IndisputableMonolith.Foundation.PhiForcing
The PhiForcing module establishes that the golden ratio φ satisfies φ² = φ + 1 from the J-cost functional together with ledger axioms. Researchers deriving physical constants from the φ-ladder cite this result. The module assembles discreteness and ledger forcing to reach the self-similar fixed point.
claimThe unique positive real φ satisfying φ² = φ + 1 is the fixed point of the recognition cost landscape under discrete scale invariance.
background
The module sits in the Foundation domain and imports LawOfExistence (existence iff defect zero), DiscretenessForcing (J(x) = ½(x + x⁻¹) - 1 has unique minimum at x = 1, or J(e^t) = cosh(t) - 1), LedgerForcing (J-symmetry forces double-entry structure), and PhiForcingDerived (derives r² = r + 1 from geometric scale sequences and additive ledger composition). Sibling declarations include phi_equation together with bounds such as phi_gt_onePointSixOneEight and phi_lt_onePointSixOneNine.
proof idea
This is a definition module, no proofs. The core equation is supplied by the imported PhiForcingDerived and specialized via the listed sibling declarations.
why it matters in Recognition Science
This module supplies the golden ratio φ that feeds constant derivations in ElectronMass, FineStructureConstant, GravitationalConstant, and PlanckScaleMatching, plus cosmological models in DarkMatter and FlatnessProblem. It fills the T6 step of the forcing chain where phi is forced as the self-similar fixed point.
scope and limits
- Does not derive numerical values of constants.
- Does not address non-self-similar scales.
- Does not treat quantum corrections to the φ-ladder.
- Does not prove uniqueness outside the stated axioms.
used by (40)
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IndisputableMonolith.Constants.ElectronMass -
IndisputableMonolith.Constants.FineStructureConstant -
IndisputableMonolith.Constants.GravitationalConstant -
IndisputableMonolith.Constants.PlanckScaleMatching -
IndisputableMonolith.Cosmology.DarkMatter -
IndisputableMonolith.Cosmology.FlatnessProblem -
IndisputableMonolith.Cosmology.GalaxyRotation -
IndisputableMonolith.Cosmology.Nucleosynthesis -
IndisputableMonolith.Foundation.ConstantDerivations -
IndisputableMonolith.Foundation.DimensionForcing -
IndisputableMonolith.Foundation.HierarchyDissolution -
IndisputableMonolith.Foundation.HierarchyEmergence -
IndisputableMonolith.Foundation.HierarchyMinimality -
IndisputableMonolith.Foundation.InevitabilityStructure -
IndisputableMonolith.Foundation.OntologyPredicates -
IndisputableMonolith.Foundation.ParticleGenerations -
IndisputableMonolith.Foundation.StillnessGenerative -
IndisputableMonolith.Gravity.GalacticTimescale -
IndisputableMonolith.Masses.LeptonMassLadder -
IndisputableMonolith.Masses.MassHierarchy -
IndisputableMonolith.Masses.MassRatiosProved -
IndisputableMonolith.Mathematics.Euler -
IndisputableMonolith.Papers.GCIC.DiscreteGauge -
IndisputableMonolith.Physics.ElectroweakBosons -
IndisputableMonolith.Physics.KaonMasses -
IndisputableMonolith.Physics.PionMasses -
IndisputableMonolith.Physics.ThermalFixedPoint -
IndisputableMonolith.Physics.WeakForceEmergence -
IndisputableMonolith.QFT.RunningCouplings -
IndisputableMonolith.QFT.UVCutoff
depends on (5)
declarations in this module (24)
-
theorem
phi_equation -
theorem
phi_pos -
theorem
phi_gt_one -
theorem
phi_lt_two -
theorem
phi_gt_onePointSixOneEight -
theorem
phi_lt_onePointSixOneNine -
theorem
phi_lt_onePointEight -
theorem
phi_gt_onePointSix -
theorem
phi_inv -
theorem
J_phi -
structure
SelfSimilar -
def
satisfies_golden_constraint -
theorem
self_similar_forces_golden_constraint -
theorem
phi_satisfies -
theorem
golden_constraint_unique -
theorem
phi_unique_self_similar -
structure
DiscreteLedger -
def
is_self_similar -
theorem
phi_forced -
def
J_bit -
theorem
J_bit_pos -
def
E_coh -
theorem
E_coh_pos -
theorem
phi_forcing_principle