Gravity Discriminator Matrix Cell Bohmian Rung Phase Positive

A positive phase signal

In quantum gravity research, several competing approaches predict different observable signatures. The Recognition Science framework organizes these predictions into a discriminator matrix: a table where each row names a rival theory and each column names a measurable sector. One cell in that table, labeled for the Bohmian approach, states a simple inequality: the phase delay is greater than zero. The phase delay here refers to a timing shift in a gravitational wave signal, a delay that would accumulate as the wave passes through a quantum-gravity structure. The theorem proves this quantity is positive, meaning the framework predicts a real, nonzero signal in this sector.

The classical context matters. Bohmian mechanics, and related stochastic-collapse proposals such as the Diosi-Penrose approach, generally predict no quantum-gravity signal in the relevant sector. The Recognition Science framework takes the opposite position: it derives, from its own axioms, that the phase delay must be positive. The declaration cell_Bohmian_RungPhase_positive is a theorem in the machine-checked library of formal theorems. It states 0 < rungPhaseDelay, and it carries no empirical input, no fitted parameters, and no additional axioms beyond the framework's standard three. The proof rests on a previously established positivity result for the phase delay.

What the theorem does not claim is equally important. It does not specify how large the phase delay is, only that it is positive. It does not name a particular experiment or a required sensitivity level for detection. The matrix structure organizes the theorem-grade discriminators into a comparison format, but it does not replace the separate falsifier register that ties each prediction to specific observational channels such as LIGO, Virgo, or LISA. The theorem also does not claim that the Bohmian approach is wrong; it claims only that the framework's prediction differs from the rival's prediction in this one sector.

For the general reader, the practical consequence is a testable distinction. If future gravitational wave observations show a positive phase delay in the predicted range, that counts as evidence for the framework's account. If observations show no signal, or a negative one, the framework's prediction fails. The theorem makes the framework vulnerable in a precise, measurable way, which is exactly what a scientific claim should do.

/-- (Bohmian, RungPhase): Bohmian / DP substrates do not produce this
φ-rung phase algebra. -/
theorem cell_Bohmian_RungPhase_positive : 0 < rungPhaseDelay :=
  rungPhaseDelay_pos

/-- (Bohmian, RungPhase): Bohmian / DP substrates do not produce this
φ-rung phase algebra. -/
theorem cell_Bohmian_RungPhase_positive : 0 < rungPhaseDelay :=
  rungPhaseDelay_pos

/-- (Bohmian, RungPhase): Bohmian / DP substrates do not produce this
φ-rung phase algebra. -/
theorem cell_Bohmian_RungPhase_positive : 0 < rungPhaseDelay :=
  rungPhaseDelay_pos

What this page does not claim

The theorem does not specify the magnitude of the phase delay, only its sign. The theorem does not name a specific experiment or required sensitivity level. The theorem does not claim that Bohmian mechanics is incorrect, only that its prediction differs in this sector.

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

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