Gravity No Graviton Unit Bridge Unit Bridge Theorem Inhabited

The unit bridge

The unit bridge is the step where a dimensionless number inside a theory becomes a quantity an experiment can measure. In the Recognition Science framework, gravity is characterized by a pure number, the coupling κ_rs, which the framework derives to lie in a narrow band between 85.6 and 90.4. The declaration unitBridgeTheorem_inhabited proves that this theoretical quantity can be converted, by a fixed formula, into the rate at which two masses would entangle a quantum phase in a proposed tabletop experiment. That rate, in the framework's own units, is a closed expression built only from the golden ratio φ: it equals φ¹⁰/π times the product of the two masses times a geometric factor depending on their separation.

The theorem itself is a statement about the existence of a bridge object. It says the structure UnitBridgeTheorem is inhabited, meaning all its required parts can be assembled from already-proved results. Those parts include the positivity of a related constant, an identity linking the coupling to the ratio G/ħ, and a closed form for the phase rate in SI units. The bridge object packages these together, so that anyone who accepts the framework's internal definitions can compute the predicted phase rate for any given masses and distances.

What the theorem does not do is connect that prediction to actual numbers measured in kilograms and meters. The conversion to SI units requires an inhabitant of ExternalCalibration, a structure that lives at the named open frontier of the framework's dimensional bridge. Until that calibration is supplied, the bridge theorem is conditional: it proves the formula, but the formula's output cannot be compared with experiment. The framework treats this as an open problem, not a failure of the derivation.

In the broader picture, the unit bridge is the load-bearing connection between the framework's abstract constants and the world of laboratory apparatus. The theorem establishes that the connection is mathematically well-formed and internally consistent. The missing calibration is the one remaining step before the framework's prediction for the entangling phase rate becomes a testable number. That is the difference between a derived structure and a measured result, and the framework keeps the two carefully apart.

theorem unitBridgeTheorem_inhabited : Nonempty UnitBridgeTheorem :=
  ⟨unitBridgeTheorem⟩

/-- **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 any laboratory experiment has measured the BMV phase rate. It does not claim that the framework's prediction matches any existing experimental result. It does not claim that the ExternalCalibration frontier has been discharged.

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)

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Derived articles

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