`ph006_probability_certificate`

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module: IndisputableMonolith.Philosophy.ProbabilityMeaningStructure
domain: Philosophy
line: 273 · github
papers citing: none yet

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IndisputableMonolith.Philosophy.ProbabilityMeaningStructure on GitHub at line 273.

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 270
 271    The RS resolution: probability is NOT fundamental — it is the
 272    projection shadow of deterministic ledger dynamics. -/
 273theorem ph006_probability_certificate :
 274    -- Reality is deterministic
 275    (∃! x : ℝ, 0 < x ∧ Foundation.LawOfExistence.defect x = 0) ∧
 276    -- Probability arises from projection
 277    (∀ obs : Observer, ∃ x y : ℝ, x ≠ y ∧ project obs x = project obs y) ∧
 278    -- Fibers cover all states
 279    (∀ obs : Observer, ∀ x : ℝ, ∃! v : Fin obs.resolution, x ∈ Fiber obs v) ∧
 280    -- Each outcome is possible
 281    (∀ obs : Observer, ∀ v : Fin obs.resolution, (Fiber obs v).Nonempty) :=
 282  ⟨⟨1, ⟨by norm_num, Foundation.LawOfExistence.defect_at_one⟩,
 283    fun y ⟨hy_pos, hy_zero⟩ =>
 284      (Foundation.LawOfExistence.defect_zero_iff_one hy_pos).mp hy_zero⟩,
 285   projection_lossy,
 286   fibers_cover,
 287   each_fiber_nonempty⟩
 288
 289end ProbabilityMeaningStructure
 290end Philosophy
 291end IndisputableMonolith

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