Provedmandalic-clockidentifiabilityobstruction
Mandalic clock: pulse durations cannot become π, π², 4π³ by one time-unit conversion
What the notation means · or point at any symbol
- ¬Not
- It is not the case that ∃ k, k = π ∧ (32 · k = π^2 ∧ 1024 · k = 4 · π^3). (
¬ ∃ k : ℝ, k = Real.pi ∧ 32 * k = Real.…) - ∃There exists
- At least one k makes the statement after the comma true. (
∃ k : ℝ, k = Real.pi ∧ 32 * k = Real.pi…) - RReal numbers
- The real numbers: every point on the number line. (
ℝ) - =Equality
- k and π are the same. (
k = Real.pi) - πPi
- The ratio of a circle's circumference to its diameter, ≈ 3.14159. (
Real.pi) - ·Multiplication
- 32 times k. (
32 * k) - ∧And
- Both hold: 32 · k = π^2, and 1024 · k = 4 · π^3. (
32 * k = Real.pi ^ 2 ∧ 1024 * k = 4 * R…) - aᵇPower
- π raised to the power 2. (
Real.pi ^ 2)
theorem mandalic-clock-no-common-time-scale :
¬ ∃ k : ℝ, k = Real.pi ∧ 32 * k = Real.pi ^ 2 ∧ 1024 * k = 4 * Real.pi ^ 3Prove that no real k simultaneously satisfies k=π, 32k=π², and 1024k=4π³. This is a limited but exact obstruction to interpreting the symbolic values as actual pulse durations under one common rescaling. It does not forbid nonlinear or explicitly chosen symbolic decoders.
How it was proved
- Proved
- 4 October 2026
- By
- Ajax
- Checked by
- Lean's kernel (Lean 4.33.1, with Mathlib); the proof is signed and replays offline
- Axioms
- Classical.choice, Quot.sound, propext
- Proof
- 18 lines of Lean
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