The Arithmon Program

The hypothesis: the dimensionless constants of physics are counts, arithmetic and topological invariants of a compact geometry, with no continuously adjustable parameter.

This repository is the program's charter and its list of open problems. The map of adjacent work lives in the atlas; the methodology standard (how surprising is a claimed exact relation?) lives in the Sieve; the founding framework's proofs live in gift-framework/core.

The structure below follows Lakatos: a research program is a hard core that does not move, a protective belt of implementations that can be revised or falsified, and explicit rules for what counts as fair play.

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Start here

Read one thing: the hard core below, the whole claim in one sentence. Read three:

1. the hard core: the sentence that does not move;
2. the open problems (indexed in INDEX.md): what the program is actually trying to settle, refuted routes included;
3. the confrontations scoreboard: the dated predictions that will make or break it.

New to all of this? The plain-language door is the organization profile at github.com/arithmon. Whether any of it is more than coincidence is the Sieve's question. Want to contribute, or to attack the program? See CONTRIBUTING.md.

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Hard core

The dimensionless constants of physics are arithmetic and topological invariants of a compact geometry. None of them is a free parameter.

One sentence. Everything else is negotiable; this is not.

Protective belt

The implementations, revisable and falsifiable without touching the core:

• GIFT, the founding framework: the manifold K7, the Betti pair (21, 77), the E8xE8-motivated exceptional architecture, the 33 exact relations, the assignment of formulas to observables.
• The calibrated dynamical mechanisms (quarantined from the statistics).
• The second-stage hypothesis: particles themselves read as arithmetic-geometric objects. Stronger and more speculative than the core; it lives here, not in the core.

A framework can fall. The program is the question it answers to.

Negative heuristic

What is never done, whatever the pressure:

1. Never fit. No parameter is tuned to data, ever.
2. Never revise a frozen prediction after the fact. A prediction, once dated, stands or falls as stated.
3. Never add an undeclared constant to the vocabulary. The algebraic vocabulary is closed and public; the null model draws from it.
4. Never claim beyond the register. Proven, computed, conjectured and falsifiable-bet are distinct shelves; every statement sits on exactly one.
5. Never force the object into an existing taxonomy. The geometry is mapped by its own contours; resemblance to a known template is a question, not an answer.
6. Every register move is logged. A statement changing shelf is a dated event, never a silent edit.

Positive heuristic

The ordered list of problems the program commits to attack, one file per problem in problems/, indexed in INDEX.md, across five axes: geometry, selection, formalization, epistemic, experimental. Each problem carries its known constraints, including the negative results: refuted routes are listed as theorems about the territory, not buried.

The test

Lakatos distinguishes progressive programs (they predict novel facts) from degenerating ones (they only absorb anomalies). The program does not declare itself progressive; it publishes the scoreboard and lets the reader judge. The scoreboard is CONFRONTATIONS.md: frozen predictions, dated, against scheduled experimental data.

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_{GIFT is the founding framework of the Arithmon program. Program: arithmon.com · github.com/arithmon}