`postural_coupling_cost`

definition

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module: IndisputableMonolith.Applied.PosturalAlignment
domain: Applied
line: 43 · github
papers citing: none yet

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IndisputableMonolith.Applied.PosturalAlignment on GitHub at line 43.

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formal source

  40/-- **DEFINITION: Postural Coupling Cost**
  41    The cost associated with misalignment between the biological axis
  42    and the underlying metric grid. -/
  43def postural_coupling_cost (pa : PosturalAxis) : ℝ :=
  44  1 - (alignment_quality pa) ^ 2
  45
  46/-- **THEOREM: Postural Strain Minimization**
  47    Aligning the postural axis with a resonant axis (alignment_quality = 1)
  48    identically minimizes the geometric coupling cost. -/
  49theorem postural_minimization (pa : PosturalAxis) :
  50    alignment_quality pa = 1 →
  51    postural_coupling_cost pa = 0 := by
  52  intro h_qual
  53  unfold postural_coupling_cost
  54  rw [h_qual]
  55  ring
  56
  57/-- **DEFINITION: System Stability (Posture)**
  58    Biological stability derived from postural alignment. -/
  59def SystemStability (pa : PosturalAxis) : ℝ :=
  60  1 / (1 + postural_coupling_cost pa)
  61
  62/-- **THEOREM: Posture and Stability**
  63    A resonant posture increases the System Stability to its maximum (1.0). -/
  64theorem posture_increases_stability (pa : PosturalAxis) :
  65    alignment_quality pa = 1 →
  66    SystemStability pa = 1.0 := by
  67  intro h_qual
  68  have h_cost := postural_minimization pa h_qual
  69  unfold SystemStability
  70  rw [h_cost]
  71  simp
  72
  73end Posture

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