Gravity No Graviton Ilg Zero Params If Conjecture

The zero-parameter statement

In physics, a theory's parameter count is the number of constants that must be fixed by experiment before the theory makes predictions. General relativity has one such constant, Newton's G. The Recognition Science framework's machine-checked library of formal theorems contains a definition, ilg_parameter_count, that counts parameters for its gravity sector: it returns 1 when a flag is false, and 0 when the flag is true. The flag is named fibonacci_square_conjecture, a proposition that asserts a specific numerical coincidence involving the number 142 and the 12th Fibonacci number.

The theorem ilg_zero_params_if_conjecture proves, by direct computation, that if that conjecture holds, the parameter count is exactly zero. Its companion theorem ilg_one_param_if_not proves that if the conjecture fails, the count is exactly one. Together they form a conditional: the framework's gravity model is either fully parameter-free or has a single free constant, depending on an unresolved number-theoretic claim. The framework itself proves the conjecture is consistent, meaning no contradiction arises from assuming it, but consistency is not the same as truth.

What the declaration does not claim is just as important. It does not prove the conjecture true, so it does not establish that gravity actually has zero parameters. It only establishes the conditional structure: zero parameters if the conjecture holds, one if it does not. The theorem also says nothing about whether the framework's gravity model matches observation; it is a statement about the internal logic of the framework's definitions, not an empirical result.

In the broader context of the framework's gravity section, this conditional sits alongside stronger claims: a theorem that the gravitational coupling constant equals 8 times the golden ratio to the fifth power, and a theorem that gravitational waves have exactly two polarizations in three spatial dimensions. Those are unconditional. The zero-parameter statement is the one piece that explicitly depends on an unproved conjecture, which is why the framework's own documentation flags it as a target rather than a settled result.

theorem ilg_zero_params_if_conjecture :
    ilg_parameter_count true = 0 := rfl

theorem ilg_one_param_if_not :
    ilg_parameter_count false = 1 := rfl

theorem fibonacci_square_conjecture_consistent : fibonacci_square_conjecture := by
  exact ⟨142, rfl, by native_decide, by native_decide⟩

/-- κ is a polynomial function of φ alone. -/
theorem kappa_from_phi_alone :
    ZeroParameterGravity.kappa_rs = 8 * phi ^ 5 :=
  ZeroParameterGravity.kappa_rs_closed_form

/-- In D = 3 spatial dimensions, there are exactly 2 GW polarizations. -/
theorem gw_polarizations_eq_two : gw_polarization_count 3 = 2 := by native_decide

What this page does not claim

The conjecture is proved true, only that its truth would force zero parameters. The framework's gravity model is confirmed by experiment. The parameter count applies to any theory outside the framework's own definitions.

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/Gravity/NoGraviton.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: