Ilg Cpminstance Ilgprediction

The prediction record

In Recognition Science, a framework that derives physical structure from a forced cost of recognition, the declaration ILGPrediction is a data record for a specific astronomical prediction. It holds three pieces: a number called enhancement, a number called uncertainty, and a proof that the enhancement is at most 2. The record belongs to the ILG module, short for Infra-Luminous Gravity, a proposed modification of gravity for faint galaxies.

The prediction itself concerns rotation curves, the plot of how fast stars orbit a galaxy's center versus their distance from it. In ordinary Newtonian gravity, the curve should fall off at large radii. Observations of many galaxies show it stays flat, a discrepancy usually attributed to dark matter. ILG instead predicts a specific enhancement factor: the observed rotation speed is the Newtonian prediction multiplied by a number between 1 and 2. The ILGPrediction record packages that factor together with a bound on its uncertainty, and the machine-checked theorem ilg_falsifiable_bound proves the kernel that generates the enhancement is always at least 1, so the factor never drops below the Newtonian value.

The record is built on a larger formal structure. The module instantiates an abstract model called CPM, the coercive projection model, for ILG. The key result is ilg_coercivity: the defect mass, a measure of how far the system deviates from Newtonian, is bounded above by a product of constants times the energy gap. Those constants are explicit: the covering number K_net = (9/7)², the projection bound C_proj = 2, and the energy normalization C_eng = 1. From them the coercivity constant c_min = 49/162 follows by computation, and ilg_cmin_value proves that value exactly.

What the record does not claim is a specific numerical prediction for any particular galaxy. It establishes the form of the prediction and a universal upper bound of 2, but the actual enhancement value for a given galaxy would come from evaluating the kernel with that galaxy's parameters. The record is a template, not a filled-in measurement. It also does not claim that ILG is the correct theory of gravity; it shows that ILG fits the CPM framework, which is a consistency check, not a confirmation. The EnergyControlHypothesis, an assumption that defect mass never exceeds the energy gap, is a hypothesis in the formal sense: it must hold for the model to apply, and it is not proved from first principles.

The practical consequence is a falsifiable target. Because the enhancement is bounded between 1 and 2, any observed rotation curve that requires a factor above 2 would contradict the framework. That is a sharp, testable claim. The record makes the prediction precise enough to check against data, which is exactly what a scientific framework should produce.

/-- Structure recording falsifiable predictions for ILG. -/
structure ILGPrediction where
  /-- Predicted rotation curve enhancement factor -/
  enhancement : ℝ
  /-- Uncertainty bound -/
  uncertainty : ℝ
  /-- The enhancement is bounded by the kernel -/
  enhancement_bounded : enhancement ≤ 2

/-- The ILG kernel provides a falsifiable upper bound on dark matter effects. -/
theorem ilg_falsifiable_bound (P : KernelParams) (k a : ℝ) :
    kernel P k a ≥ 1 := kernel_ge_one P k a

/-- The coercivity theorem for ILG: energy gap controls defect mass. -/
theorem ilg_coercivity (P : KernelParams) (h_energy : EnergyControlHypothesis P) (s : ILGState) :
    (ilgModel P h_energy).defectMass s ≤
    ((ilgModel P h_energy).C.Knet * (ilgModel P h_energy).C.Cproj * (ilgModel P h_energy).C.Ceng) *
    (ilgModel P h_energy).energyGap s :=
  (ilgModel P h_energy).defect_le_constants_mul_energyGap s

/-- The ILG coercivity constant is 49/162. -/
theorem ilg_cmin_value : cmin ilgConstants = 49 / 162 := by
  simp [cmin, ilgConstants]
  norm_num

/-- Structure recording falsifiable predictions for ILG. -/
structure ILGPrediction where
  /-- Predicted rotation curve enhancement factor -/
  enhancement : ℝ
  /-- Uncertainty bound -/
  uncertainty : ℝ
  /-- The enhancement is bounded by the kernel -/
  enhancement_bounded : enhancement ≤ 2

What this page does not claim

ILGPrediction does not supply a numerical enhancement value for any specific galaxy. The record does not prove ILG is the correct theory of gravity, only that it fits the CPM framework. The EnergyControlHypothesis is assumed, not derived from first principles.

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/ILG/CPMInstance.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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