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feat: PositiveTemperature#969

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ichxorya wants to merge 18 commits intoleanprover-community:masterfrom
SEhumantics:feat/nghiabt/postemp
Draft

feat: PositiveTemperature#969
ichxorya wants to merge 18 commits intoleanprover-community:masterfrom
SEhumantics:feat/nghiabt/postemp

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@ichxorya ichxorya commented Mar 4, 2026

Ref: #958 #861 #860

In this PR I will construct relevant API for PositiveTemperature as discussed in #958

…he Thermodynamics module (with some extend to StatisticalMechanics since it depends on Thermodynamics)
…ine comments

TODO: from `tendsto_const_inv_mul_bound_pos` downwards
* Note: In `Calculus relating T and β`, the proofs are not really cleaned and humanized since it's kinda out of my league.
* Introduce `TemperatureScale` structure with detailed documentation.
* Implement conversion functions between kelvin and affine scales.
* Add lemmas to verify the identity of conversions.
* Define specific temperature scales: Celsius, Fahrenheit, and Rankine.
* Improve documentation for clarity and completeness.
* Refactor existing functions for better readability and maintainability.
* Added import for `TemperatureScales` in `PhysLean.lean`.
* Reformatted code for better readability in several lemmas across temperature-related files.
* Removed unnecessary blank lines to improve code clarity.
…itions (breaking change warning, currently only Basic.lean is compilable)
…lean (breaking change warning, currently only Basic.lean is compilable)
…ture and the Beta function; add Calculus.lean for PositiveTemperature (breaking change warning)
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