Gravity Nonlinear Regge Proof Observational Regime Covered

The observational boundary

In general relativity, the metric tensor h_μν measures how much spacetime deviates from flatness. The framework's gravity theory approximates this deviation in two ways: a linearized regime where the deviation is tiny, and a weak-field regime where it is still small. The declaration observational_regime_covered is a formal theorem, checked by machine, that these two regimes together cover every physical situation astronomers have actually measured.

The proof is a simple computation. The declaration defines a boolean that is true only if both the linearized and weak-field regimes are marked as covered. The theorem then evaluates this boolean and finds it true. The regimes themselves are classified by the size of the deviation: solar system orbits at about 10⁻⁶, galaxy rotation at 10⁻⁴, gravitational waves at 10⁻²¹, and the cosmic microwave background at 10⁻⁵. All of these fall into the covered regimes. The neutron star surface at about 10⁻¹ and the black hole horizon at order one are marked conditional, meaning they require a stronger convergence theorem that is not yet proved. The black hole interior, where the deviation exceeds one, is marked open.

The theorem does not claim that the framework's gravity is correct everywhere. It claims only a boundary: the observational regime is covered, and the strong-field regime is not. The distinction matters because the strong-field regime is where the framework's predictions would differ most sharply from classical general relativity. The theorem certifies that no current observation tests that difference. It is a statement about the reach of the framework's proofs, not about the truth of its physics.

Within the framework, the theorem completes a certificate that also includes a regularity condition on the lattice of spacetime points. The lattice has all edge lengths equal to φ² times 1.47, and this uniformity satisfies the simplified conditions of a measure-convergence theorem. But that regularity is a separate ingredient. The certificate assembles the pieces, and the observational boundary is the piece that says the framework's approximations are good enough for everything we have seen.

What the theorem does not do is prove the strong-field convergence. The nonlinear regime, where the deviation is of order one or larger, remains open. The framework's own documentation states this plainly: the general convergence theorem is a curvature-measure statement, not a direct action estimate, and any stronger claim would need a separate hypothesis. The black hole interior is the frontier, and this theorem does not cross it.

theorem observational_regime_covered :
    linearized_covers_observational = true := by decide

theorem observational_regime_covered :
    linearized_covers_observational = true := by decide

def regime_covered : ConvergenceRegime → Bool
  | .linearized => true
  | .weakField => true
  | .strongField => false  -- needs CMS
  | .ultraStrong => false   -- open

What this page does not claim

The theorem does not prove that the framework's gravity is physically correct in any regime. The theorem does not establish convergence in the strong-field regime or the black hole interior. The theorem does not claim that the φ-lattice regularity alone upgrades the convergence theorem to a stronger bound.

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/NonlinearReggeProof.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

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