`predictions`

definition

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module: IndisputableMonolith.Mathematics.ComplexNumbers
domain: Mathematics
line: 253 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.Mathematics.ComplexNumbers on GitHub at line 253.

browse module

All declarations in this module, on Recognition.

explainer page

Tracked in the explainer inventory; generation is lazy so crawlers do not trigger LLM jobs.

open explainer

depends on

formal source

 250    2. Interference requires complex amplitudes ✓
 251    3. 8-tick structure appears in physics ✓ (spin statistics)
 252    4. Phase is ubiquitous in physics ✓ -/
 253def predictions : List String := [
 254  "Real QM experimentally distinguishable and ruled out (2021)",
 255  "Interference patterns require complex amplitudes",
 256  "Spinor structure reflects 8-tick (4π rotation = identity)",
 257  "Berry phase is geometric (complex)"
 258]
 259
 260/-! ## Falsification Criteria -/
 261
 262/-- The complex necessity derivation would be falsified by:
 263    1. Consistent real-only quantum mechanics
 264    2. Physics without phases
 265    3. Alternative to 8-tick structure
 266    4. Rotation in fewer than 2 dimensions -/
 267structure ComplexFalsifier where
 268  /-- Type of potential falsification. -/
 269  falsifier : String
 270  /-- Status. -/
 271  status : String
 272
 273/-- All evidence supports complex necessity. -/
 274def experimentalStatus : List ComplexFalsifier := [
 275  ⟨"Real QM", "Ruled out by Renou et al. (2021)"⟩,
 276  ⟨"Phase in experiments", "Ubiquitous and essential"⟩,
 277  ⟨"8-tick structure", "Appears in spin statistics"⟩
 278]
 279
 280end ComplexNumbers
 281end Mathematics
 282end IndisputableMonolith

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