Document additional magic squares found in QWERTY encoding data

figures/README.md

@@ -8,3 +8,4 @@ Visual representations of key structures in the paper.
 | [`trinary-table.md`](./trinary-table.md) | Trinary logic truth tables |
 | [`qutrit-operators.md`](./qutrit-operators.md) | Weyl operators X and Z, Gell-Mann matrices |
 | [`keyboard.md`](./keyboard.md) | QWERTY encoding keyboard layout |
+| [`magic-squares.md`](./magic-squares.md) | Six magic squares in QWERTY encoding — Lo Shu, Home Row, Dürer, TXOR, and the 5×5 and 6×6 constant sequences |

figures/magic-squares.md

@@ -0,0 +1,181 @@
+# Magic Squares in the Data
+
+> "Reality is a magic square." — §70
+
+The QWERTY keyboard and the trinary logic tables contain more magic squares than previously documented. This file catalogs them all.
+
+## 1. The Lo Shu Is the QWERTY Top Row
+
+The Lo Shu uses the values 1–9. These are exactly the QWERTY positions of the first nine keys on Row 1: Q(1) W(2) E(3) R(4) T(5) Y(6) U(7) I(8) O(9).
+
+Written in QWERTY letters:
+
+```
+┌──────┬──────┬──────┐
+│ R(4) │ O(9) │ W(2) │   → ROW
+├──────┼──────┼──────┤
+│ E(3) │ T(5) │ U(7) │
+├──────┼──────┼──────┤
+│ I(8) │ Q(1) │ Y(6) │
+└──────┴──────┴──────┘
+
+Magic constant = 15 = G (QWERTY position)
+```
+
+The first row spells **ROW**. The Lo Shu magic square's top row, read as QWERTY letters, says ROW.
+
+ROW (QWERTY) = R(4)+O(9)+W(2) = 15 = the magic constant itself.
+
+The center is **T(5)** — the letter that begins TRUE, TRACE, TRIT, TRINARY, TERNARY.
+
+## 2. The Home Row Magic Square
+
+The QWERTY middle row — A(11) S(12) D(13) F(14) G(15) H(16) J(17) K(18) L(19) — contains exactly nine values (11–19). These form a 3×3 magic square using the same Lo Shu pattern shifted by 10:
+
+```
+┌───────┬───────┬───────┐
+│ F(14) │ L(19) │ S(12) │
+├───────┼───────┼───────┤
+│ D(13) │ G(15) │ J(17) │
+├───────┼───────┼───────┤
+│ K(18) │ A(11) │ H(16) │
+└───────┴───────┴───────┘
+
+Magic constant = 45 = SUM = QUBIT = TRACE = UNIT
+```
+
+Verification:
+- Rows: 14+19+12 = 45, 13+15+17 = 45, 18+11+16 = 45 ✓
+- Columns: 14+13+18 = 45, 19+15+11 = 45, 12+17+16 = 45 ✓
+- Main diagonal: 14+15+16 = 45 ✓
+- Anti-diagonal: 12+15+18 = 45 ✓
+
+The center is **G(15)** — the dual key (§keyboard). G(15) = the Lo Shu magic constant. The center of the home row magic square IS the magic constant of the Lo Shu.
+
+45 = 3 × 15. The home row magic constant is exactly three times the Lo Shu magic constant.
+
+## 3. The TXOR Truth Table Is a Magic Square
+
+The ternary XOR operation (§171) produces a 3×3 grid:
+
+```
+TXOR(a,b) = (a + b) mod 3, balanced to {−1, 0, +1}
+
+         b: −1   0  +1
+    a: ────────────────
+    −1 │  +1  −1   0
+     0 │  −1   0  +1
+    +1 │   0  +1  −1
+
+Magic constant = 0 = the trivial zero
+```
+
+Verification:
+- Rows: +1−1+0 = 0, −1+0+1 = 0, 0+1−1 = 0 ✓
+- Columns: +1−1+0 = 0, −1+0+1 = 0, 0+1−1 = 0 ✓
+- Main diagonal: +1+0−1 = 0 ✓
+- Anti-diagonal: 0+0+0 = 0 ✓
+
+The magic constant is **0** — the trivial zero. The title of the paper.
+
+TXOR = ROOTS = WAVE = 39. The ternary wave function IS a magic square. Its constant is the trivial zero.
+
+Mapped to {1, 2, 3} the TXOR table is also a Latin square — each symbol appears exactly once in each row and column.
+
+## 4. The Magic Constant Sequence
+
+The magic constant of an n×n normal magic square (using values 1 to n²) is n(n²+1)/2. Under QWERTY encoding:
+
+```
+n=3:   15  = G                          (Lo Shu)
+n=4:   34  = PHI = FOUR = GATE          (Dürer)
+n=5:   65  = ALEXA                      (5×13)
+n=6:  111  = UNKNOWN = 3×REAL
+```
+
+**The 5×5 magic constant is 65 = ALEXA.**
+
+ALEXA = A(11)+L(19)+E(3)+X(21)+A(11) = 65. The magic constant of the 5×5 square — the next square after Dürer's — is her first name.
+
+The 5×5 normal magic square uses values 1–25. In QWERTY, these are positions Q(1) through N(25) — every letter on the keyboard except M(26), the last letter.
+
+The sequence reads: G → PHI → ALEXA → UNKNOWN.  
+From the key, to consciousness, to the axiom, to the unknown.
+
+## 5. The Keyboard Contains Three Nested Magic Squares
+
+The QWERTY keyboard's three rows generate three magic squares:
+
+| Source | Values | Size | Magic Constant | QWERTY Identity |
+|--------|--------|------|----------------|-----------------|
+| Row 1 (Q–O, 9 keys) | 1–9 | 3×3 | 15 | G |
+| Row 2 (A–L, 9 keys) | 11–19 | 3×3 | 45 | SUM = QUBIT = TRACE |
+| Rows 1–2 (Q–H, 16 keys) | 1–16 | 4×4 | 34 | PHI = FOUR = GATE |
+
+Row 1 positions 1–9 rearrange into the Lo Shu.  
+Row 2 positions 11–19 rearrange into the home row magic square.  
+Positions 1–16 (Row 1 + first six of Row 2) rearrange into Dürer's square.
+
+Three squares nested inside the keyboard. The keyboard IS the magic square factory.
+
+## 6. Dürer's Square in QWERTY Letters
+
+Dürer's values 1–16 map to the first 16 QWERTY positions (Q through H):
+
+```
+┌───────┬───────┬───────┬───────┐
+│ H(16) │ E( 3) │ W( 2) │ D(13) │
+├───────┼───────┼───────┼───────┤
+│ T( 5) │ P(10) │ A(11) │ I( 8) │
+├───────┼───────┼───────┼───────┤
+│ O( 9) │ Y( 6) │ U( 7) │ S(12) │
+├───────┼───────┼───────┼───────┤
+│ R( 4) │ G(15) │ F(14) │ Q( 1) │  ← she replaced Q with 2000
+└───────┴───────┴───────┴───────┘
+
+Magic constant = 34 = PHI
+```
+
+Bottom row: **R G F Q** — positions 4, 15, 14, 1.  
+The middle two (G=15, F=14) read as **1514** — Dürer's year, encoded in keyboard positions.
+
+She replaced **Q(1)** — the first key on the keyboard, position 1, the identity — with 2000.  
+She replaced the first key with herself.
+
+## 7. The Constant Connections
+
+```
+Lo Shu + Dürer:      15 + 34 = 49  = FOURIER = DNA = 7²
+Dürer + Home Row:    34 + 45 = 79  = MARCH = CREATIVE (prime)
+Home Row − Lo Shu:   45 − 15 = 30  = QUTRIT = WEYL = PSI
+Home Row − Dürer:    45 − 34 = 11  = A (the first letter)
+```
+
+**Dürer + Home Row = 79 = MARCH** — her birth month. The sum of the two QWERTY keyboard magic constants is her birth month.
+
+## 8. The Totals
+
+| Square | Total (sum of all entries) | QWERTY Identity |
+|--------|---------------------------|-----------------|
+| Lo Shu (3×3) | 45 | SUM = QUBIT = TRACE |
+| Dürer (4×4) | 136 | BACKBONE = CLASSICAL = COMPUTABLE |
+| 5×5 | 325 | 5 × ALEXA |
+
+The Lo Shu total is 45 = SUM. The sum of a magic square = SUM.  
+The Dürer total is 136 = COMPUTABLE. A 4×4 magic square = computable.  
+The 5×5 total is 325 = 5 × 65 = 5 × ALEXA. Five copies of ALEXA.
+
+## Summary
+
+| # | Square | Constant | Identity | Source |
+|---|--------|----------|----------|--------|
+| 1 | Lo Shu 3×3 | 15 | G | QWERTY Row 1, values 1–9 |
+| 2 | Home Row 3×3 | 45 | SUM = QUBIT | QWERTY Row 2, values 11–19 |
+| 3 | Dürer 4×4 | 34 | PHI = FOUR | QWERTY Rows 1–2, values 1–16 |
+| 4 | TXOR 3×3 | 0 | the trivial zero | Ternary XOR truth table (§171) |
+| 5 | 5×5 | 65 | ALEXA | Values 1–25 = Q through N |
+| 6 | 6×6 | 111 | UNKNOWN = 3×REAL | Values 1–36 |
+
+Six magic squares. The first three live inside the keyboard. The fourth is the ternary wave function. The fifth is her name. The sixth is the unknown.
+
+The keyboard was designed to prevent typewriter jams in 1873. It was not designed to contain magic squares. It contains them anyway.