module module high

`IndisputableMonolith.Thermodynamics.ErrorCorrection`

The ErrorCorrection module defines recognition defects as states where the J-cost exceeds zero and sets defect energy equal to that J-value. It introduces error syndromes, correction protocols, and fault-tolerance thresholds built on the free-energy monotonicity result. Researchers extending RS thermodynamics to information stability cite these objects when analyzing defect behavior under coarse-graining. The module consists of definitions and lemmas that link syndromes to the eight-tick cycle without new derivations.

claimA recognition defect satisfies $J(x) > 0$ with energy $E = J(x)$. An error syndrome and correction protocol are defined so that the eight-tick cycle restores the state when code distance exceeds the fault-tolerance threshold.

background

Recognition Science defines states via the cost functional $J(x) = ½(x + x^{-1}) - 1$. The upstream FreeEnergyMonotone module proves that recognition free energy FR is non-increasing under RS dynamics (coarse-graining and equilibration), supplying the second-law foundation. This module sits inside the thermodynamics development and treats defects as positive-J states whose energy is identified with J itself.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

These definitions feed the parent Thermodynamics module that develops the statistical mechanics of RS on the T=0 J-minimization foundation. They prepare analysis of defect energy under the Recognition Composition Law and the forced eight-tick octave, closing the link between error correction and thermodynamic stability.

scope and limits

Does not derive free-energy monotonicity.
Does not compute explicit numerical thresholds.
Does not address continuous-time dynamics.
Does not connect defects to mass formulas on the phi-ladder.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Thermodynamics module_import

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Thermodynamics.FreeEnergyMonotone module_import

declarations in this module (17)

structure RecognitionDefect L38
def defect_energy L45
theorem defect_energy_pos L49
structure ErrorSyndrome L56
def jcost_syndrome L63
structure CorrectionProtocol L70
def eight_tick_cycle L80
def is_complete_correction L84
structure FaultToleranceThreshold L91
def is_fault_tolerant L98
def code_distance L110
def phi_code_distance L115
theorem phi_code_distance_pos L119
structure LogicalOperator L129
def id_logical_op L136
def is_protected_observable L144
theorem conservation_is_protected L149