t_planck
plain-language theorem explainer
Recognition Science cosmology fixes the Planck time at 5.4e-44 seconds to set the base scale for ledger-tension derivations of dark energy. Workers on cosmic hierarchies cite this constant when forming ratios such as t_universe over t_planck to recover the observed smallness of Lambda. The definition is a direct numerical assignment with no computation or proof steps.
Claim. The Planck time is defined by the numerical value $t_P = 5.4 × 10^{-44}$ seconds.
background
The Cosmology.DarkEnergy module derives the cosmological constant from ledger tension: global J-cost balance must hold while expansion creates new spacetime volume, leaving a residual energy density. J-cost is the function J(x) = (x + x^{-1})/2 - 1 whose minimum at x = 1 is strictly convex, as established in the upstream PhysicsComplexityStructure structure. LedgerFactorization supplies the underlying (R_+, ×) structure and calibration of J, while PhiForcingDerived and SpectralEmergence fix the discrete tiering and gauge content that set the Planck scale itself.
proof idea
The definition is a direct noncomputable assignment of the literal real number 5.4e-44; no lemmas or tactics are applied.
why it matters
t_planck supplies the denominator for cosmicRatio and thereby enters lambda_smallness_natural, which states that Lambda / M_planck^4 scales as (t_planck / t_universe)^2 and is therefore set by the cosmic hierarchy rather than fine-tuning. The constant anchors the Planck-to-Hubble gap that appears in the eight-tick octave and phi-ladder constructions of the forcing chain (T0-T8). It closes the numerical link between the ledger-tension model and the observed Lambda order of magnitude.
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