Mathematics Eight Fold Way From Rs Decuplet Eq 2 Times 5

The decuplet count

The baryon decuplet is the family of ten particles in the eight-fold way that includes the Delta baryons and the Omega minus. Gell-Mann's classification, proposed in 1961, groups strongly interacting particles by their quantum numbers. The decuplet's ten members are a standard fact of particle physics, confirmed by experiment.

The Recognition Science library contains a declaration named decuplet_eq_2_times_5 that states: baryonDecupletCount = 2 * 5. This is a theorem proved by the decide tactic, meaning the machine checked that the natural number 10 equals the product 2 times 5. The library also proves that the meson octet's eight members equal 2 cubed, and that five canonical hadron families (pion, kaon, eta, rho, omega) exist. These are arithmetic identities about named constants, not derivations of particle physics from first principles.

In Recognition Science, the framework models the eight-tick period as 2 to the power of the spatial dimension D, and at D=3 that gives 8. The decuplet's 10 is read as 2 times the configuration dimension 5. This is a definitional choice: the framework chooses to identify the particle counts with these arithmetic expressions. The theorem itself only establishes the equality of the numbers; it does not prove that the decuplet must have ten members or that the identification with 2 times 5 is physically meaningful.

The declaration is a small piece of a larger machine-checked library of formal theorems. Its value is in the audit trail: the arithmetic is verified with zero axioms beyond the standard logical ones. What it does not claim is any empirical content. The theorem does not predict a new particle, does not explain why the decuplet has ten members, and does not derive the eight-fold way from the framework's cost function. Those remain separate questions.

theorem decuplet_eq_2_times_5 : baryonDecupletCount = 2 * 5 := by decide

theorem mesonOctet_eq_2cubeD : mesonOctetCount = 2 ^ 3 := by decide

theorem hadronFamilyCount : Fintype.card HadronFamily = 5 := by decide

What this page does not claim

The theorem does not derive the decuplet's ten members from the framework's cost function. The theorem does not predict any new particle or experimental outcome. The identification of 10 with 2 times the configuration dimension is a definitional choice, not a proved physical law.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Mathematics/EightFoldWayFromRS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: