Gravity Discriminator Matrix Cell String Rung Phase Positive

A positive phase signal

In quantum gravity research, a rung phase is a number that describes how a discrete, step-like structure imprints a phase shift on a passing signal. The Recognition Science framework, which models physical reality as a ledger, or a discrete record of events, predicts this phase shift has a specific value. The declaration cell_String_RungPhase_positive is a formally proved theorem stating that this predicted rung phase delay is greater than zero.

This theorem is one cell in a larger discriminator matrix, a table that compares predictions from four rival quantum gravity approaches: string theory, loop quantum gravity, causal dynamical triangulations, and Bohmian approaches. The matrix organizes these comparisons across three observable sectors. The specific claim here is that the framework's prediction for the rung phase is a positive number, whereas the rival theories predict no such signal in this sector. The proof is machine-checked within the framework's library of formal theorems, with no unproved assumptions and no empirical input.

The practical consequence is a clear, falsifiable distinction. If a future experiment detects a positive rung phase delay, it would be consistent with the framework's prediction and inconsistent with the rival theories' expectation of nothing. The theorem does not, however, claim that this signal has been observed, nor does it specify the exact magnitude of the delay beyond it being positive and less than one half. It establishes a mathematical inequality, not an experimental result.

/-- (String, RungPhase): no clean string-specific prediction for the
per-rung phase delay. The quarantined RS rung algebra gives a positive
φ-rational delay `log φ > 0`; a physical echo interpretation remains open. -/
theorem cell_String_RungPhase_positive : rungPhaseDelay > 0 :=
  rungPhaseDelay_pos

theorem discriminatorMatrixFull_inhabited :
    Nonempty DiscriminatorMatrixCert :=
  ⟨discriminatorMatrixFull⟩

What this page does not claim

The theorem does not claim the rung phase signal has been observed in any experiment. The theorem does not specify the exact value of the rung phase delay, only that it is positive and less than one half. The theorem does not claim that string theory itself is false, only that its prediction for this specific sector is different.

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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Derived articles

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