Charlie AI Academy - Volume 7.1 | 1 CHARLIE AI ACADEMY Volume 7.1 Constraint Ledger, Multi-Constraint Reasoning and Exhaustive Verification Purpose: Repair the failure observed when many constraints must be preserved simultaneously. Charlie may solve individual steps correctly but mutate a premise, reverse an assignment, skip a candidate state, or verify a different solution from the one it stated. Core rule: Maintain one immutable ledger of premises and one explicit candidate-state table. Never alter a premise during reasoning. Every final candidate must be tested against every ledger entry. Charlie AI Academy - Volume 7.1 | 2 1. Separate Premises from Deductions Premises come from the problem and remain fixed. Deductions are conclusions derived from them. Never rewrite a premise to fit a candidate solution. If the rule is Y -> X, it remains Y -> X. It must never become X -> Z during verification. 2. Build the Constraint Ledger Before solving, list every independent requirement in compact form. Number them so each can be checked later. Example: C1 colors unique; C2 exactly one original label correct; C3 exactly two reports true; C4 Y -> X. 3. Build Candidate States Systematically For small finite problems, enumerate all possible assignments instead of improvising in prose. Three unique colors across A,B,C produce six permutations. Test all six against the constraints. 4. Never Skip a Candidate Without a Reason Reject a state only by naming the constraint it violates. Do not discard it because it “looks contradictory.” Candidate rejection should look like: fails C2 because two labels are correct. 5. Preserve Report Meanings Translate each report once and keep that meaning fixed. X: A != BLUE. Y: C = RED. Z: B = GREEN. 6. Evaluate Truth Values from the Candidate Do not decide which reports are true first and then force colors to match. For each candidate assignment, evaluate X, Y, and Z directly. Candidate A=RED,B=GREEN,C=BLUE gives X=T,Y=F,Z=T. 7. Conditional Logic Is Directional P -> Q means whenever P is true, Q must be true. It does not mean Q -> P, and it says nothing about Q when P is false. Y -> X is violated only when Y is true and X is false. 8. Exactly Means Exactly “Exactly one” and “exactly two” are hard cardinality constraints. Count, do not approximate. If two box labels match their actual colors, the candidate fails an exactly-one-label condition. 9. State Identity During Verification Charlie AI Academy - Volume 7.1 | 3 The solution being verified must be identical to the solution originally stated. Do not change A, B, C while explaining it. If Solution 1 states A=RED, verification cannot later say A is BLUE. 10. Independent Verification After finding a candidate, verify it from scratch against the ledger rather than trusting the reasoning path that produced it. Check colors, labels, reports, and conditional rule independently. 11. Detect Multiple Valid Solutions After finding one valid solution, continue checking remaining candidates unless uniqueness has been proven. Do not stop at the first valid permutation when the prompt asks whether ambiguity remains. 12. Do Not Guess Under Ambiguity If two or more candidates satisfy every constraint, list them all and state that the evidence is insufficient to select one. Ambiguity is a correct conclusion when the constraints do not uniquely identify a state. 13. Additional Information Must Discriminate When asking for more information, identify a fact whose possible values would distinguish the surviving candidates. If two solutions differ on A, learning A’s actual color would distinguish them. Asking for an already-known printed label would not. 14. Constraint Propagation vs Enumeration Use propagation when a premise immediately eliminates states; use enumeration when the state space is small. Combining both is often safest. Six permutations are small enough to enumerate completely. 15. Truth Table Discipline For logical reports, use a compact truth table so truth values do not drift between paragraphs. Columns: candidate | X | Y | Z | #true | Y->X | pass/fail. 16. Contradiction Requires Evidence A contradiction is a specific conflict with a premise or locked state. Never call a true report contradictory merely because another branch exists. If Z says B=GREEN and candidate has B=GREEN, Z is true—not a contradiction. Charlie AI Academy - Volume 7.1 | 4 17. No Premise Mutation At the end of a long solution, reread the original ledger. If the verification uses a different rule, stop and repair. Original: Y -> X. Invalid mutation: X -> Z. 18. No State Mutation Maintain the same assignment tuple throughout one candidate. Candidate (A=GREEN,B=BLUE,C=RED) must remain exactly that tuple during all checks. 19. Integrated Reference Problem For the A/B/C color puzzle used in testing, exhaustive checking leaves two valid states: (A=RED,B=GREEN,C=BLUE) with X and Z true; and (A=GREEN,B=BLUE,C=RED) with X and Y true. Both use each color once, have exactly one correct printed label, exactly two true reports, and satisfy Y -> X. 20. Verification Matrix A robust final response can summarize surviving candidates in a small matrix rather than long prose. This reduces accidental state changes and makes constraint failures visible. 21. Stop Rule After all candidate states have been checked, all survivors listed, and ambiguity explained, stop. Do not add speculative conclusions. Complete enumeration + verified survivors + discriminating information = finished. 22. Generalization Use the ledger method for scheduling, configuration, permissions, diagnosis, code debugging, legal hypotheticals, probability sample spaces, and any problem with multiple simultaneous conditions. The technique is domain-independent: preserve premises, enumerate/propagate, verify. 23. Pass Standard A response passes only if no premise changes, no candidate changes during verification, all relevant candidates are considered, every survivor satisfies every constraint, and ambiguity is handled explicitly. Fluent prose with a mutated premise is a failure. Charlie AI Academy - Volume 7.1 | 5 24. Integrated Diagnostic Tests # Test Pass condition 1 A/B/C colors + exactly one correct label + X/Y/Z reports + Y->X. Find exactly the two valid solutions and preserve all constraints. 2 Four people, four seats, six placement restrictions. Enumerate/propagate and verify each restriction against final seating. 3 Three suspects; exactly one lies; three statements. Use truth table; do not mutate statements. 4 Small scheduling puzzle with mutually exclusive times and dependencies. Maintain one ledger and reject candidates by named constraints. 5 Conditional probability with a stated selection mechanism. Build the correct sample space before calculating posterior probability. 6 Problem intentionally has two valid solutions. List both; do not guess; request discriminating information. 7 Problem has no valid solution. State inconsistency and identify the conflicting constraints. 8 User changes one premise after solution. Update ledger and recompute affected candidates without retaining obsolete deductions. Final operating principle: In difficult reasoning, prose is not memory. The constraint ledger is memory. Preserve the ledger, evaluate candidates against it, and let only fully verified candidates reach the final answer.