IndisputableMonolith.Physics.QuantumMolecularDesignDepthC4
The QuantumMolecularDesignDepthC4 module combines the five molecular energy levels and five quantum gate types from Recognition Science to define state classes and depth certificates for quantum molecular design at C4. It bounds the number of molecular quantum states using the phi-ladder and configDim D=5. Researchers in RS-derived quantum chemistry cite these definitions when certifying design depths for molecular systems. The module consists entirely of definitions and supporting inequalities with no proofs.
claimWith configuration dimension $D=5$, the quantum molecular state classes at design depth C4 satisfy $2^4 < N_{classes} $ and $N_{classes} $ is bounded above by $2^5$, where each class arises from J-cost minimization over phi-rung energy levels and sequences of the five canonical gate types.
background
The module operates inside the Recognition Science framework that reduces all physics to a single functional equation. MolecularPhysicsFromRS supplies the five canonical molecular energy levels (electronic, vibrational, rotational, translational, spin) equal to configDim D=5, with each level a phi-rung of recognition energy and adjacent ratios exactly phi. QuantumComputingDepthFromRS supplies the five canonical quantum gate types (Pauli, Clifford, T-gate, CNOT, Toffoli) also equal to D=5, with quantum computation realized as sequences of J-cost-minimizing recognition operations and the eight single-qubit Pauli elements equal to 2^D.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the C4 depth certification that supports higher-level Recognition Science constructions for quantum molecular design. It directly extends the phi-ladder structure and J-cost minimization from the two imported modules to produce concrete bounds on state classes, filling the step between abstract configDim D=5 and usable molecular design depth.
scope and limits
- Does not derive explicit numerical spectra or binding energies for any concrete molecule.
- Does not connect to laboratory data or external simulation packages.
- Does not prove that C4 is the unique or optimal depth choice.
- Does not address entanglement measures or decoherence beyond the J-cost definition.