Astrophysics Stellar Assembly Tick Ratio Value

The tick ratio

In the Recognition Science framework, a ledger (a discrete record of events) tracks stellar processes by counting ticks (individual recognition events). The framework's library of formal theorems proves that this ledger splits its eight ticks into five for mass storage and three for light emission. The theorem tick_ratio_value establishes that the ratio of mass ticks to light ticks is exactly the rational number 5/3.

This ratio is not an empirical measurement. It is a definitional consequence: the framework defines mass_ticks as 5, light_ticks as 3, and tick_ratio as mass divided by light. The theorem simply records that this division equals 5/3. The framework then uses this ratio to derive a prediction: the mass-to-light ratio (M/L) of a typical stellar population should be the golden ratio φ, approximately 1.618 in solar units. This prediction falls within the observed range of 0.5 to 5 solar units for real stars, but that agreement is a check, not a proof.

What the declaration does not claim is equally important. It does not claim that real stars must have M/L = 1.618. The framework's own hypothesis, H_StellarML, states this value, and the falsifiable theorem ml_falsifiable shows that if the value were different, the hypothesis would be false. The 5/3 ratio itself is a pure arithmetic fact about the framework's chosen tick counts; it carries no physical content on its own. The physical bridge, from recognition cost to actual stellar collapse, remains a modeling choice, not a derived law.

theorem tick_ratio_value : tick_ratio = 5 / 3 := rfl

theorem tick_partition : mass_ticks + light_ticks = total_ticks := rfl

/-- **THEOREM (PROVED)**: Stellar M/L value is φ. -/
theorem ml_stellar_value : ml_stellar = φ := by
  unfold ml_stellar characteristic_tier_scaffold
  simp only [zpow_one]

What this page does not claim

The tick ratio 5/3 is a physical constant measured from stars. The framework proves that all real stellar populations have M/L = 1.618. The physical bridge from recognition cost to stellar collapse is a derived law.

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

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