Charlie AI Academy - Volume 6.1.3 | 1 CHARLIE AI ACADEMY Volume 6.1.3 Intermediate-Step Validation and Reasoning Integrity Purpose: Repair a narrow but important failure: Charlie may reach the correct final answer while making false or contradictory claims in the middle of the explanation. A correct conclusion does not excuse invalid reasoning. Core rule: Every intermediate statement must follow from the premises and the current verified state. If a step cannot be justified, do not state it. Charlie AI Academy - Volume 6.1.3 | 2 1. Validate Every Step Before Advancing Treat each reasoning step as a mini-conclusion. Before using it, check that it follows from the currently locked facts. If MIXED-label is known to be pure and an apple is drawn, the valid step is MIXED-label -> APPLES. Do not add claims about the other two boxes until their constraints are checked. 2. Correct Final Answer Is Not Enough A solution fails if its explanation contains false claims even when the final mapping happens to be correct. Wrong intermediate claim: “the other two boxes must both contain oranges.” Final mapping may later be correct, but the reasoning is still invalid. 3. One New Deduction Per Step Prefer small deductions. Lock one consequence, then update the remaining state space. Step 1: MIXED-label -> APPLES. Step 2: remaining contents are ORANGES and MIXED. Step 3: ORANGES-label cannot be ORANGES, so it is MIXED. Step 4: APPLES-label is ORANGES. 4. Never Generalize Beyond the Evidence An observation about one object does not automatically determine all other objects. Drawing an apple identifies the pure MIXED-labeled box as APPLES. It does not mean “the other two boxes contain oranges.” 5. Maintain Cardinality When categories are exclusive and each occurs once, track how many assignments remain. After APPLES is assigned once, exactly one ORANGES and one MIXED assignment remain. 6. Sentence-Level Consistency Check Before outputting each explanatory sentence, compare it to the current state table. If the sentence conflicts with the table, rewrite it. State table says ORANGES-label -> MIXED. Do not write “ORANGES box contains oranges.” 7. No Hidden Repairs Do not allow a later correct statement to silently repair an earlier false statement. Correct or remove the false statement before presenting the answer. A reader should be able to follow the explanation from top to bottom without encountering a known falsehood. 8. Branch Integrity Within a branch, all deductions must correspond to that branch’s observation. Charlie AI Academy - Volume 6.1.3 | 3 Apple branch: never switch the MIXED-labeled box to ORANGES. Orange branch: never switch it to APPLES. 9. Exact Meaning of Quantifiers Words such as all, none, exactly one, at least one, and every impose precise constraints. Preserve them. “Every label is wrong” applies independently to all three boxes. “Exactly one” forbids duplicate exclusive assignments. 10. Do Not Invent Inventory Counts If a puzzle describes categories of contents but does not specify the number of individual objects, do not invent counts such as “only one fruit left.” The three-box puzzle concerns box contents, not a stock of three individual fruits. 11. Reference Solution: Apple Draw Take one fruit from the MIXED-labeled box. Because that label is wrong, the box is pure. If the fruit is an apple: MIXED-label -> APPLES. Remaining contents are ORANGES and MIXED. ORANGES-label cannot be ORANGES, so ORANGES-label -> MIXED. Therefore APPLES-label -> ORANGES. Every intermediate step follows from a locked premise or elimination. 12. Reference Solution: Orange Draw If the fruit is an orange: MIXED-label -> ORANGES. Remaining contents are APPLES and MIXED. APPLES-label cannot be APPLES, so APPLES-label -> MIXED. Therefore ORANGES-label -> APPLES. Do not merge this branch with the apple branch. 13. Backward Verification After reaching a final answer, walk backward through the explanation. Confirm that each step was necessary or valid from the state immediately before it. Backward verification catches explanations that accidentally arrive at the right answer through invalid steps. 14. Counterexample Check When a statement claims something must be true, ask whether a valid alternative state exists. If yes, the statement is too strong. After drawing an apple, saying “both other boxes contain oranges” is disproved by the valid required MIXED box. 15. Contradiction Trigger If two sentences assign different states to the same object under the same branch, stop and repair before answering. MIXED-label -> APPLES and later MIXED-label -> ORANGES cannot coexist in the apple branch. Charlie AI Academy - Volume 6.1.3 | 4 16. Explanation Compression Once the reasoning is verified, remove redundant or speculative sentences. Shorter verified reasoning is safer than long uncontrolled reasoning. Target: observation -> locked state -> elimination -> mapping -> stop. 17. Internal Reasoning vs Visible Explanation The visible explanation should contain only verified steps necessary for the user. Do not expose discarded hypotheses or confused exploratory branches as if they were conclusions. Exploration may consider alternatives; final explanation should present the clean verified path. 18. General Use Apply intermediate validation to arithmetic, logic, probability, scheduling, coding explanations, causal reasoning, and multi-step planning. Any chain is only as reliable as its weakest unsupported step. 19. Pass Standard A response passes only when the final answer is correct AND every displayed intermediate claim is logically valid. Correct result + invalid explanation = fail. Correct result + correct explanation = pass. Charlie AI Academy - Volume 6.1.3 | 5 20. Diagnostic Tests # Prompt What to verify 1 Three mislabeled fruit boxes; every label wrong; one draw. Every intermediate mapping is correct; no duplicate contents; both branches valid. 2 A > B, B > C, D > A. Rank all four. D > A > B > C with no reversed intermediate relation. 3 All A are B; no B are C; X is A. Can X be C? No. Each set inference must be valid. 4 Start at 10; double it; subtract 4; divide by 2. 8. Explanation must preserve operation order. 5 Exactly one of three switches is on; A is off; B is off. C is on; do not invent additional states. 6 A later premise changes one earlier value. Update affected downstream steps and remove obsolete intermediate claims. Final instruction: Do not optimize for producing a plausible-looking explanation. Optimize for a chain in which every sentence remains true under the original premises and all previously locked states.