IndisputableMonolith.Foundation.InitialCondition
This module defines the initial ledger configuration in Recognition Science as a finite list of positive real ratios. Cosmologists modeling t=0 conditions and foundational researchers deriving ground-state properties cite it to anchor the zero-defect starting point. The module supplies direct definitions of total defect, entropy, and the unity minimizer together with immediate non-negativity and uniqueness lemmas.
claimAn initial configuration is a finite sequence $C = (x_1, x_2, ..., x_N)$ with each $x_i > 0$. The total defect is defined as the sum of $J(x_i)$ over the entries, where $J$ is the Recognition Science cost function, and the unity configuration has every $x_i = 1$.
background
The module imports the J-cost from Cost, the Law of Existence (x exists iff defect(x) = 0), and the RS ontology predicates that treat existence and truth as outcomes of cost minimization. It introduces Configuration as the basic object for ledger states and defines total_defect, entropy, and the unity configuration. These notions sit at the start of the forcing chain before any dynamics or topology is imposed.
proof idea
This is a definition module, no proofs. It consists of the Configuration type, direct definitions of total_defect and entropy, and short lemmas (total_defect_nonneg, unity_defect_zero, unity_unique_minimizer) that follow immediately from the definitions and the properties of J.
why it matters in Recognition Science
The module supplies the initial state required by Cosmology.EarlyUniverse for deriving t=0 conditions and the dark sector, by StillnessGenerative for the ground-state instability theorem, and by VariationalDynamics and TopologicalConservation for subsequent ledger evolution and charge conservation. It closes the setup gap before the T5–T8 steps that force phi, the eight-tick octave, and D = 3.
scope and limits
- Does not fix the ledger length N.
- Does not define time evolution or update rules.
- Does not introduce topological winding or charges.
- Does not compute numerical values of constants or mass spectra.
used by (5)
depends on (3)
declarations in this module (12)
-
structure
Configuration -
def
total_defect -
theorem
total_defect_nonneg -
def
unity_config -
theorem
unity_defect_zero -
theorem
zero_defect_iff_unity -
theorem
unity_is_global_minimum -
theorem
unity_unique_minimizer -
def
entropy -
theorem
initial_state_minimum_entropy -
theorem
nonunity_positive_entropy -
theorem
past_theorem