Gravity Qgobservable Signal Models All Channels Separated

The separation theorem

In physics, a falsifiable prediction must differ from the established theory's expectation. If a new model predicts exactly what the old one does, no experiment can tell them apart. The Recognition Science framework encodes this requirement in a machine-checked library of formal theorems, and its declaration all_channels_separated proves a precise, narrow version of it: for each of five observation channels, the framework's predicted value is not equal to the standard baseline value, and the absolute difference is positive.

The five channels are named in the library: the PTA stochastic background, the EHT shadow radius, S-star periapsis timing, the Cassini/Shapiro delay, and a ringdown echo formula. For the first four, the framework predicts a specific positive number, while the standard model baseline is zero. For example, the PTA channel predicts a spectral amplitude of phi to the power -44, a tiny positive number, against a pure inflation baseline of zero. The Cassini channel predicts three times that same small number. The separation theorem simply states what the structure already guarantees: each prediction is not zero, so the difference from zero is positive.

The theorem does not claim any signal has been detected. It does not claim the predicted values are correct, or that the framework's physics is right. It only proves an arithmetic fact about the numbers written into the channel definitions. The library is explicit about this: the ringdown channel is quarantined. Its formula is carried as algebraic content, but it is not part of the physical strong-field witness, because no horizon-consistent mechanism for echoes has been derived. The physical witness uses only the three horizon-exterior channels: EHT, S-star, and Cassini.

What the theorem does establish is structure. It shows the framework's predictions are distinct from the standard baselines in a formal, checkable way. That is the necessary condition for a future experiment to distinguish them. The separation is proved; the measurement is not.

/-- Every channel in the collection has a positive separation between RS
prediction and null baseline. -/
theorem all_channels_separated :
    ∀ c ∈ qgChannels, 0 < |c.rsPrediction - c.nullBaseline| :=
  fun c _ => c.separation_pos

/-- The five listed QG channels.  The ringdown entry is retained only as
quarantined algebraic content; it is not consumed by the physical strong-field
witness below. -/
noncomputable def qgChannels : List ObservationChannelSignalModel :=
  [ptaChannel, ehtChannel, sStarChannel, cassiniChannel, ringdownChannel]

theorem ringdownChannelStatus_not_physical_witness :
    ringdownChannelStatus.phi_ratio_formula_carried = true ∧
    ringdownChannelStatus.physical_strong_field_witness = false ∧
    ringdownChannelStatus.horizon_consistent_mechanism_open = true :=
  ⟨rfl, rfl, rfl⟩

What this page does not claim

No signal has been detected in any channel. The predicted values are not claimed to be correct physics. The theorem does not prove that the framework's gravity model is true.

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

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