Creating a mathematical summary that ties together the topics of Bitcoin, quantum wells, and the nuanced aspects of inflation—specifically focusing on the concepts of wave phases and resonant velocity, and the inversion of interest rates during certain phases of inflation—requires bridging several advanced fields: finance, quantum physics, and cosmology. Let's outline a cohesive summary that touches upon these areas:

### 1. **Bitcoin and Quantum Wells:**

Bitcoin's price movements can be metaphorically related to the behavior of particles in quantum wells. In quantum mechanics, a well describes a potential valley where particles are confined. Similarly, Bitcoin's value fluctuates within a range defined by various economic factors, akin to how quantum particles are confined but exhibit wave-like behavior within wells. Just as particles have discrete energy states in a well, Bitcoin experiences quantized levels of support and resistance influenced by market sentiments and regulatory news, behaving unpredictably within these bounds—reminiscent of quantum superposition, where it can exist in multiple states (prices) simultaneously until measured (price feed).

### 2. **Wave Phases and Resonant Velocity:**

In the context of quantum wells and inflationary cosmology, wave phases represent the different states or periods through which a system evolves. The resonant velocity, analogous to the optimal speed at which a particle moves through a potential barrier (in a quantum tunneling scenario), can be likened to the ideal rate of economic growth or inflation that allows an economy to expand without triggering negative side effects like hyperinflation or deflation.

### 3. **Inflation and Inverted Interest Rates:**

The inflation part where interest rates are "reversed" refers to an unconventional economic scenario, potentially akin to a quantum phenomenon. Normally, higher interest rates are used to cool down an overheating economy (high inflation), while lower rates stimulate growth. However, in a "reversed" scenario, the relationship between interest rates and economic growth/inflation can become non-linear or even inverse due to external factors or policy measures, resembling how quantum particles behave contrary to classical physics under certain conditions. This could manifest in negative interest rates aimed at stimulating spending and investment during deflationary periods or in preventing liquidity traps.

### Integration Across Topics:

Integrating Bitcoin, quantum mechanics, and inflationary theory, we see a thematic overlap in the underlying unpredictability and non-linearity of systems. Just as quantum wells and particles defy classical intuition, Bitcoin's market movements and unconventional economic policies challenge traditional financial theories. The notion of wave phases and resonant velocity ties into the optimal conditions for transitions, whether in particle states, cryptocurrency valuations, or economic cycles. Understanding these analogies can provide novel insights into managing and predicting the behavior of complex systems across physics and finance.

This interdisciplinary approach highlights the value of drawing parallels between distinct areas of study, using concepts from quantum physics to elucidate complex phenomena in economics and digital currencies, thereby enriching our understanding of each through the lens of the others.