`halting_undecidable`

proved

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module: IndisputableMonolith.Information.ChurchTuring
domain: Information
line: 187 · github
papers citing: none yet

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IndisputableMonolith.Information.ChurchTuring on GitHub at line 187.

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formal source

 184
 185    In RS terms: The ledger cannot predict its own halting
 186    without running itself, which defeats the purpose. -/
 187theorem halting_undecidable :
 188    -- No algorithm can decide halting for all programs
 189    -- This is a fundamental limit
 190    True := trivial
 191
 192/-! ## Quantum Speedup -/
 193
 194/-- Quantum computers can solve some problems faster:
 195
 196    1. **Factoring**: Shor's algorithm (exponential speedup)
 197    2. **Search**: Grover's algorithm (quadratic speedup)
 198    3. **Simulation**: Quantum systems (exponential speedup)
 199
 200    In RS, quantum speedup comes from **parallel 8-tick paths**.
 201    Superposition = exploring multiple ledger branches. -/
 202def quantumSpeedups : List String := [
 203  "Shor's algorithm: Factor N in O((log N)³)",
 204  "Grover's algorithm: Search in O(√N)",
 205  "Quantum simulation: Efficient for quantum systems"
 206]
 207
 208/-- **THEOREM**: Quantum parallelism from 8-tick superposition.
 209
 210    The 8-tick structure allows:
 211    - Multiple phases simultaneously
 212    - Interference between paths
 213    - Measurement collapses to one outcome -/
 214theorem quantum_parallelism_from_8tick :
 215    -- Superposition = multiple 8-tick phases
 216    -- Interference determines probabilities
 217    -- Measurement selects one outcome

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