standardInflation
Standard inflation parameters are instantiated with 65 e-folds, GUT-scale Hubble rate, and 10^{-32} s duration. Cosmologists comparing horizon-problem resolutions cite this record to benchmark the conventional exponential-expansion account against the 8-tick ledger synchronization. The definition assembles the structure by direct field assignment and applies norm_num to confirm the e-folds exceed 60.
claimThe standard inflation parameters consist of $N=65$ e-foldings, Hubble rate $H=10^{13}×1.602×10^{-10}/ℏ$ at the GUT scale, duration $10^{-32}$ s, and the verified condition $N>60$.
background
InflationParameters is the structure that records the number of e-foldings, the Hubble expansion rate during inflation, the duration in seconds, and the proof obligation that the number of e-foldings exceeds 60. The module COS-004 states the horizon problem as the observed CMB uniformity to 1 part in 10^5 despite regions that remain causally disconnected in the standard Big Bang timeline. The conventional solution invokes early exponential expansion that stretches one small causally connected patch across the observable universe. Upstream constants supply ℏ as the reduced Planck constant in RS-native units (φ^{-5}) and the fundamental tick as the time quantum of 1.
proof idea
The definition constructs the InflationParameters record by direct assignment of the three numerical fields. The remaining field is discharged by the norm_num tactic, which reduces the inequality 65 > 60 to a decidable numerical comparison.
why it matters in Recognition Science
This definition supplies the conventional inflationary benchmark inside the COS-004 module, enabling explicit comparison with the Recognition Science account that treats the eight-tick octave as a universal ledger property rather than a local causal process. It therefore sits at the interface between the standard T7 eight-tick construction and the J-cost minimization that enforces homogeneity as a consistency condition. The module doc-comment notes that the ledger structure itself provides the required synchronization without light-speed communication.
scope and limits
- Does not derive the numerical values from the phi-ladder or Recognition Composition Law.
- Does not prove that inflation resolves the horizon problem.
- Does not connect the parameters to defectDist or costOfInhomogeneity.
- Does not address the Berry creation threshold or Z_cf.
formal statement (Lean)
105noncomputable def standardInflation : InflationParameters := {
proof body
Definition body.
106 e_folds := 65,
107 hubble := 1e13 * 1.602e-10 / hbar, -- GUT scale (~10^13 GeV)
108 duration := 1e-32, -- seconds
109 e_folds_sufficient := by norm_num
110}
111
112/-! ## The RS Solution: Universal Clock -/
113
114/-- Recognition Science offers a different perspective:
115
116 The 8-tick clock is NOT a local phenomenon.
117 It is a property of the ledger ITSELF, which is universal.
118
119 This means:
120 1. All regions are synchronized by the ledger structure
121 2. Homogeneity is a consistency condition, not a coincidence
122 3. The initial state was constrained by J-cost minimization -/