now. What do you think ?

In bucking coil configuration the magnetic flux of one half of the coil opposes the flux of the other half. In an ideal bucking coil the two fluxes cancel each other and the result is zero net flux and zero self-inductance. In real coils there is always some leakage flux and leakage inductance between the two winding halves and if the winding does not span the whole circumference of the core, the flux leakage is increased (see the attachment for an illustration of this effect in a single layer toroidal winding).  Flux leakage also is exaggerated in windings with odd number of layers (1, 3, 5...) asymmetrical windings or in high-pitch windings.  There is also a very small interwinding capacitance that becomes significant in the MHz range.

Anyway, because ideal bucking coils have no effective self-inductance, then they cannot form an LCR circuit. They can only form an RC circuit, because a coil without self-inductance acts as a resistor.  Series RC circuit does not exhibit any resonance, only high pass filtering (parallel RC - low pass).

Also, since ideal bucking coils have no effective self-inductance they also have no mutual-inductance (one without the other, on a common core, would be an anomaly).
Lack of mutual-inductance is good between W1 and W2 but very bad between W1 and W3 as well as between W2 and W3, because without mutual-inductance no power can be transferred to W3 according to conventional theory

If you are getting power transfer to W3 anyway, then:
1) The coils are not in bucking configuration (e.g. one W1 dot is moved)
2) The coils are imperfect and have leakage (causing mutual and self-inductance)
3) There is an anomaly worth investigating (mutual-inductance without self-inductance)

Now, don't get excited about pt.3 before you eliminate the possibility of pt.1 and pt.2

[Jack Noskills]

I use series caduceus so there is start, middle and end points. Enamelled wires go side by side and no layers, one round for whole toroid. I counted 72 knots. Then secondary on top of caduceus, so far tested plain and bifilar but cannot compare them as number of turns were not equal (I got no meters). Parallel cap is between middle point and start and series cap is between end and source, as depicted in the picture I made. I got resonance point, my halogen lamp dimms and then it comes back to light again slowly so it is not RC filter. Just learned what RC filter is, thanks for that. I have seen this few times when testing other coil configurations and did not understand then.

pt1 is eliminated, but don't know about pt2. How should the circuit behave to eliminate pt2 ? I can take power from it without any change occurring in source, is this enough or is something else needed ?

[verpies]

How should the circuit behave to eliminate pt2 ?

a) You can measure the self-inductance of W1 with a decent multimeter (the low-quality ones do not have this function)
b) You can measure mutual-inductance by applying e.g. sinewave AC to W1 and measure if any AC voltage is induced at W2. If voltage is induced at W2 then mutual-inductance is not zero.

Both without any capacitors.

[elementSix]

Hey jacknoskills,  Have you read this page or tryed this circuit schematic???

http://tarielkapanadze.ru/science-eng.htm

here is their circuit diagram..

[verpies]

Have you read this page or tryed this circuit schematic???

I can't open the link.
Are those air cored coils?