IndisputableMonolith.Foundation.InitialCondition
The InitialCondition module defines a configuration as a finite tuple of positive real ratios serving as ledger entries. It establishes the unity configuration (all entries equal to 1) as the unique state with zero total defect and minimum entropy, consistent with the Law of Existence. Cosmologists and foundational RS researchers cite it for t=0 conditions and ground-state derivations. The module consists of successive definitions followed by direct verification lemmas on defect and entropy.
claimA configuration is a tuple $(x_1,…,x_N)$ with each $x_i>0$. The total defect is the sum of individual defects, vanishing if and only if the tuple is the unity configuration with all $x_i=1$. The initial state is this unity configuration, which also minimizes the associated entropy functional.
background
The module sits inside the Recognition Science foundation and imports the J-cost from the Cost module together with the Law of Existence (x exists iff defect(x)=0) and the OntologyPredicates that tie existence to cost minimization under the unique J function. It introduces Configuration as a finite sequence of positive real ledger-entry ratios, total_defect as their summed defect, unity_config as the all-ones tuple, and entropy as a non-negative measure that is zero precisely on the unity tuple.
proof idea
This is a definition module, no proofs. It defines Configuration, total_defect, unity_config, entropy and initial_state, then states the lemmas total_defect_nonneg, unity_defect_zero, zero_defect_iff_unity, unity_is_global_minimum, unity_unique_minimizer, initial_state_minimum_entropy and nonunity_positive_entropy.
why it matters in Recognition Science
The module supplies the initial ledger state required by EarlyUniverse (EU-001 on t=0), StillnessGenerative (ground-state instability from T0–T8), VariationalDynamics (ledger update rule), TopologicalConservation and WindingCharges (topological conservation in D=3). It closes the gap between the Law of Existence and the first concrete state from which all structure is generated by cost minimization.
scope and limits
- Does not fix the number N of ledger entries.
- Does not derive the J function or Recognition Composition Law.
- Does not model time evolution or dynamics.
- Does not incorporate spatial dimensions or topology.
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