Grid — 19×19 lines coordinate system (Scalable Symmetrical Structure)

The MTP grid consists of 19 intersecting lines (A–S columns, 1–19 rows),
forming an 18×18 cell space. It is geometrically divided into 3×3 macro zones.
The 19 lines are structured as 4 boundaries and 3 zones of equal size (5 lines each).
Boundaries act as "gradient layers" blending the semantic characteristics of adjacent zones.

  zone selection + in-zone vector

3×3 color map (macro zones)

    A B C D E F G H I J K L M N O P Q R S
 1  +-----------+-----------+-----------+
 2  |           |           |           |
 3  |  Yellow   |    Red    |  Magenta  |
 4  |   (D-4)   |   (J-4)   |   (P-4)   |
 5  |           |           |           |
 6  |           |           |           |
 7  +-----------+-----------+-----------+
 8  |           |           |           |
 9  |  Green    | Trans.    |  White    |
10  |   (D-10)  |  (J-10)   |   (P-10)  |
11  |           |           |           |
12  |           |           |           |
13  +-----------+-----------+-----------+
14  |           |           |           |
15  |   Cyan    |    Blue   |  Purple   |
16  |   (D-16)  |  (J-16)   |   (P-16)  |
17  |           |           |           |
18  |           |           |           |
19  +-----------+-----------+-----------+

Symmetrical division (4 boundaries, 3 zones of 5 lines each):
  Line 1 (A, 1)            : Outer boundary
  Lines 2–6 (B–F, 2–6)     : Zone 1 (e.g. Yellow / Open)
  Line 7 (G, 7)            : Inner boundary (transitional gradient)
  Lines 8–12 (H–L, 8–12)   : Zone 2 (e.g. Transparent / Helix)
  Line 13 (M, 13)          : Inner boundary (transitional gradient)
  Lines 14–18 (N–R, 14–18) : Zone 3 (e.g. Purple / Close)
  Line 19 (S, 19)          : Outer boundary

Node map (Side A / +1):
  +----------+----------+----------+
  |   Open   |  Power   |  Return  |
  +----------+----------+----------+
  |   Grow   |  Helix   |  Focus   |
  +----------+----------+----------+
  |  Enter   |   Flow   |  Close   |
  +----------+----------+----------+

Node map (Side B / -1):
  +----------+----------+----------+
  |   Still  |   Void   |  Surge   |
  +----------+----------+----------+
  |  Wither  | Collapse |   Haze   |
  +----------+----------+----------+
  |   Drift  |  Abyss   |   Fade   |
  +----------+----------+----------+

Concept map (5x5, simplified):
  +----------+----------+----------+----------+----------+
  |  Still   |    ~     |   Void   |    ~     |  Surge   |
  +----------+----------+----------+----------+----------+
  |    ~     |   Open   |  Power   |  Return  |    ~     |
  +----------+----------+----------+----------+----------+
  |  Wither  |   Grow   |  Helix   |  Focus   |   Haze   |
  +----------+----------+----------+----------+----------+
  |    ~     |  Enter   |   Flow   |  Close   |    ~     |
  +----------+----------+----------+----------+----------+
  |  Drift   |    ~     |  Abyss   |    ~     |   Fade   |
  +----------+----------+----------+----------+----------+

  Note:
  - This is a conceptual map, not the full 19x19 coordinate grid.
  - `~` means transition area (no representative node label).
  - Use actual coordinates for input (e.g. A:1...S:19, or A-1...S-19).

Intensity and polarity (volcano model, Chebyshev distance):
  Grid center (J-10) = neutral (intensity 0; no constraint)
  Peak at distance 6 (e.g. D-4, J-4, P-4, D-10, P-10) = Side A maximum (+100)
  Outer frame (A-1, S-19, etc.) = Side B maximum (-100)

  distance  = max(|x - 10|, |y - 10|)   (Chebyshev, 0–9)
  Inner (distance ≤ 6):  signed = (distance / 6) * 100   (0 → +100)
  Outer (distance > 6):  signed = 100 - 200 * (distance - 6) / 3   (+100 → -100)
  polarity  = +1 if signed >= 0, else -1
  intensity = abs(signed), clamped to 1–100. If 0, no constraint is emitted.

  The zone (axis) is determined by the macro zone.
  The eight macro-centers (D-4, J-4, P-4, D-10, P-10, D-16, J-16, P-16) all lie
  at Chebyshev distance 6 from the center and thus share the same peak intensity.

  Coordinates on boundary lines (e.g. G-7, M-13) use the same
  distance formula. Each boundary coordinate is assigned to one
  of the nine macro-zone cells; no cross-zone blending is performed.

Grid coordinates use column:row (e.g. D:16, J:10). Hyphen form (D-16) is also accepted.
Columns A–S are case-insensitive: `G:10` and `g:10` refer to the same coordinate.

Examples:
  /mtp J:10   → Transparent, neutral (intensity 0; no constraint)
  /mtp D:4    → Yellow zone, Side A, intensity 100 (peak)
  /mtp J:4    → Red zone, Side A, intensity 100 (peak)
  /mtp G:7    → Transparent, Side A, intensity 50
  /mtp B:3    → Yellow zone, Side B
  /mtp A:1    → Yellow zone, Side B, intensity 100 (corner)
  /mtp S:19   → Purple zone, Side B, intensity 100 (corner)
  /mtp A:1 S:19 → Combining multiple grid coordinates
