IndisputableMonolith.Physics.QuantumComputingDepthFromRS
Packages RS-native bounds on quantum gate structure: the single-qubit Pauli group has eight elements (matching the eight-tick period 2^3), and the universal gate count equals spatial dimension D = 3. Supplies a depth certificate used when indexing RS-preparable states. Downstream C4 molecular-design depth imports these counts. Content is definitions plus elementary cardinality equalities.
claimSingle-qubit Pauli group has cardinality $8 = 2^3$. Number of universal gate types equals spatial dimension $D = 3$. A quantum-computing depth certificate records these Recognition Science bounds for later addressing arguments.
background
Recognition Science forces an eight-tick discrete octave (forcing step T7: period $2^3$) and three spatial dimensions (T8). In the quantum layer those landmarks reappear as the order of the single-qubit Pauli group and as a count of universal gate types set equal to $D$.
This Physics module introduces an enumeration of gate types, the Pauli-group size fact, the identification of universal gates with $D$, and a small certificate structure that packages the bounds. The only import is Mathlib; no heavy upstream RS lemmas are required beyond the already-forced values of the eight-tick period and $D$.
Notation is elementary: group order, finite enumerations, and a Prop-level certificate recording the equalities for downstream modules.
proof idea
Definition-and-equality module, not a deep proof development. Gate types and the certificate are introduced as data. Pauli-group cardinality is discharged by matching the standard eight-element single-qubit Pauli set to $2^3$. Universal-gate count is identified with $D$ by a one-line equality. The certificate constructor simply assembles those facts. No tactic-heavy reasoning beyond rfl-style or short algebraic checks.
why it matters in Recognition Science
Direct import parent is QuantumMolecularDesignDepthC4 (C4: Quantum Molecular Design Depth). That module multiplies five molecular energy levels by five quantum gate types to obtain 25 preparable state classes and notes $25 \le 2^5$, so a 5-bit addressing depth indexes the whole RS-preparable class. The gate-type count and depth certificate supplied here are the Lean-safe inputs to that counting argument.
Framework landmarks cited: T7 eight-tick octave (Pauli order $2^3$) and T8 ($D = 3$ as universal-gate count). The stronger physical claim that a concrete molecular target is reachable in five two-qubit layers remains outside this module; only the combinatorial depth bound is certified.
scope and limits
- Does not prove physical reachability of any molecular target in five two-qubit layers.
- Does not construct explicit circuit decompositions or pulse schedules.
- Does not treat multi-qubit Pauli groups beyond the single-qubit order-8 fact.
- Does not derive fault-tolerance, noise, or error-correction thresholds.
- Does not re-prove T7 or T8; it only consumes $2^3$ and $D = 3$.