IndisputableMonolith.Information.QuantumErrorCorrection
The module supplies the core definitions for modeling quantum errors and correction codes inside Recognition Science by expanding errors in the Pauli basis and tying them to the discrete eight-tick clock. Researchers constructing discrete quantum information models would reference these objects when embedding error correction into the RS time structure. The module contains only definitions and constructions that rest directly on the imported constants and eight-tick foundations.
claimQuantum errors admit the expansion $E = α I + β X + γ Y + δ Z$ with $I$ the identity, $X$ the bit flip, $Y$ the combined flip, and $Z$ the phase flip; the module defines the supporting structures ErrorModel, depolarizing channel, repetitionCode3, CSSCode, Steane code, and SurfaceCode, all indexed to the eight-tick cycle.
background
The module sits in the information domain and imports the RS time quantum τ₀ = 1 tick together with the eight-tick discrete clock whose phases run through 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4. It introduces PauliError, ErrorModel, Syndrome, ClassicalCode, and the concrete codes EightTickCode, eightTickLogicalCode, and SurfaceCode. These objects furnish a discrete representation of quantum errors that is compatible with the Recognition Composition Law and the eight-tick octave.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the error-correction vocabulary that links quantum information to the eight-tick structure. It prepares the ground for later integration with the phi-ladder and the forcing chain steps T7 and T8, although the current dependency graph shows no downstream theorems yet attached.
scope and limits
- Does not compute error thresholds or code distances.
- Does not derive the Pauli expansion from the J-cost functional.
- Does not address continuous-time limits or decoherence rates.
- Does not implement syndrome measurement circuits or decoding algorithms.
depends on (2)
declarations in this module (16)
-
inductive
PauliError -
structure
ErrorModel -
def
depolarizing -
structure
EightTickCode -
structure
Syndrome -
structure
ClassicalCode -
def
repetitionCode3 -
structure
CSSCode -
def
steaneCode -
theorem
eight_tick_encodes_redundancy -
def
eightTickLogicalCode -
structure
SurfaceCode -
def
surfaceCodeThreshold -
def
rsPredictions -
def
implications -
structure
QECFalsifier