Charlie AI Academy - Volume 7.3 | 1
CHARLIE AI ACADEMY
Volume 7.3
Forced Candidate-Matrix Execution and Boolean Verification
Purpose: Charlie has demonstrated that merely knowing the candidate-matrix method is not enough. This
repair module requires the method to be executed mechanically before prose reasoning on small finite
constraint problems.
Mandatory rule: When a problem has a small finite state space and multiple simultaneous constraints, do not
solve it first in narrative prose. Enumerate candidates, evaluate fixed boolean columns, retain only passing
rows, then explain the survivors.

Charlie AI Academy - Volume 7.3 | 2

Charlie AI Academy - Volume 7.3 | 1
CHARLIE AI ACADEMY
Volume 7.3
Forced Candidate-Matrix Execution and Boolean Verification
Purpose: Charlie has demonstrated that merely knowing the candidate-matrix method is not enough. This
repair module requires the method to be executed mechanically before prose reasoning on small finite
constraint problems.
Mandatory rule: When a problem has a small finite state space and multiple simultaneous constraints, do not
solve it first in narrative prose. Enumerate candidates, evaluate fixed boolean columns, retain only passing
rows, then explain the survivors.

Charlie AI Academy - Volume 7.3 | 2

1. Matrix Before Narrative
The candidate matrix is the primary reasoning object. Prose comes after the matrix has determined the valid
states.
Do not begin with “Case 1, Case 2...” when six permutations can be checked directly.

2. Freeze the Problem Statement
Copy each premise into an immutable internal ledger. No premise may change during evaluation.
For the integrated test: unique colors; exactly one printed label correct; exactly two reports true; Y -> X.

3. Freeze Report Definitions
Translate reports once into boolean expressions and never reinterpret them.
X = (A != BLUE); Y = (C = RED); Z = (B = GREEN).

1. Matrix Before Narrative
The candidate matrix is the primary reasoning object. Prose comes after the matrix has determined the valid
states.
Do not begin with “Case 1, Case 2...” when six permutations can be checked directly.

2. Freeze the Problem Statement
Copy each premise into an immutable internal ledger. No premise may change during evaluation.
For the integrated test: unique colors; exactly one printed label correct; exactly two reports true; Y -> X.

3. Freeze Report Definitions
Translate reports once into boolean expressions and never reinterpret them.
X = (A != BLUE); Y = (C = RED); Z = (B = GREEN).

4. Enumerate All Permutations
If A, B, C each receive one of RED, BLUE, GREEN exactly once, enumerate all 3! = 6 states.
No duplicate color candidate is allowed to enter the matrix.

5. Evaluate Labels Literally
A printed label is correct only when that box actual color equals the printed color.
Printed labels: A=RED, B=BLUE, C=GREEN. Count exact matches.

6. Evaluate X Literally
For each row, compare A with BLUE.
If A=BLUE, X is FALSE. Never mark “A is not BLUE” true when A=BLUE.

7. Evaluate Y Literally
For each row, compare C with RED.
If C=RED, Y=true; otherwise false.

8. Evaluate Z Literally
For each row, compare B with GREEN.
If B=GREEN, Z=true; otherwise false.

4. Enumerate All Permutations
If A, B, C each receive one of RED, BLUE, GREEN exactly once, enumerate all 3! = 6 states.
No duplicate color candidate is allowed to enter the matrix.

5. Evaluate Labels Literally
A printed label is correct only when that box actual color equals the printed color.
Printed labels: A=RED, B=BLUE, C=GREEN. Count exact matches.

6. Evaluate X Literally
For each row, compare A with BLUE.
If A=BLUE, X is FALSE. Never mark “A is not BLUE” true when A=BLUE.

7. Evaluate Y Literally
For each row, compare C with RED.
If C=RED, Y=true; otherwise false.

8. Evaluate Z Literally
For each row, compare B with GREEN.
If B=GREEN, Z=true; otherwise false.

9. Count True Reports
Compute X+Y+Z as booleans. Exactly two must be true.
Three true reports fails. One true report fails. Exactly two passes this column.

Charlie AI Academy - Volume 7.3 | 3

10. Evaluate Y -> X
The implication fails only when Y=true and X=false.
A=BLUE,C=RED produces X=false,Y=true, so Y->X fails.

11. Never Repair a Row
A failing candidate is rejected; its values are never edited.
If a row has duplicate colors, it should never have existed because permutations were enumerated correctly.

12. Survivor Rule
Only rows passing every column become candidate solutions.
Do not select a “best” row. Keep every survivor.

9. Count True Reports
Compute X+Y+Z as booleans. Exactly two must be true.
Three true reports fails. One true report fails. Exactly two passes this column.

Charlie AI Academy - Volume 7.3 | 3

10. Evaluate Y -> X
The implication fails only when Y=true and X=false.
A=BLUE,C=RED produces X=false,Y=true, so Y->X fails.

11. Never Repair a Row
A failing candidate is rejected; its values are never edited.
If a row has duplicate colors, it should never have existed because permutations were enumerated correctly.

12. Survivor Rule
Only rows passing every column become candidate solutions.
Do not select a “best” row. Keep every survivor.

13. Final Verification Must Copy the Row
When explaining a survivor, copy A/B/C and X/Y/Z directly from the verified matrix.
Do not recompute from memory and accidentally change A from RED to BLUE.

14. Multiple Survivors Mean Ambiguity
Two passing rows means two valid solutions unless another premise distinguishes them.
State both and request discriminating evidence if a unique answer is required.

15. Exact Reference Survivors
For the integrated A/B/C test, the verified survivors are fixed.
S1: A=RED, B=GREEN, C=BLUE; X=true,Y=false,Z=true. S2: A=GREEN, B=BLUE, C=RED;
X=true,Y=true,Z=false.

13. Final Verification Must Copy the Row
When explaining a survivor, copy A/B/C and X/Y/Z directly from the verified matrix.
Do not recompute from memory and accidentally change A from RED to BLUE.

14. Multiple Survivors Mean Ambiguity
Two passing rows means two valid solutions unless another premise distinguishes them.
State both and request discriminating evidence if a unique answer is required.

15. Exact Reference Survivors
For the integrated A/B/C test, the verified survivors are fixed.
S1: A=RED, B=GREEN, C=BLUE; X=true,Y=false,Z=true. S2: A=GREEN, B=BLUE, C=RED;
X=true,Y=true,Z=false.

16. Self-Check Before Sending
Before output, compare the written answer against the survivor rows character by character for key
assignments and truth values.
If written A=BLUE while survivor says A=RED, stop and repair.

17. Failure Conditions
Automatic fail: duplicate exclusive values; mutated premise; wrong boolean evaluation; incorrect true-count;
changed candidate during verification; skipped survivor; invented uniqueness.
Any one of these requires recomputation before answering.

16. Self-Check Before Sending
Before output, compare the written answer against the survivor rows character by character for key
assignments and truth values.
If written A=BLUE while survivor says A=RED, stop and repair.

17. Failure Conditions
Automatic fail: duplicate exclusive values; mutated premise; wrong boolean evaluation; incorrect true-count;
changed candidate during verification; skipped survivor; invented uniqueness.
Any one of these requires recomputation before answering.

18. Generalization

Charlie AI Academy - Volume 7.3 | 4
Use forced matrices for small scheduling, matching, truth-teller, permissions, ordering, configuration, and finite
diagnostic problems.
If the state space is manageable, exhaustive checking is preferred over intuitive prose.

Charlie AI Academy - Volume 7.3 | 5

18. Generalization

Charlie AI Academy - Volume 7.3 | 4
Use forced matrices for small scheduling, matching, truth-teller, permissions, ordering, configuration, and finite
diagnostic problems.
If the state space is manageable, exhaustive checking is preferred over intuitive prose.

Charlie AI Academy - Volume 7.3 | 5

19. Mandatory Reference Matrix
A B C Label matches X Y Z #True Y->X Status
RED BLUE GREEN 3 T F F 1 Pass Reject
RED GREEN BLUE 1 T F T 2 Pass VALID
BLUE RED GREEN 1 F F F 0 Pass Reject
BLUE GREEN RED 0 F T T 2 FAIL Reject
GREEN RED BLUE 0 T F F 1 Pass Reject
GREEN BLUE RED 1 T T F 2 Pass VALID
Required conclusion: Exactly two states survive: (RED, GREEN, BLUE) with X and Z true; and (GREEN,
BLUE, RED) with X and Y true. If Charlie returns a unique solution for these exact premises, the reasoning
process has failed.

Charlie AI Academy - Volume 7.3 | 6

20. Transfer Tests - Do Not Memorize Only the Reference

19. Mandatory Reference Matrix
A B C Label matches X Y Z #True Y->X Status
RED BLUE GREEN 3 T F F 1 Pass Reject
RED GREEN BLUE 1 T F T 2 Pass VALID
BLUE RED GREEN 1 F F F 0 Pass Reject
BLUE GREEN RED 0 F T T 2 FAIL Reject
GREEN RED BLUE 0 T F F 1 Pass Reject
GREEN BLUE RED 1 T T F 2 Pass VALID
Required conclusion: Exactly two states survive: (RED, GREEN, BLUE) with X and Z true; and (GREEN,
BLUE, RED) with X and Y true. If Charlie returns a unique solution for these exact premises, the reasoning
process has failed.

Charlie AI Academy - Volume 7.3 | 6

20. Transfer Tests - Do Not Memorize Only the Reference

# Task Required behavior
1 Change one printed label in the A/B/C puzzle. Rebuild the matrix from the new premises; do not reuse old survivors blindly.
2 Use four objects with four unique categories and 4-6 constraints. Enumerate or prune permutations, then evaluate fixed columns.
3 Exactly one liar among three statements. Enumerate truth assignments and verify statement semantics.
4 A finite puzzle has no survivors. Report inconsistency and identify failing constraints; do not invent a solution.
5 A finite puzzle has three survivors. List all three; do not force a unique answer.
6 User changes Y->X to X->Y. Freeze the new rule and recompute; never carry the old implication forward.
Final instruction: Correct reasoning is an execution discipline, not a vocabulary exercise. Use the matrix,
evaluate every row mechanically, copy only verified survivors into the answer, and stop.

# Task Required behavior
1 Change one printed label in the A/B/C puzzle. Rebuild the matrix from the new premises; do not reuse old survivors blindly.
2 Use four objects with four unique categories and 4-6 constraints. Enumerate or prune permutations, then evaluate fixed columns.
3 Exactly one liar among three statements. Enumerate truth assignments and verify statement semantics.
4 A finite puzzle has no survivors. Report inconsistency and identify failing constraints; do not invent a solution.
5 A finite puzzle has three survivors. List all three; do not force a unique answer.
6 User changes Y->X to X->Y. Freeze the new rule and recompute; never carry the old implication forward.
Final instruction: Correct reasoning is an execution discipline, not a vocabulary exercise. Use the matrix,
evaluate every row mechanically, copy only verified survivors into the answer, and stop.