module module high

`IndisputableMonolith.Constants.Derivation`

The Derivation module establishes the relation τ₀² = ℏG/(πc⁵) linking the RS time quantum to standard constants. Researchers deriving Planck-scale quantities from Recognition Science primitives would cite it. The module assembles codata definitions and applies dimensional analysis from the imported Dimensions and Constants modules to obtain the identity.

claimThe module establishes the identity $τ_0^2 = ℏG/(π c^5)$.

background

This module belongs to the Constants domain of Recognition Science. It imports the definition of τ₀ as the fundamental RS time quantum equal to one tick. The Dimensions module supplies the dimensional analysis framework for deriving physical constants from Recognition Science primitives, with fundamental units being the tick and related RS quantities.

proof idea

This is a definition module, no proofs. It assembles codata for c, ℏ, G and states the key lemma derived from the dimensional framework in the upstream modules.

why it matters in Recognition Science

This module feeds the codata definitions for c, ℏ, G. It supplies the key lemma τ₀² = ℏG/(πc⁵) which anchors the constant derivations, connecting to the phi-ladder and D = 3 from the forcing chain T5-T8.

scope and limits

Does not compute numerical values for the constants.
Does not derive the forcing chain steps T0-T8.
Does not address experimental tests of τ₀.
Does not extend to mass formulas on the phi-ladder.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Constants.Dimensions module_import

declarations in this module (40)

def c_codata L24
def hbar_codata L25
def G_codata L26
lemma c_codata_pos L28
lemma hbar_codata_pos L29
lemma G_codata_pos L30
lemma c_codata_ne_zero L32
lemma hbar_codata_ne_zero L33
lemma G_codata_ne_zero L34
def tau0 L38
lemma tau0_pos L40
lemma tau0_ne_zero L48
lemma inner_pos L50
lemma inner_nonneg L54
theorem tau0_sq_eq L58
def ell0 L71
lemma ell0_pos L73
lemma ell0_ne_zero L74
structure RSUnitSystem L78
def canonicalUnits L87
def c_derived L98
theorem c_derived_eq_codata L100
lemma c_derived_pos L107
def hbar_derived L110
lemma hbar_derived_pos L112
theorem planck_relation_satisfied L119
def G_derived L129
lemma G_derived_pos L131
theorem G_relation_satisfied L138
def planck_length L150
def planck_time L151
def planck_mass L152
lemma planck_length_pos L154
lemma planck_time_pos L158
lemma planck_mass_pos L162
lemma planck_time_inner_nonneg L166
theorem tau0_planck_relation L172
theorem units_self_consistent L227
theorem tau0_matches_foundation L249
def derivation_status L255