Take the theorem, test the claim: 3-6-9, vortex maths and a sphere
I gave 3-6-9 numerology, vortex mathematics and the Rodin coil one honest test each. Most claims didn't survive — but the mathematics hiding inside them produced the biggest engineering gain in the project.
Some ideas show up in engineering projects through the side door: the significance of 3, 6 and 9, vortex-math digital roots, the Rodin coil, golden spirals. The usual reactions are to roll your eyes or to believe it. I think both waste the one useful thing these ideas offer — a precise question.
So the rule for the Ternary-Six9 and Dictyon-net work was simple: every claim gets exactly one honest test, the result is written down, and the idea is retired or adopted on the evidence. Here's what happened.
The surprise: nine was never the problem
The Ternary-Six9 brief proposed encoding nine states as phase angles 40° apart — a nine-point dial. On a circle, that's a bad trade: nine phase states lose to eight once you account for the extra airtime needed to recover the lost margin.
But the hardware wasn't a circle. Three coils read by a three-axis magnetometer produce a 3-D vector. The right question is a nearly century-old one, the Tammes problem: how do you spread N points on a sphere as far apart as possible?
The same nine symbols on a sphere sit 70.5° apart instead of 40°.
That's +4.55 dB — the largest single gain anywhere in the project, for no extra power or hardware. And a related idea from a phyllotaxis paper, the golden angle (137.5°), gives a formula that places any number of points nearly optimally — with an advantage over the circle that keeps growing as the constellation gets bigger.
The triadic idea pointed at a sphere. The sphere is what paid.
What didn't survive
Nine isn't special. The famous structure of the doubling sequence mod 9 — 1, 2, 4, 8, 7, 5 repeating, with 3 and 6 trading places and 9 fixed — is what every prime square does. Mod 25 gives the same three tiers; so does mod 121. Nine is just the member of the family we see because we count in base ten.
The doubling map can't be a physical rotation. Its cycle structure would require three points to sit on a rotation axis, and a line only meets a sphere in two places. That's a proof, not a measurement.
3-6-9 isn't a special set in oscillation. A square-wave transmitter emits odd harmonics: 1, 3, 5, 7, 9… Six isn't one of them.
Mod-9 doesn't crack cryptography.
A spreadsheet looked for leakage between Nˣ mod p and Nˣ mod 9. The most it can reveal is about 2.58 bits of the secret exponent. The instinct behind it is real, though — it's a crude form of the Pohlig–Hellman algorithm, which is exactly why cryptographers use "safe primes".
The energy claims don't follow. The Rodin-coil mathematics in R. P. Blake's appendix is careful and correct. But correct elementary number theory doesn't support claims of fuel-free energy, and the package itself says the effects of a properly built coil "remain untested".
The part I'm proudest of
At one point I credited a finding as a correction to the vortex-maths workbook it came from. It wasn't: the workbook's author had already generalised past nine, pairing every base with its own modulus. The ledger got a correction, as prominent as the original. If you're going to hold other people's ideas to a standard, your own records have to meet it too.
The principle
Rigorous mathematics often arrives in mystical packaging. Take the theorem; test the claim.
Tammes packing, the tetrahedral "magic angle", the golden-angle spiral and Pohlig–Hellman are all solid, well-known mathematics. Each arrived here wrapped in a claim far bigger than it could carry. Unwrapping it — keeping the theorem, testing the claim — gave the project its best results.
The full write-up, with method, tables, limitations and references, is in the Academic Theory paper.