The Last Free Parameter
Why GIFT becomes Arithmon
The framework I have been developing for the past year claims to have no free parameters. Thirty-three exact relations, topological integers, nothing adjustable. That was almost true.
One poorly constrained parameter remained, and it had been under my nose from the start: the name.
A name is a hypothesis
GIFT, Geometric Information Field Theory, was the right name in 2025. It honestly described what I believed I was building at the time: an information field theory, ambitious, a little too sure of itself, the way one is at the beginning. The first preprints are still on Zenodo, dated, available. I have never withdrawn them and I never will: they are the acknowledged beginning of this story, naiveties included, and a trajectory without a starting point is not a trajectory.
But a year later, the name no longer describes the thing. The “information field” is no longer the core of the work: the core is a set of exact relations among topological invariants, machine-checked, and frozen predictions awaiting their experimental verdict. And incidentally, try searching the web for “GIFT” in December: my framework shares its name with a good portion of world commerce and a dozen academic projects.
I hold all my positions as hypotheses, to be revised when the data change. There is no reason a name should escape the rule. The data have changed. I revise.
Arithmon
Arithmon /a.riθ.mɔn/, from the Greek arithmos (ἀριθμός), number. Its -on ending is that of the particles: electron, proton, boson. The name thus carries the hypothesis within itself: number made particle, physical entities as arithmetic-geometric objects. And the word already existed under a second reading: arithmôn (ἀριθμῶν), the genitive plural, “of numbers.”
Number as particle. Particle as number.
There is the entire program in three syllables, and that is exactly what a name should do.
The new architecture is simple:
Arithmon is the program: the durable hypothesis that the dimensionless constants of physics are not free parameters to be measured, but counts: arithmetic and topological invariants of a geometry. A question, more than an answer. A research program in the strong sense, built to outlive its successive implementations.
GIFT is its founding framework: the first concrete, dated realization of that hypothesis. A specific geometry (the manifold K₇, the (21, 77) topology, an E₈×E₈-motivated architecture) and the exact relations that follow from it. A framework can be revised, sharpened, or refuted. The program is the question it answers.
Nothing is disowned, everything is nested. The preprints keep their name, the gift-framework GitHub repository remains the address of the foundations, the citation in Physics Letters B points where it has always pointed, and the paper currently under review defines GIFT as it always has. GIFT becomes a historical proper noun: the name of the first answer. Arithmon is the name of the question.
How one baptizes a research program in 2026
I have to tell the story of how the name arrived, because the method is the message.
I first asked my usual pool of AIs (half a dozen different architectures) for a communications audit. Unanimous verdict: saturation. Then, in a conversation with Claude, while searching for the program’s invariant: what would survive even if the current geometry fell, the word came out: Arithmon. I then ran a blind test: asking another AI for its own candidates before showing it this one. The comparison was useful: none held the tension between number, particle, and research program as well.
Due diligence: no Digimon bears the name (yes, we checked the -mon suffix is a minefield), the .com was available, and the few visible occupants of the word are ancient Greek itself: biblical concordances and number-theory textbooks, theoria arithmon, “theory of numbers.” The genitive had been waiting for its program for twenty-six centuries.
The Twitter handle, for its part, is squatted by a 22-year-old vampire. We will live with that. Every pedigree has its next-door neighbors.
And then came the find I was not expecting. While checking the terrain, a search surfaced Arignote of Croton, a Pythagorean philosopher of the sixth century BCE, reputed daughter of Pythagoras and Theano, to whom tradition attributes this fragment:
“The eternal essence of number is the most providential cause of the whole heaven, earth and the region in between.”
I do not believe in signs. But I believe in lineages, and this one I will take: accepting what comes with it: yes, this is a Pythagorean intuition. The difference between counting and fantasizing is the 33 falsifiable relations, the null model, and the Lean code running behind it. The day DUNE decides, it is not Pythagoras who will be questioned; it will be the measurement.
What changes, what does not
Changes: the name, the domain (arithmon.com), this publication, the profiles.
Does not change: the mathematics, the frozen predictions (δ_CP = 197°, the θ₂₃ octant, the exact ratios), the experimental timeline, and the method. The furrow goes on. Only the signpost at the edge of the field has been repainted.
New substack address: arithmon.substack.com
Current landing page W.I.P.: github.com/Arithmon
Instagram: instagram.com/arithmon
X/Twitter: x.com/ArithmonProgram