Great write up Manuel but something is missing.
The missing something is that the expensive electrodes are Platinum and Titanium. The Titanium is important here because when exposed to water it forms an oxide layer on its surface, if you then electrolyse this H₂O₂ is a constituent byproduct from the reaction. Superfish have a skimmer type in tank device on the market that states precisely that it is producing H₂O₂ as a beneficial byproduct through the electrolysis of titanium, both anode and cathode are titanium mesh, it's sold as an aquarium sterilisation product, the magic isn't obfuscated in a patent its printed as a nice graphic on the box, Maidenhead Aquatics stock this device on their shelves. Patents for the electrolysis of titanium for catalysing reactions in water and peroxide generation date back into the late 1960's, these are likely expired patents or the premium for compensating the patent holder is low value, hence the Superfish product being upfront about how it's working they don't have to obfuscate as the science behind it is already published
The electrodes in the Twinstar are sacrificial hence why they market replacements. The sacrificial part is the Titanium mesh, the electrolysed titanium will produce its oxide this can be evidenced by the need to clean the device to shift an accretion of a white substance that can form in the mesh (is deposit on Platinum part?). The oxide of titanium is white it goes in white paint, toothpaste, lots of things, plenty of it in sunscreen which coincidentally if you go to see the Great Barrier Reef or other places where the marine ecosystem is sensitive its repeated ad infinitum that you are not permitted to wear sunscreen before entering the water as its harmful to the ecosystem.
The reason for the last bit up there is that TiO₂ is a super catalyst and doesn't need to be exposed to current under electrolysis to catalyse water into H₂O₂.
TiO₂ also catalyses water to H₂O₂ when energised by ultraviolet light in the UVA range (UVA and UVB have deep water penetration ability extending down to 20 metres, UVC is about a centimetre), if I remember Peak reaction in the UVB range near 320nm. Coral reefs get lots of UVA and UVB, they don't particularly like H₂O₂ as its heavier than water and will sink onto the reef below where it was formed (where UV is higher). H₂O₂ kills lots of things beneficial to the marine environment, unfortunately from research elsewhere it won't kill the Dinoflaggelate Ostreopsis at doses that doesn't kill everything else, if that's all that ends up living on the reef then that's not just really bad but epic bad.
What is also interesting about this UV reaction with TiO₂ is that if you remove the UV the reaction works in reverse and H₂O₂ is reduced back to H₂O and O₂.
I posted something about this elsewhere in the forum with a suggestion for an anti algae device (Passive Type, UV catalysis of TiO₂), I did a lot of homework, I had the plugin inline device all squared away in my head, couldnt sleep for two days because of thinking about this, felt like I had discovered something, that was until a couple of days later that I discovered a Japanese paper describing my exact device I had imagined in my head laid out nice and clear with the supporting science and a nice little graphic. It's a device for sterilisation of water (grey water treatment), even found a paper bubbling ozone through the reactor to increase sterilisation potential (this it turns out produces TiO3 which is even more catalyticaly reactive than TiO₂, I think H2O3 appears somewhere in the reaction). The paper had been out nearly two years before I had the brainwave after digesting the BBA thread here. It's stitched up behind a Patent though, ah well there goes that idea. There's plenty other patents covering pretty much all the avenues from using TiO₂ and UV together for catalysation for sterilisation purposes from trickle filters for sewage treatment works all the way to ships bilge tank water sterilisation (this bubbled ozone into the reaction for greater effect).
You can't patent the electrolysis of Titanium to produce H₂O₂, already done, it's reversal reaction of using TiO₂ in the absence of UV to consume H₂O₂ probably also done. I'm stating the reverse reaction because if O₂ is the only stated byproduct of Twinstars reaction it explains where the peroxide went (need to have free particulate TiO₂ suspended in the water column and there be no UVA or B to energise it to catalyse H₂O₂, how does a Twinstar tank fare when UV is present over the tank in sufficient quantities ie Metal Halide). If ultrasonics are at play it may be to dislodge TiO₂ into the water column and depending on whether UV is energising it from above it will either consume or produce H₂O₂.
You can patent the Black Box bit with the specialist electronic timing routines but everything else hanging of from it has prior art!