def
definition
alignment_quality
show as:
view math explainer →
open explainer
Generate a durable explainer page for this declaration.
open lean source
IndisputableMonolith.Applied.PosturalAlignment on GitHub at line 37.
browse module
All declarations in this module, on Recognition.
explainer page
depends on
used by
formal source
34
35/-- **DEFINITION: Alignment Quality**
36 Measure of how well the postural axis matches a resonant axis. -/
37def alignment_quality (pa : PosturalAxis) : ℝ :=
38 max (abs (pa.vector 0)) (max (abs (pa.vector 1)) (abs (pa.vector 2)))
39
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