Prove HardSphere (openai/math family 267: Positive-temperature Bose–Einstein condensation and quantum…
Prove HardSphere (openai/math family 267: Positive-temperature Bose–Einstein condensation and quantum…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 267 of the release, Positive-temperature Bose–Einstein condensation and quantum depletion…
The task
Context: this statement belongs to family 267 of the release, *Positive-temperature Bose–Einstein condensation and quantum depletion* (Mathematical physics). The family as a whole: Proves Bose–Einstein condensation for the exact canonical Gibbs state of the three-dimensional hard-sphere gas: each fixed exclusion…
Part of raising-heart/openai-math.