module module high

`IndisputableMonolith.Engineering.FissionTransmutationStructure`

This module defines nuclear configurations in Recognition Science via a ledger ratio x, with x=1 marking stable doubly-magic nuclei. It supplies cost functions and transmutation structures built on the imported Cost and Constants modules. Engineers modeling fission processes or cost-reducing transmutation paths would reference these objects. The module consists entirely of definitions and supporting lemmas with no complex proofs.

claimA nuclear configuration is parameterized by ledger ratio $x$, where $x=1$ denotes a stable (doubly-magic) nucleus and $x≠1$ an unstable one. The associated cost function satisfies nuclear_cost_nonneg and nuclear_cost_zero_iff_stable. Transmutation steps and paths are defined to reduce total cost while respecting the J-cost composition law.

background

Recognition Science starts from a single functional equation whose solutions yield the J-cost function satisfying the Recognition Composition Law. The module imports the RS time quantum τ₀=1 tick from Constants and the cost machinery from Cost. It introduces NuclearConfig as a configuration parameterized by ledger ratio x, together with nuclearCost, TransmutationStep, TransmutationPath, and stability predicates.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the core objects for RS-native nuclear engineering, directly enabling the cost-reduction lemmas (transmutation_reduces_cost, path_reduces_total_cost, cost_reduction_bounded) that sit inside the same file. It translates the abstract J-cost and phi-ladder framework into concrete fission and transmutation modeling.

scope and limits

Does not assign numerical ledger ratios to specific isotopes or elements.
Does not derive the ledger ratio from microscopic nuclear forces.
Does not perform numerical simulations of fission dynamics.
Does not address experimental measurement of transmutation costs.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (24)

structure NuclearConfig L50
def nuclearCost L56
theorem nuclear_cost_nonneg L59
theorem nuclear_cost_zero_iff_stable L64
theorem transmutation_cost_pos L83
structure TransmutationStep L94
theorem transmutation_reduces_cost L101
theorem cost_reduction_bounded L106
structure TransmutationPath L113
theorem path_reduces_total_cost L124
def stable_config L129
theorem stable_config_zero_cost L132
theorem stable_is_optimal L137
structure DoublyMagicAttractor L145
theorem stable_is_attractor L152
theorem stable_end_state_exists L157
theorem cost_monotone_descent_terminates L168
theorem strict_transmutation_progress L181
def transmutation_efficiency L195
theorem efficiency_bounded L200
theorem perfect_transmutation_efficiency L215
theorem fission_transmutation_from_ledger L227
theorem fission_transmutation_structure L236
def en006_certificate L241