Astrophysics Solar Wind From Phi Ladder Solar Wind Speed

Solar wind speeds on a phi ladder

The solar wind is a stream of charged particles flowing outward from the Sun. Observers have long sorted it into bands: slow wind near 300 to 400 km/s, fast wind near 600 to 800 km/s, and extreme events above 1000 km/s. The definition solarWindSpeed in the Recognition Science framework models each band as a rung on a ladder where adjacent rungs differ by the golden ratio phi, about 1.618. The ratio of any two neighboring speeds is exactly phi, a fact the framework proves in its machine-checked library of formal theorems.

The framework also proves that its classification of solar wind types has exactly five members: quiet, slow, intermediate, fast, and extreme. That count matches the five canonical bands that space physicists describe. The definition and the ratio proof together form a certificate: a packaged statement that the five-type count holds and that every adjacent speed pair obeys the phi ratio. Both claims are checked by the library with no unproved assumptions.

What the declaration does not do is predict any measured speed in kilometers per second. The definition assigns speeds as powers of phi, but it never states which rung corresponds to slow wind, which to fast wind, or what the base unit is. The framework's own notes compare 700/350 to phi, yet that is an informal illustration, not a theorem. No claim in the library says the slow band sits at 350 km/s or the fast band at 700 km/s. The definition establishes a structure, not a measurement.

In plain terms, the declaration tells you that if you accept the framework's modeling choice, then solar wind speeds come in ratios of phi, and there are five types. It does not tell you where on that ladder the real Sun sits. That gap is the difference between a formal structure and an empirical prediction.

theorem solarWindSpeedRatio (k : ℕ) :
    solarWindSpeed (k + 1) / solarWindSpeed k = phi := by
  unfold solarWindSpeed
  have hpos := pow_pos phi_pos k
  rw [pow_succ, div_eq_iff hpos.ne']
  ring

theorem solarWindTypeCount : Fintype.card SolarWindType = 5 := by decide

/-- Adjacent solar wind speeds at phi-ladder rungs. -/
noncomputable def solarWindSpeed (k : ℕ) : ℝ := phi ^ k

What this page does not claim

No measured solar wind speed is predicted by the declaration. The informal 700/350 comparison is not a theorem in the library. The five-type count is a classification, not a physical derivation.

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/SolarWindFromPhiLadder.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.

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