Gravity Gravity Parameters

Gravity parameters

Gravity parameters are the numerical constants used in a phenomenological model of galactic gravity. The module GravityParameters defines seven such parameters and states, for each one, whether it is mathematically derived from the golden ratio phi, has a Recognition Science basis with a physical motivation, or is purely phenomenological with no known connection to the framework.

The dynamical-time exponent alpha is the one parameter marked DERIVED. The module proves that alpha equals 1 minus 1 over phi, which is approximately 0.382. This value matches the observed exponent to within 1.8 percent. The parameter upsilon star is also marked DERIVED, and the module proves it is exactly equal to phi itself. The other parameters, such as C_xi, p, and A, are marked HAS RS BASIS, meaning their formulas match observations but the physical motivation is not yet a proof.

The module also establishes structural facts about the numbers that appear in the galactic constraint. The constants F_12 and rung_offset are defined as 144 and 16, and the module proves that F_12 is both the square of 12 and the 12th Fibonacci number, and that rung_offset is both 2 to the 4th power and two 8-tick cycles. The conjecture N_tau_conjecture is defined as F_12 minus 2, which the module proves equals 142, and N_r_conjecture is defined as N_tau_conjecture minus rung_offset, which the module proves equals 126. These are exact arithmetic identities, not empirical approximations.

The module does not claim that all seven parameters are derived from first principles. Only alpha and upsilon star carry the DERIVED tag. The remaining parameters are either phenomenological or have a Recognition Science basis that is not yet a proof. The module also links the parameters a0 and r0 through the relation tau_star equals the square root of 2 pi r0 over a0, and proves that this relation is consistent when converting between the two.

THEOREM alpha_gravity_eq_two_alphaLock · IndisputableMonolith/Gravity/GravityParameters.lean

THEOREM upsilon_star_eq_phi · IndisputableMonolith/Gravity/GravityParameters.lean

THEOREM F_12_is_perfect_square · F_12_is_fibonacci_12 · IndisputableMonolith/Gravity/GravityParameters.lean

THEOREM rung_offset_is_power_of_2 · rung_offset_is_two_8tick_cycles · IndisputableMonolith/Gravity/GravityParameters.lean

THEOREM N_tau_conjecture_eq_142 · N_r_conjecture_eq_126 · IndisputableMonolith/Gravity/GravityParameters.lean

What this page does not claim

Not all seven gravity parameters are derived from first principles in this module. The match of alpha to observation within 1.8 percent is not a proof of the model. No claim is made that the phenomenological parameters have a Recognition Science 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/Gravity/GravityParameters.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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