pith. machine review for the scientific record. sign in
module module high

IndisputableMonolith.Information.QuantumErrorCorrection

show as:
view Lean formalization →

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

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (16)