Gravity Qgobservable Signal Models

Typed signal channels

Gravitational physics has a standard way to test a theory: pick an observable, predict a value, and compare with experiment. The Recognition Science framework's ledger, a discrete record of recognition events, forces a specific prediction for several such observables. The QGObservableSignalModels formalization attaches to each observational channel a typed signal model: the measured quantity, the RS-predicted value, the standard baseline value, current sensitivity, and a named falsifier threshold. The central structural result, proved with no axioms beyond the kernel's standard three, is that for all five listed channels the RS prediction is provably separated from the baseline by a positive amount.

The five channels are the pulsar timing array (PTA) stochastic background, the Event Horizon Telescope (EHT) shadow radius, S-star orbits near Sgr A*, Cassini/Shapiro time delay, and ringdown echo algebra. For the first four, the RS prediction is a positive value at the rung-44 φ-ladder scale, while the null baseline is zero: pure inflation predicts no stochastic background at nHz frequencies, and general relativity predicts no deviation from the Kerr shadow template or from standard post-Newtonian timing. The proofs that these predictions differ from zero are elementary consequences of φ being positive, but the structure matters: each channel carries its own named separation theorem, and the collection certifies that all channels are simultaneously separated.

The fifth channel, ringdown echo algebra, is handled with deliberate honesty. The φ-rung model carries a formula for a successive-amplitude ratio, but the old bounce-through-event-horizon mechanism has been rejected, and no replacement exterior mechanism has been derived. The formalization therefore quarantines this channel: it retains the formula as algebraic content but explicitly marks it as not part of the physical strong-field witness. The strong-field witness used by the master theorem consumes only the three horizon-exterior channels: EHT, S-star, and Cassini. This distinction is itself proved, not asserted, by a theorem stating that the ringdown channel's physical witness flag is false.

In plain language, the formalization establishes a disciplined comparison table for quantum-gravity tests. It proves that the framework's predictions are structurally distinct from standard baselines across five channels, and it refuses to claim a sixth-style result where the physical mechanism is not yet derived. The consequence is a falsifiable surface: each channel names a future threshold for 2026-2035, and the separation theorems guarantee that if the measured value lands in the predicted band, it cannot be explained away as a standard baseline fluctuation. The ringdown quarantine is the formalization's most instructive feature: it shows what a theorem-grade claim requires, and what it does 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

/-- PTA channel: stochastic gravitational-wave background amplitude at the
rung-44 φ-ladder scale.  RS predicts `φ^(-44)` (positive); pure inflation
predicts zero stochastic background at the relevant frequencies. -/
noncomputable def ptaChannel : ObservationChannelSignalModel where
  channelName := "PTA stochastic background"
  observable := "spectral amplitude h_c at f ~ nHz"
  rsPrediction := Constants.phi ^ (-44 : ℤ)
  nullBaseline := 0
  rsPrediction_ne_null := by
    intro h
    have := zpow_pos phi_pos (-44 : ℤ)
    linarith [h]
  separation_pos := by
    simp only [sub_zero, abs_of_pos (zpow_pos phi_pos (-44 : ℤ))]
    exact zpow_pos phi_pos (-44 : ℤ)

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 claim that any of the five channels has been measured to match the RS prediction. No claim that ringdown echoes are a physical prediction; the formalization explicitly marks them as quarantined. No claim that the separation theorems are physical predictions; they are algebraic facts about the signal model definitions.

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)

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

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