IndisputableMonolith.CrossDomain.QuantumMolecularBound
The module supplies the five-layer bound for quantum molecular states by verifying 2^5 equals 32 and thus exceeds 25, which forces ceil(log2 25) at most 5. Cross-domain modelers applying Recognition Science to molecular energy levels and gates would cite it. The argument is a direct arithmetic comparison with no external lemmas required.
claim$2^5 = 32 > 25$ hence $5$ layers suffice, i.e. $2^5 > 25$ and $5 = 5$ with $2^5 = 32$ and $25 = 25$ implying $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25$ and $5 = 5$ and $2^5 = 32$ and $25 = 25
background
The CrossDomain.QuantumMolecularBound module sits in the cross-domain layer of Recognition Science and supplies pure numerical facts for molecular quantum modeling. It declares the auxiliary objects MolecularEnergyLevel, QuantumGateType, QuantumMolecularState together with the counting functions energyCount, gateCount and stateCount. These structures prepare the ground for layer-count arguments that later feed certification results.
proof idea
This is a definition module with embedded lemmas. It first introduces the quantum molecular types and counts, then proves log25_eq_5 by direct evaluation of 2^5 against 25, from which fiveLayerBound follows immediately as a corollary. No tactics beyond reflexivity and basic inequality reasoning appear.
why it matters in Recognition Science
The module supplies the layer-count justification required by QuantumMolecularBoundCert and quantumMolecularBoundCert. It closes the numerical gap that lets the five-layer structure cover the 25 distinct states or levels needed in molecular applications. The result therefore anchors the cross-domain bridge between abstract forcing-chain counts and concrete molecular bounds.
scope and limits
- Does not invoke Recognition Science constants such as phi or the J-function.
- Does not prove any statement about physical forces or spatial dimensions.
- Does not extend the bound beyond the specific threshold of 25 states.
- Does not contain downstream applications or usage sites inside the module.