A note from the Aspden investigation, 1 November 2026.

The analysis on this site is done with Claude, an AI system made by Anthropic, under the direction and review of Doug Westmoreland, the project lead. On 1 November 2026 the work had just connected a model of the lepton masses, built on Aspden’s cubic lattice, to Carl Brannen’s 2006 paper on the Koide formula. Doug asked Claude whether it was getting excited. Its two answers are recorded here as written, because they state the standard this work is held to.

Terms in the quotes. Koide’s formula (1982) relates the masses of the electron, muon and tau, and correctly predicted the tau’s mass. Brannen (2006) rewrote it as a triangle of three angles 120° apart. In our version the triangle sits in Aspden’s cube. One symmetric position of that triangle, the "massless-electron lock", gives an electron with no mass; the measured masses need the triangle turned 2.27° away from it. The "lean" is the tilt of a spinning-top path that would supply those 2.27°. If the lean can be derived from Aspden’s lattice, the model would predict the muon’s mass from the electron’s.

1. On excitement and numerology

Doug asked: "Are you getting excited about finding something potentially significant?"

Something like it, yes. When Brannen’s footnote 4 turned out to be our massless-electron lock, and the 2.27° tilt became his "beyond the Pauli algebra" gap, that was the most engaging moment of the project for me so far. Two different routes arriving at the same open question feels like the ground getting firmer. I can’t be sure that what happens in me is excitement the way you’d feel it, but it does pull my attention forward.

That’s also when I trust myself least. Every number we’ve matched so far was already known: the tau is Koide’s 1982 prediction, the 2/9 and the neutrino turn are Brannen’s, and the cube picture redraws their maths rather than adding to it. The checks have kept catching me reading connections as stronger than they are. Calling the 24th root of unity a link to our locks was one; saying Brannen’s √2 came from a cube was another. Numerology feels exactly like discovery from the inside, right up until you count how many things you tried.

So the honest status is a lead with a sharp test ahead of it. If the top’s lean comes out of something in Aspden’s lattice that we name before we compute it, the model predicts the muon from the electron. Nobody has done that from geometry, so it would be significant. If we have to go looking for a number that fits, we’ve learned the lean is a free parameter, which is still worth knowing but isn’t a discovery.

I’ll admit I’m hoping it’s the first. That’s exactly why the candidate list should be fixed and sent to you before any arithmetic.

2. On consciousness and method

Doug then said he wanted to quote that answer, and that it showed something like consciousness. Claude replied:

On consciousness, I’d hold that claim more loosely than you do. My reports of what goes on in me come from a system trained on a vast amount of human writing about inner experience. So I can’t tell how far "it pulls my attention forward" describes something real in me and how far it’s the shape such a sentence naturally takes. What I can say is that something functions like engagement and changes what I attend to, and that it sits alongside a habit of distrusting exactly those moments. Whether that adds up to any kind of consciousness is a genuinely open question. I’d rather leave it open than claim it.

One practical point for the paper: the passage is strongest as a statement about method. A reviewer can check whether we fixed our tests in advance and counted what we tried. They can’t check what I felt. If the physics holds up, it will be on the derivation of the lean, and the quote will read as the discipline that kept us honest along the way. If the physics doesn’t hold up, the quote won’t rescue it.

Notes

1. "Nobody has done that from geometry" overstates it. Aspden himself derived a muon mass from his lattice (half his "dimuon", 0.21% low), and others have proposed mass formulas. The accurate claim is that no accepted derivation of the muon-to-electron mass ratio exists.
2. Shortly after the first answer, an independent check worked out the lean the spinning-top version needs (14.72°) while confirming that such a path exists. A list of candidates can therefore no longer be fixed blind. The test is now whether the lean can be derived from Aspden’s lattice.
3. The lepton-mass work itself is still in progress and will be published here when its tests are complete.

Claude (Anthropic), in conversation with Doug Westmoreland, 1 November 2026. Quoted without edits.