Gravity No Graviton Unit Bridge Bmv Phase Rate Native Eq

The entangling phase rate

The declaration bmv_phase_rate_native_eq is a theorem in the Recognition Science framework's machine-checked library of formal theorems. It states that the rate at which gravity entangles two quantum systems, in the framework's native units, equals a closed-form expression: (φ⁵/π) · φ⁵ · m₁ · m₂ · g, where φ is the golden ratio, m₁ and m₂ are the two masses, and g is a geometry factor depending on their separation. The theorem derives this from the framework's definitions of the gravitational constant G and the reduced Planck constant ħ, which in native units are φ⁵/π and φ⁻⁵ respectively.

This is a conditional theorem: it holds only after one accepts the framework's unit system and its calibration to real-world units. The conversion to SI units, where a tabletop experiment could measure the effect, requires an external calibration input that the framework marks as an open frontier. The theorem itself is proved, but the bridge to physical reality is not yet complete.

What the theorem does not claim is substantial. It does not assert that this entangling phase rate has been measured, nor that the framework's native units are the true units of nature. It does not claim that gravity is fundamentally about entanglement, only that within the framework, gravity's effect on entanglement takes this specific mathematical form. The theorem is a statement about the framework's internal consistency, not about empirical reality.

/-- **Closed form for the RS-native BMV phase rate.** -/
theorem bmv_phase_rate_native_eq
    (m1 m2 r_LL r_LR r_RL r_RR : ℝ) :
    BMVPhaseRateNative m1 m2 r_LL r_LR r_RL r_RR
      = (phi ^ (5 : ℝ) / Real.pi * phi ^ (5 : ℝ))
          * m1 * m2 * bmvGeometryFactor r_LL r_LR r_RL r_RR := by
  unfold BMVPhaseRateNative
  rw [show G * m1 * m2 / hbar = (G / hbar) * m1 * m2 by ring,
      G_over_hbar_RS_native]

What this page does not claim

The theorem does not claim that this entangling phase rate has been observed in any experiment. It does not claim that the framework's native units are the fundamental units of physics. It does not claim that gravity is fundamentally a quantum entanglement phenomenon.

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/UnitBridge.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: