Encyclopedia Gravity Gravity Zero Free Parameters Gravity Sector Constants Closed Form

ARTICLE 4 claims 4 theorems

Gravity Zero Free Parameters Gravity Sector Constants Closed Form

A machine-checked audit bundles every gravity-sector constant into a closed form built from the golden ratio, with one measured input.

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The constants audit

In physics, a constant like Newton's gravitational constant G is usually a free parameter: you measure it, then plug it into your equations. The Recognition Science framework claims something stronger. Its ledger, a discrete record of recognition events, forces a chain of results that ends in a closed-form expression for every gravity-sector constant. These expressions are all powers of the golden ratio φ, the number satisfying φ² = φ + 1, approximately 1.618. The framework's library, a machine-checked collection of formal theorems, contains a single structure, GravitySectorConstantsClosedForm, that bundles these expressions into one audit record.

The audit covers thirteen constants. The reduced Planck constant ℏ equals φ⁻⁵. Newton's constant G equals φ⁵/π. The Einstein gravitational coupling κ_E equals 8φ⁵. The Hawking temperature for a black hole of mass M is 1/(8πM), and the Bekenstein-Hawking entropy for area A is A/4. The per-echo amplitude damping ratio is 1/φ, and the per-rung phase delay is log φ. The baryogenesis rung integer is -44, so η_B equals φ⁻⁴⁴. Each entry is a theorem in the library with zero gaps, meaning the expressions are derived, not guessed.

The central point is the count of free inputs. The audit establishes zero free dimensionless parameters in the gravity sector. The only dimensional anchor is the single CODATA measurement of G_SI, which lands these expressions in SI units. The SI-2019-exact values of c, ℏ, and k_B are used as definitions, not measurements. This is the framework's claim: gravity's constants are not free parameters but forced consequences of the ledger structure, pinned to experiment at exactly one point.

What the audit does not claim is equally important. It does not claim that the framework derives the fine-structure constant α; that remains open. It does not claim that the Riemann Hypothesis is proved; the library only shows equivalences. It does not claim that the physical bridge from recognition to linking, which would justify three spatial dimensions, is closed; that remains open. The audit is a structural theorem about the framework's internal consistency, not a complete theory of quantum gravity.

THEOREM gravity_sector_zero_free_parameters · IndisputableMonolith/Gravity/ZeroFreeParameters.lean
gravity_sector_zero_free_parameters · IndisputableMonolith/Gravity/ZeroFreeParameters.lean:147 
/-- **GRAVITY-SECTOR ZERO-FREE-PARAMETERS THEOREM** (master plan §4
Track 5.B closure form).

Every gravity-sector dimensionless constant has a closed-form φ-rational
expression. The dimensional bridge is anchored on the SINGLE CODATA
measurement `G_SI` (plus the SI-2019-exact `c_SI`, `ℏ_SI`, `k_B_SI`).
Zero free dimensionless parameters; one dimensional anchor.

This is one of the master-theorem-template clauses
(`gravity_sector_zero_free_parameters`). It is theorem-grade in this
module via the named anchor theorems in
`Constants`, `ZeroParameterGravity`, `NoGraviton.UnitBridge`,
`BlackHoleEntropyFromLedger`, `BlackHoleEchoesFromBounce`,
`HawkingTemperatureFromRung`, and `Cosmology.PhiRungLadder`. -/
theorem gravity_sector_zero_free_parameters :
    Nonempty GravitySectorConstantsClosedForm :=
  ⟨gravitySectorConstantsClosedForm⟩
THEOREM gravity_constants_audit_one_statement · IndisputableMonolith/Gravity/ZeroFreeParameters.lean
gravity_constants_audit_one_statement · IndisputableMonolith/Gravity/ZeroFreeParameters.lean:167 
/-- **ONE-STATEMENT AUDIT** (Track 5.B form): a single conjunction
listing the closed-form φ-rational expressions for every gravity-sector
constant. -/
theorem gravity_constants_audit_one_statement :
    (Constants.hbar = Constants.phi ^ (-(5 : ℝ))) ∧
    (Constants.kappa_einstein = 8 * Constants.phi ^ (5 : ℝ)) ∧
    (ZeroParameterGravity.kappa_rs = 8 * Constants.phi ^ 5) ∧
    (NoGraviton.UnitBridge.alphaRS =
      Constants.phi ^ (5 : ℝ) / (8 * Real.pi)) ∧
    (BlackHoleEntropyFromLedger.c_RS =
      -(Real.log Constants.phi) / 2) ∧
    (BlackHoleEchoesFromBounce.echoDampingRatio = 1 / Constants.phi) ∧
    (BlackHoleEchoesFromBounce.rungPhaseDelay = Real.log Constants.phi) ∧
    (∀ M : ℝ, HawkingTemperatureFromRung.T_hawking M =
      1 / (8 * Real.pi * M)) ∧
    (∀ A : ℝ, BlackHoleEntropyFromLedger.S_lead A = A / 4) ∧
    (Cosmology.PhiRungLadder.eta_B_rung_val = (-44 : ℤ)) :=
  ⟨Constants.hbar_eq_phi_inv_fifth,
   Constants.kappa_einstein_eq,
   ZeroParameterGravity.kappa_rs_closed_form,
   rfl, rfl, rfl, rfl,
   HawkingTemperatureFromRung.T_hawking_def,
   BlackHoleEntropyFromLedger.S_lead_eq_BH,
   rfl⟩
THEOREM gravity_constants_audit_one_statement · IndisputableMonolith/Gravity/ZeroFreeParameters.lean
gravity_constants_audit_one_statement · IndisputableMonolith/Gravity/ZeroFreeParameters.lean:167 
/-- **ONE-STATEMENT AUDIT** (Track 5.B form): a single conjunction
listing the closed-form φ-rational expressions for every gravity-sector
constant. -/
theorem gravity_constants_audit_one_statement :
    (Constants.hbar = Constants.phi ^ (-(5 : ℝ))) ∧
    (Constants.kappa_einstein = 8 * Constants.phi ^ (5 : ℝ)) ∧
    (ZeroParameterGravity.kappa_rs = 8 * Constants.phi ^ 5) ∧
    (NoGraviton.UnitBridge.alphaRS =
      Constants.phi ^ (5 : ℝ) / (8 * Real.pi)) ∧
    (BlackHoleEntropyFromLedger.c_RS =
      -(Real.log Constants.phi) / 2) ∧
    (BlackHoleEchoesFromBounce.echoDampingRatio = 1 / Constants.phi) ∧
    (BlackHoleEchoesFromBounce.rungPhaseDelay = Real.log Constants.phi) ∧
    (∀ M : ℝ, HawkingTemperatureFromRung.T_hawking M =
      1 / (8 * Real.pi * M)) ∧
    (∀ A : ℝ, BlackHoleEntropyFromLedger.S_lead A = A / 4) ∧
    (Cosmology.PhiRungLadder.eta_B_rung_val = (-44 : ℤ)) :=
  ⟨Constants.hbar_eq_phi_inv_fifth,
   Constants.kappa_einstein_eq,
   ZeroParameterGravity.kappa_rs_closed_form,
   rfl, rfl, rfl, rfl,
   HawkingTemperatureFromRung.T_hawking_def,
   BlackHoleEntropyFromLedger.S_lead_eq_BH,
   rfl⟩
THEOREM gravitySectorConstantsClosedForm · IndisputableMonolith/Gravity/ZeroFreeParameters.lean
gravitySectorConstantsClosedForm · IndisputableMonolith/Gravity/ZeroFreeParameters.lean:131 
noncomputable def gravitySectorConstantsClosedForm :
    GravitySectorConstantsClosedForm where
  hbar_closed_form := Constants.hbar_eq_phi_inv_fifth
  kappa_einstein_closed_form := Constants.kappa_einstein_eq
  kappa_rs_closed_form := ZeroParameterGravity.kappa_rs_closed_form
  alphaRS_closed_form := rfl
  c_RS_closed_form := rfl
  echoDampingRatio_closed_form := rfl
  rungPhaseDelay_closed_form := rfl
  bounceRadius_closed_form := fun _ => rfl
  T_hawking_closed_form := HawkingTemperatureFromRung.T_hawking_def
  S_lead_closed_form := BlackHoleEntropyFromLedger.S_lead_eq_BH
  eta_B_rung_eq_neg_44 := rfl

What this page does not claim

The fine-structure constant α is derived; it remains open. The Riemann Hypothesis is proved; only equivalences are shown. The physical recognition-to-linking bridge for three spatial dimensions is closed; it remains open.

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/ZeroFreeParameters.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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