module module high

`IndisputableMonolith.Information.QuantumErrorCorrection`

This module defines quantum error correction primitives in Recognition Science, centering on Pauli-basis expansions and codes linked to the eight-tick cycle. Researchers modeling discrete quantum information would cite it when connecting errors to the RS time quantum. The module consists entirely of definitions with no theorems or proofs.

claim$E = \alpha I + \beta X + \gamma Y + \delta Z$ (Pauli error expansion) together with ErrorModel, depolarizing channel, EightTickCode, Syndrome, repetitionCode3, CSSCode, steaneCode, and eightTickLogicalCode.

background

The module resides in the Information domain. It imports Constants, where the fundamental RS time quantum satisfies $\tau_0 = 1$ tick, and Foundation.EightTick, which supplies the discrete 8-tick cycle whose phases are $0, \pi/4, \pi/2, 3\pi/4, \pi, 5\pi/4, 3\pi/2, 7\pi/4$. The module doc-comment states that quantum errors expand in the Pauli basis as $E = \alpha I + \beta X + \gamma Y + \delta Z$, with $I$ the identity (no error), $X$ a bit flip, $Y$ a combined bit-phase flip, and $Z$ a phase flip.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the quantum error correction layer that supports information-theoretic constructions in Recognition Science. It directly extends the eight-tick structure imported from Foundation.EightTick and populates sibling definitions such as eight_tick_encodes_redundancy and eightTickLogicalCode for later use in discrete quantum models.

scope and limits

Does not derive any error thresholds or correction capacities.
Does not relate Pauli errors to the J-cost function or Recognition Composition Law.
Does not assign numerical error rates in RS-native units.
Does not prove logical equivalence between quantum and classical codes.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Foundation.EightTick module_import

declarations in this module (16)

inductive PauliError L44
structure ErrorModel L52
def depolarizing L65
structure EightTickCode L85
structure Syndrome L100
structure ClassicalCode L112
def repetitionCode3 L125
structure CSSCode L141
def steaneCode L151
theorem eight_tick_encodes_redundancy L167
def eightTickLogicalCode L179
structure SurfaceCode L195
def surfaceCodeThreshold L209
def rsPredictions L219
def implications L234
structure QECFalsifier L247