Gravity Gravity Parameters Rung Offset Is Power Of 2

The rung offset

The rung offset is the number 16. In the Recognition Science account of galactic rotation, it appears as a fixed gap between two counting parameters: the conjectured number of time ticks in a galactic cycle, 142, and the conjectured number of radial rungs, 126. The offset is their difference, 142 minus 126 equals 16. The declaration rung_offset_is_power_of_2 proves, by direct computation, that this offset equals 2 raised to the fourth power, or 2 times 2 times 2 times 2.

That is the entire content of the theorem. It does not derive the number 16 from any deeper principle. It does not say why the offset should be 16, or why it should be a power of two, or that any physical measurement confirms it. The proof is a simple arithmetic check on a definition, not a law of nature. The offset is a defined constant in the framework's library, and the theorem merely records a property of that definition.

The same definition also satisfies two other arithmetic identities, each proved the same way: 16 is 4 squared, and 16 is 2 times 8. These are not independent discoveries. They are three ways of saying the same small fact about the number 16, all following from the same definition by computation.

What the declaration does not claim is worth stating plainly. It does not claim that the offset 16 is forced by the framework's axioms, or that the number 16 has any special physical status. It does not claim that the conjectures it connects, N_tau_conjecture and N_r_conjecture, are true. Those conjectures are separate definitions, and the offset theorem says nothing about whether they match any galaxy. The theorem is a fact about arithmetic, not a fact about the universe.

/-- The 16-rung offset is 2^4 = 4² (second non-trivial perfect square). -/
def rung_offset : ℕ := 16

theorem rung_offset_is_power_of_2 : rung_offset = 2 ^ 4 := by native_decide

theorem N_tau_conjecture_eq_142 : N_tau_conjecture = 142 := by native_decide

theorem N_r_conjecture_eq_126 : N_r_conjecture = 126 := by native_decide

What this page does not claim

The theorem does not derive the offset 16 from the framework's axioms. The theorem does not claim the conjectures N_tau_conjecture and N_r_conjecture are true. The theorem does not attribute any physical significance to the number 16.

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

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