Astrophysics Gravitational Wave From Jcost Gwsource Category

The five source classes

Gravitational waves are ripples in spacetime, and astronomers group their sources by the objects that make them. The standard categories are neutron star pairs (NS-NS), black hole with neutron star (BH-NS), black hole pairs (BH-BH), supermassive black holes (SMBH), and the combined background hum called stochastic. The Recognition Science framework defines exactly these five as its source categories, a discrete classification of merger types, and proves in its machine-checked library of formal theorems that the count is five.

The framework then assigns each category a rung on a ladder. The strain, the fractional stretching of space a wave causes, at rung k is phi^k, where phi is the golden ratio, about 1.618. A proved theorem states that the strain of one rung divided by the strain of the previous rung equals phi. In plain terms, adjacent source classes differ in peak strain by the golden ratio, a specific numerical factor that links the classification to the framework's forced cost structure.

This is a definitional choice plus a derived ratio, not a measured astrophysical law. The framework models the five categories and proves the ratio that follows from its definitions. It does not claim that real detectors measure exactly this ratio, nor that the classification is the only possible one. The declaration establishes a consistent internal structure, and the empirical check against actual gravitational wave observations remains a separate question.

theorem gwSourceCount : Fintype.card GWSourceCategory = 5 := by decide

theorem strainRatio (k : ℕ) :
    strainAtRung (k + 1) / strainAtRung k = phi := by
  unfold strainAtRung
  have hpos := pow_pos phi_pos k
  rw [pow_succ]; field_simp [hpos.ne']

What this page does not claim

No claim that real gravitational wave detectors measure strain ratios exactly equal to phi. No claim that the five categories are the only possible classification of gravitational wave sources. No claim that the framework derives the absolute strain amplitude, only the ratio between adjacent classes.

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

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