{"schema_version":"teacher-skill-representation.payload.v1","representation":{"schema_version":"teacher-skill-representation.v1","skill_ref":"logic.proof-counterexample.artifacts","domain_slug":"logic","skill_slug":"proof-counterexample-artifacts","canonical_url":"/math/skills/logic/proof-counterexample-artifacts","public_title":"Proof and counterexample artifacts","family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","family_name":"Logic, Constraint, Deduction, and Combinatorics","pattern_cluster_refs":["pattern-cluster.logic.visible-clue-elimination.v1","pattern-cluster.logic.deductive-sequences-logic-grids.v1","pattern-cluster.logic.systematic-listing-tree-combinatorics.v1","pattern-cluster.logic.parity-invariants-move-reasoning.v1","pattern-cluster.logic.proof-counterexample-truth-contradiction.v1","pattern-cluster.logic.olympiad-method-adapters.v1"],"task_pattern_refs":["task-pattern.logic.visible-clue-single-survivor.v1","task-pattern.logic.near-miss-elimination.v1","task-pattern.logic.violated-clue-marking.v1","task-pattern.logic.ambiguity-repair.v1","task-pattern.logic.clue-sufficiency-minimality.v1","task-pattern.logic.grid-consistency-repair.v1","task-pattern.logic.list-duplicate-missing-repair.v1","task-pattern.logic.parity-pairing-proof.v1","task-pattern.logic.invariant-move-check.v1","task-pattern.logic.truth-status-visible-state.v1","task-pattern.logic.proof-artifact-selection.v1","task-pattern.logic.counterexample-build-select.v1","task-pattern.logic.contradiction-location.v1","task-pattern.logic.pigeonhole-guarantee.v1","task-pattern.logic.olympiad-invariant-game.v1"],"task_form_refs":["task-form.logic.clue-card-candidate-choice.v1","task-form.logic.candidate-elimination-markboard.v1","task-form.logic.violated-clue-marker.v1","task-form.logic.ambiguity-repair-clue-choice.v1","task-form.logic.minimal-clue-set-choice.v1","task-form.logic.grid-consistency-repair.v1","task-form.logic.list-missing-duplicate-repair.v1","task-form.logic.parity-pairing-proof-choice.v1","task-form.logic.invariant-move-legal-illegal-mark.v1","task-form.logic.truth-card-verifier.v1","task-form.logic.proof-card-evidence-choice.v1","task-form.logic.counterexample-card-build-select.v1","task-form.logic.contradiction-clue-mark.v1","task-form.logic.pigeonhole-box-guarantee-choice.v1","task-form.logic.invariant-game-challenge-choice.v1"],"teacher_summary":"Proof and counterexample artifacts builds logic, constraint, deduction, and combinatorics through visual tasks, examples, and next-step routes.","teacher_explanation_md":"Produce a visible example, counterexample, or short proof artifact that justifies or rejects a mathematical claim.","child_surface_summary_md":"Children may meet this skill through task formats such as Clue-card candidate choice, Candidate elimination markboard, Violated-clue marker, Ambiguity repair clue choice, Minimal clue set choice, Grid consistency repair, List missing or duplicate repair, Parity pairing proof choice, Invariant move legal-illegal mark, Truth card verifier, Proof card evidence choice, Counterexample card build-select, Contradiction clue mark, Pigeonhole box guarantee choice, Invariant game challenge choice.","common_mistake_tags":["Treats one confirming example as proof of a universal claim.","Gives a counterexample that does not actually satisfy the claim conditions."],"hint_reveal_summary_md":"Hints keep the child oriented to the visible structure; reveals show the path without counting as independent evidence.","adaptation_summary_md":"Fresh independent work can move the child toward Core, Transfer, or Challenge routes; help use or confusion keeps support visible.","route_variant_refs":["support_repair","core","stretch_transfer","challenge_ready"],"age_band_refs":["age_6_7","age_8_9","age_10_11"],"practice_focus_refs":["practice-focus.balanced.v1","practice-focus.word-problems.v1"],"standards_refs":[],"school_program_refs":[],"challenge_refs":["challenge.logic.proof-counterexample.artifacts"],"story_fit_tags":["story beats with visible logic state, manipulable evidence, and a bounded child action"],"prerequisite_skill_refs":[],"next_skill_refs":[],"next_family_refs":["module-family.prealg.equations-expressions-inequalities.v1","module-family.geom.spatial-transformations-coordinates.v1","module-family.data.classification-tables-graphs.v1","module-family.oa.whole-number-operations-fluency.v1"],"public_example_refs":[],"retrieval":{"aliases":["Proof and counterexample artifacts","logic.proof-counterexample.artifacts","Logic, Constraint, Deduction, and Combinatorics","Clue-card candidate choice","Candidate elimination markboard","Violated-clue marker","Ambiguity repair clue choice","Minimal clue set choice","Grid consistency repair","List missing or duplicate repair","Parity pairing proof choice","Invariant move legal-illegal mark","Truth card verifier","Proof card evidence choice","Counterexample card build-select","Contradiction clue mark","Pigeonhole box guarantee choice","Invariant game challenge choice"],"teacher_questions":["What does Proof and counterexample artifacts mean?","How does Proof and counterexample artifacts adapt for my child?","Can I see an example of Proof and counterexample artifacts?"],"keywords":["proof and counterexample artifacts","logic","proof-counterexample-artifacts","logic, constraint, deduction, and combinatorics","task-form.logic.clue-card-candidate-choice.v1","task-form.logic.candidate-elimination-markboard.v1","task-form.logic.violated-clue-marker.v1","task-form.logic.ambiguity-repair-clue-choice.v1","task-form.logic.minimal-clue-set-choice.v1","task-form.logic.grid-consistency-repair.v1","task-form.logic.list-missing-duplicate-repair.v1","task-form.logic.parity-pairing-proof-choice.v1","task-form.logic.invariant-move-legal-illegal-mark.v1","task-form.logic.truth-card-verifier.v1","task-form.logic.proof-card-evidence-choice.v1","task-form.logic.counterexample-card-build-select.v1","task-form.logic.contradiction-clue-mark.v1","task-form.logic.pigeonhole-box-guarantee-choice.v1","task-form.logic.invariant-game-challenge-choice.v1"],"short_answer_public":"Proof and counterexample artifacts builds logic, constraint, deduction, and combinatorics through visual tasks, examples, and next-step routes.","canonical_links":[{"label":"Proof and counterexample artifacts","url":"/math/skills/logic/proof-counterexample-artifacts"}],"safe_to_quote_snippets":["Proof and counterexample artifacts builds logic, constraint, deduction, and combinatorics through visual tasks, examples, and next-step routes."],"example_refs":[]}},"task_forms":[{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.ambiguity-repair-clue-choice.v1","public_slug":"ambiguity-repair-clue-choice","owning_skill_refs":["logic.constraints.elimination","logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.visible-clue-elimination.v1","task_pattern_ref":"task-pattern.logic.ambiguity-repair.v1","public_title":"Ambiguity repair clue choice","teacher_summary":"Ambiguity repair clue choice asks children to choose a clue action that changes an ambiguous clue set into a valid unique solution.","teacher_purpose_md":"Repair zero-survivor or multiple-survivor clue sets by selecting an added, removed, or clarified clue.","child_action_public":"Choose a clue action that changes an ambiguous clue set into a valid unique solution.","answer_affordance_public":"Choose the answer that matches the visible prompt.","visual_primitive_public_refs":["clue_set","survivor_count_meter","repair_clue_cards"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: candidate cards.","Story object role: clue cards.","Story object role: elimination marks.","Story object role: repair clue cards.","Story object role: survivor tray."],"retrieval":{"aliases":["Ambiguity repair clue choice","task-form.logic.ambiguity-repair-clue-choice.v1","ambiguity_repair_choice","clue_set","survivor_count_meter","repair_clue_cards"],"teacher_questions":["What does Ambiguity repair clue choice mean?","How does Ambiguity repair clue choice adapt for my child?","Can I see an example of Ambiguity repair clue choice?"],"keywords":["ambiguity repair clue choice","ambiguity_repair_choice","logic.constraints.elimination","logic.proof-counterexample.artifacts"],"short_answer_public":"Ambiguity repair clue choice asks children to choose a clue action that changes an ambiguous clue set into a valid unique solution.","canonical_links":[{"label":"Ambiguity repair clue choice","url":"#taskform-ambiguity-repair-clue-choice"}],"safe_to_quote_snippets":["Ambiguity repair clue choice asks children to choose a clue action that changes an ambiguous clue set into a valid unique solution."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.candidate-elimination-markboard.v1","public_slug":"candidate-elimination-markboard","owning_skill_refs":["logic.constraints.elimination","logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.visible-clue-elimination.v1","task_pattern_ref":"task-pattern.logic.near-miss-elimination.v1","public_title":"Candidate elimination markboard","teacher_summary":"Candidate elimination markboard asks children to mark candidates eliminated by a highlighted clue or all clues.","teacher_purpose_md":"Distinguish candidates that almost fit from candidates that satisfy every clue by marking the decisive failed clue or candidate.","child_action_public":"Mark candidates eliminated by a highlighted clue or all clues.","answer_affordance_public":"Complete the candidate elimination markboard action.","visual_primitive_public_refs":["candidate_row","clue_focus","elimination_marks"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: candidate cards.","Story object role: clue cards.","Story object role: elimination marks.","Story object role: repair clue cards.","Story object role: survivor tray."],"retrieval":{"aliases":["Candidate elimination markboard","task-form.logic.candidate-elimination-markboard.v1","candidate_elimination_mark_set","candidate_row","clue_focus","elimination_marks"],"teacher_questions":["What does Candidate elimination markboard mean?","How does Candidate elimination markboard adapt for my child?","Can I see an example of Candidate elimination markboard?"],"keywords":["candidate elimination markboard","candidate_elimination_mark_set","logic.constraints.elimination","logic.proof-counterexample.artifacts"],"short_answer_public":"Candidate elimination markboard asks children to mark candidates eliminated by a highlighted clue or all clues.","canonical_links":[{"label":"Candidate elimination markboard","url":"#taskform-candidate-elimination-markboard"}],"safe_to_quote_snippets":["Candidate elimination markboard asks children to mark candidates eliminated by a highlighted clue or all clues."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.clue-card-candidate-choice.v1","public_slug":"clue-card-candidate-choice","owning_skill_refs":["logic.constraints.elimination","logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.visible-clue-elimination.v1","task_pattern_ref":"task-pattern.logic.visible-clue-single-survivor.v1","public_title":"Clue-card candidate choice","teacher_summary":"Clue-card candidate choice asks children to use clue cards to eliminate visible candidates and choose the single survivor.","teacher_purpose_md":"Use visible clue cards to eliminate candidates until exactly one valid survivor remains.","child_action_public":"Use clue cards to eliminate visible candidates and choose the single survivor.","answer_affordance_public":"Choose the answer that matches the visible prompt.","visual_primitive_public_refs":["candidate_cards","clue_cards","elimination_marks"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"independent_solve","public_label":"Independent solve","teacher_note_md":"A fresh correct solve can count toward stronger evidence."},{"id":"supported_solve","public_label":"Supported solve","teacher_note_md":"Help was useful, so the next step should keep support visible."},{"id":"challenge_ready_signal","public_label":"Challenge ready","teacher_note_md":"Strong fresh evidence can open a deeper example when the task form supports it."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."},{"id":"challenge_ready","public_label":"Challenge","teacher_note_md":"Offer a deeper reasoning example only when the task form has a real challenge boundary."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":["Challenge examples must change the reasoning demand, not only make the row busier."],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: candidate cards.","Story object role: clue cards.","Story object role: elimination marks.","Story object role: repair clue cards.","Story object role: survivor tray."],"retrieval":{"aliases":["Clue-card candidate choice","task-form.logic.clue-card-candidate-choice.v1","single_survivor_choice_with_elimination_evidence","candidate_cards","clue_cards","elimination_marks"],"teacher_questions":["What does Clue-card candidate choice mean?","How does Clue-card candidate choice adapt for my child?","Can I see an example of Clue-card candidate choice?"],"keywords":["clue-card candidate choice","single_survivor_choice_with_elimination_evidence","logic.constraints.elimination","logic.proof-counterexample.artifacts"],"short_answer_public":"Clue-card candidate choice asks children to use clue cards to eliminate visible candidates and choose the single survivor.","canonical_links":[{"label":"Clue-card candidate choice","url":"#taskform-clue-card-candidate-choice"}],"safe_to_quote_snippets":["Clue-card candidate choice asks children to use clue cards to eliminate visible candidates and choose the single survivor."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.contradiction-clue-mark.v1","public_slug":"contradiction-clue-mark","owning_skill_refs":["logic.proof-counterexample.artifacts","logic.logic-grid.basic"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.proof-counterexample-truth-contradiction.v1","task_pattern_ref":"task-pattern.logic.contradiction-location.v1","public_title":"Contradiction clue mark","teacher_summary":"Contradiction clue mark asks children to mark the clue, statement, or grid mark that contradicts the rest.","teacher_purpose_md":"Locate the clue, mark, or statement that contradicts the current state.","child_action_public":"Mark the clue, statement, or grid mark that contradicts the rest.","answer_affordance_public":"Complete the contradiction clue mark action.","visual_primitive_public_refs":["clue_cards","state_board","contradiction_marker"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: statement cards.","Story object role: proof cards.","Story object role: counterexample cards.","Story object role: contradiction marker.","Story object role: visible state board."],"retrieval":{"aliases":["Contradiction clue mark","task-form.logic.contradiction-clue-mark.v1","contradiction_source_mark","clue_cards","state_board","contradiction_marker"],"teacher_questions":["What does Contradiction clue mark mean?","How does Contradiction clue mark adapt for my child?","Can I see an example of Contradiction clue mark?"],"keywords":["contradiction clue mark","contradiction_source_mark","logic.proof-counterexample.artifacts","logic.logic-grid.basic"],"short_answer_public":"Contradiction clue mark asks children to mark the clue, statement, or grid mark that contradicts the rest.","canonical_links":[{"label":"Contradiction clue mark","url":"#taskform-contradiction-clue-mark"}],"safe_to_quote_snippets":["Contradiction clue mark asks children to mark the clue, statement, or grid mark that contradicts the rest."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.counterexample-card-build-select.v1","public_slug":"counterexample-card-build-select","owning_skill_refs":["logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.proof-counterexample-truth-contradiction.v1","task_pattern_ref":"task-pattern.logic.counterexample-build-select.v1","public_title":"Counterexample card build-select","teacher_summary":"Counterexample card build-select asks children to select or build one valid counterexample to disprove a claim.","teacher_purpose_md":"Build or select one valid counterexample to disprove a claim.","child_action_public":"Select or build one valid counterexample to disprove a claim.","answer_affordance_public":"Complete the counterexample card build-select action.","visual_primitive_public_refs":["claim_card","construction_slots","counterexample_cards"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: statement cards.","Story object role: proof cards.","Story object role: counterexample cards.","Story object role: contradiction marker.","Story object role: visible state board."],"retrieval":{"aliases":["Counterexample card build-select","task-form.logic.counterexample-card-build-select.v1","counterexample_artifact","claim_card","construction_slots","counterexample_cards"],"teacher_questions":["What does Counterexample card build-select mean?","How does Counterexample card build-select adapt for my child?","Can I see an example of Counterexample card build-select?"],"keywords":["counterexample card build-select","counterexample_artifact","logic.proof-counterexample.artifacts"],"short_answer_public":"Counterexample card build-select asks children to select or build one valid counterexample to disprove a claim.","canonical_links":[{"label":"Counterexample card build-select","url":"#taskform-counterexample-card-build-select"}],"safe_to_quote_snippets":["Counterexample card build-select asks children to select or build one valid counterexample to disprove a claim."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.grid-consistency-repair.v1","public_slug":"grid-consistency-repair","owning_skill_refs":["logic.logic-grid.basic","logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.deductive-sequences-logic-grids.v1","task_pattern_ref":"task-pattern.logic.grid-consistency-repair.v1","public_title":"Grid consistency repair","teacher_summary":"Grid consistency repair asks children to find and fix a wrong mark in a partially filled grid.","teacher_purpose_md":"Find and repair a conflicting grid mark, row, column, or clue.","child_action_public":"Find and fix a wrong mark in a partially filled grid.","answer_affordance_public":"Complete the grid consistency repair action.","visual_primitive_public_refs":["logic_grid","wrong_mark","clue_cards","repair_control"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: ordered 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invariant.","teacher_purpose_md":"Decide whether a move preserves or breaks an invariant.","child_action_public":"Mark whether a proposed move preserves a named invariant.","answer_affordance_public":"Complete the invariant move legal-illegal mark action.","visual_primitive_public_refs":["state_board","move_card","invariant_badge"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work 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children to mark whether a proposed move preserves a named invariant.","canonical_links":[{"label":"Invariant move legal-illegal mark","url":"#taskform-invariant-move-legal-illegal-mark"}],"safe_to_quote_snippets":["Invariant move legal-illegal mark asks children to mark whether a proposed move preserves a named invariant."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.list-missing-duplicate-repair.v1","public_slug":"list-missing-or-duplicate-repair","owning_skill_refs":["logic.combinatorics.counting-list","logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.systematic-listing-tree-combinatorics.v1","task_pattern_ref":"task-pattern.logic.list-duplicate-missing-repair.v1","public_title":"List missing or duplicate repair","teacher_summary":"List missing or duplicate repair asks children to mark duplicate, missing, or illegal cases in a list.","teacher_purpose_md":"Repair a list by marking a duplicate, missing case, or illegal case.","child_action_public":"Mark duplicate, missing, or illegal cases in a list.","answer_affordance_public":"Complete the list missing or duplicate repair action.","visual_primitive_public_refs":["list_cards","duplicate_marker","missing_marker","illegal_marker"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by 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set choice","teacher_summary":"Minimal clue set choice asks children to select the smallest sufficient clue set or mark a redundant or necessary clue.","teacher_purpose_md":"Select the smallest sufficient clue set or mark redundant or necessary clues while preserving one survivor.","child_action_public":"Select the smallest sufficient clue set or mark a redundant or necessary clue.","answer_affordance_public":"Complete the minimal clue set choice action.","visual_primitive_public_refs":["clue_chips","survivor_tray","sufficiency_badge"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This 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choice","minimal_sufficient_clue_set","logic.constraints.elimination","logic.proof-counterexample.artifacts"],"short_answer_public":"Minimal clue set choice asks children to select the smallest sufficient clue set or mark a redundant or necessary clue.","canonical_links":[{"label":"Minimal clue set choice","url":"#taskform-minimal-clue-set-choice"}],"safe_to_quote_snippets":["Minimal clue set choice asks children to select the smallest sufficient clue set or mark a redundant or necessary clue."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.parity-pairing-proof-choice.v1","public_slug":"parity-pairing-proof-choice","owning_skill_refs":["logic.parity.even-odd-reasoning","logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.parity-invariants-move-reasoning.v1","task_pattern_ref":"task-pattern.logic.parity-pairing-proof.v1","public_title":"Parity pairing proof choice","teacher_summary":"Parity pairing proof choice asks children to pair objects or choose a proof card to justify even, odd, or impossible.","teacher_purpose_md":"Use pairs or leftovers to justify an even or odd outcome or impossibility.","child_action_public":"Pair objects or choose a proof card to justify even, odd, or impossible.","answer_affordance_public":"Choose the answer that matches the visible prompt.","visual_primitive_public_refs":["object_pairs","leftover_token","proof_card"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change 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role: move card.","Story object role: invariant badge."],"retrieval":{"aliases":["Parity pairing proof choice","task-form.logic.parity-pairing-proof-choice.v1","parity_pairing_proof_choice","object_pairs","leftover_token","proof_card"],"teacher_questions":["What does Parity pairing proof choice mean?","How does Parity pairing proof choice adapt for my child?","Can I see an example of Parity pairing proof choice?"],"keywords":["parity pairing proof choice","parity_pairing_proof_choice","logic.parity.even-odd-reasoning","logic.proof-counterexample.artifacts"],"short_answer_public":"Parity pairing proof choice asks children to pair objects or choose a proof card to justify even, odd, or impossible.","canonical_links":[{"label":"Parity pairing proof choice","url":"#taskform-parity-pairing-proof-choice"}],"safe_to_quote_snippets":["Parity pairing proof choice asks children to pair objects or choose a proof card to justify even, odd, or impossible."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.pigeonhole-box-guarantee-choice.v1","public_slug":"pigeonhole-box-guarantee-choice","owning_skill_refs":["logic.olympiad.invariants-casework-pigeonhole","logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.olympiad-method-adapters.v1","task_pattern_ref":"task-pattern.logic.pigeonhole-guarantee.v1","public_title":"Pigeonhole box guarantee choice","teacher_summary":"Pigeonhole box guarantee choice asks children to choose the guaranteed conclusion from objects and boxes or capacities.","teacher_purpose_md":"Use boxes and objects to decide a guaranteed shared box, overflow, or minimum certainty condition.","child_action_public":"Choose the guaranteed conclusion from objects and boxes or capacities.","answer_affordance_public":"Choose the answer that matches the visible prompt.","visual_primitive_public_refs":["boxes","tokens","capacity_labels","guarantee_cards"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: pigeonhole boxes.","Story object role: casework chips.","Story object role: move rules.","Story object role: target state cards.","Story object role: proof card."],"retrieval":{"aliases":["Pigeonhole box guarantee choice","task-form.logic.pigeonhole-box-guarantee-choice.v1","pigeonhole_guarantee_choice","boxes","tokens","capacity_labels","guarantee_cards"],"teacher_questions":["What does Pigeonhole box guarantee choice mean?","How does Pigeonhole box guarantee choice adapt for my child?","Can I see an example of Pigeonhole box guarantee choice?"],"keywords":["pigeonhole box guarantee choice","pigeonhole_guarantee_choice","logic.olympiad.invariants-casework-pigeonhole","logic.proof-counterexample.artifacts"],"short_answer_public":"Pigeonhole box guarantee choice asks children to choose the guaranteed conclusion from objects and boxes or capacities.","canonical_links":[{"label":"Pigeonhole box guarantee choice","url":"#taskform-pigeonhole-box-guarantee-choice"}],"safe_to_quote_snippets":["Pigeonhole box guarantee choice asks children to choose the guaranteed conclusion from objects and boxes or capacities."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.proof-card-evidence-choice.v1","public_slug":"proof-card-evidence-choice","owning_skill_refs":["logic.proof-counterexample.artifacts","logic.constraints.elimination"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.proof-counterexample-truth-contradiction.v1","task_pattern_ref":"task-pattern.logic.proof-artifact-selection.v1","public_title":"Proof card evidence choice","teacher_summary":"Proof card evidence choice asks children to select the proof card that supports a visible claim.","teacher_purpose_md":"Select the proof card that justifies a claim from visible evidence.","child_action_public":"Select the proof card that supports a visible claim.","answer_affordance_public":"Choose the answer that matches the visible prompt.","visual_primitive_public_refs":["claim_card","evidence_cards","proof_stamp"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: statement cards.","Story object role: proof cards.","Story object role: counterexample cards.","Story object role: contradiction marker.","Story object role: visible state board."],"retrieval":{"aliases":["Proof card evidence choice","task-form.logic.proof-card-evidence-choice.v1","proof_artifact_choice","claim_card","evidence_cards","proof_stamp"],"teacher_questions":["What does Proof card evidence choice mean?","How does Proof card evidence choice adapt for my child?","Can I see an example of Proof card evidence choice?"],"keywords":["proof card evidence choice","proof_artifact_choice","logic.proof-counterexample.artifacts","logic.constraints.elimination"],"short_answer_public":"Proof card evidence choice asks children to select the proof card that supports a visible claim.","canonical_links":[{"label":"Proof card evidence choice","url":"#taskform-proof-card-evidence-choice"}],"safe_to_quote_snippets":["Proof card evidence choice asks children to select the proof card that supports a visible claim."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.truth-card-verifier.v1","public_slug":"truth-card-verifier","owning_skill_refs":["logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.proof-counterexample-truth-contradiction.v1","task_pattern_ref":"task-pattern.logic.truth-status-visible-state.v1","public_title":"Truth card verifier","teacher_summary":"Truth card verifier asks children to mark a visible statement as true, false, or not determined and choose evidence when required.","teacher_purpose_md":"Mark a visible statement as true, false, or not determined from the shown state.","child_action_public":"Mark a visible statement as true, false, or not determined and choose evidence when required.","answer_affordance_public":"Complete the truth card verifier action.","visual_primitive_public_refs":["statement_card","visible_state","truth_value_chips"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: statement cards.","Story object role: proof cards.","Story object role: counterexample cards.","Story object role: contradiction marker.","Story object role: visible state board."],"retrieval":{"aliases":["Truth card verifier","task-form.logic.truth-card-verifier.v1","truth_false_unknown_with_evidence","statement_card","visible_state","truth_value_chips"],"teacher_questions":["What does Truth card verifier mean?","How does Truth card verifier adapt for my child?","Can I see an example of Truth card verifier?"],"keywords":["truth card verifier","truth_false_unknown_with_evidence","logic.proof-counterexample.artifacts"],"short_answer_public":"Truth card verifier asks children to mark a visible statement as true, false, or not determined and choose evidence when required.","canonical_links":[{"label":"Truth card verifier","url":"#taskform-truth-card-verifier"}],"safe_to_quote_snippets":["Truth card verifier asks children to mark a visible statement as true, false, or not determined and choose evidence when required."],"example_refs":[]}},{"schema_version":"task-form-representation.v1","task_form_ref":"task-form.logic.violated-clue-marker.v1","public_slug":"violated-clue-marker","owning_skill_refs":["logic.constraints.elimination","logic.proof-counterexample.artifacts"],"primary_family_ref":"module-family.logic.constraint-deduction-combinatorics.v1","pattern_cluster_ref":"pattern-cluster.logic.visible-clue-elimination.v1","task_pattern_ref":"task-pattern.logic.violated-clue-marking.v1","public_title":"Violated-clue marker","teacher_summary":"Violated-clue marker asks children to given a proposed candidate or arrangement, mark the clue it breaks.","teacher_purpose_md":"Given a proposed candidate or arrangement, mark which clue is violated.","child_action_public":"Given a proposed candidate or arrangement, mark the clue it breaks.","answer_affordance_public":"Choose the answer that matches the visible prompt.","visual_primitive_public_refs":["proposed_answer_card","clue_cards","violation_marker"],"child_surface_preview":{"availability":"not_available","preview_asset_refs":[],"absence_md":""},"public_example_refs":[],"non_example_refs":[],"common_mistake_tags":[],"hint_reveal_public":["Hints should point attention to the visible structure before giving away the solution.","Reveals should show the answer path separately from independent evidence."],"public_evidence_signals":[{"id":"check_only","public_label":"Check only","teacher_note_md":"This observation can check the session without moving the child forward by itself."}],"route_variants":[{"id":"support_repair","public_label":"Support","teacher_note_md":"Use a more guided version when recent work shows confusion or heavy help use."},{"id":"core","public_label":"Core","teacher_note_md":"Use the normal version when the child solves fresh examples steadily."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"age_presentation_differences":[{"id":"age_6_7","public_label":"6-7","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"age_8_9","public_label":"8-9","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"age_10_11","public_label":"10-11","teacher_note_md":"Keep the presentation older and allow explanation, proof, and transfer when evidence supports it."}],"practice_focus_compatibility":[{"id":"practice-focus.word-problems.v1","public_label":"Word problems are confusing","teacher_note_md":"Schedule visual model or bar-model review when the story lane is incompatible."}],"challenge_enrichment_public":[],"story_fit_public":["story beats with visible logic state, manipulable evidence, and a bounded child action","Story object role: candidate cards.","Story object role: clue cards.","Story object role: elimination marks.","Story object role: repair clue cards.","Story object role: survivor tray."],"retrieval":{"aliases":["Violated-clue marker","task-form.logic.violated-clue-marker.v1","violated_clue_id_choice","proposed_answer_card","clue_cards","violation_marker"],"teacher_questions":["What does Violated-clue marker mean?","How does Violated-clue marker adapt for my child?","Can I see an example of Violated-clue marker?"],"keywords":["violated-clue marker","violated_clue_id_choice","logic.constraints.elimination","logic.proof-counterexample.artifacts"],"short_answer_public":"Violated-clue marker asks children to given a proposed candidate or arrangement, mark the clue it breaks.","canonical_links":[{"label":"Violated-clue marker","url":"#taskform-violated-clue-marker"}],"safe_to_quote_snippets":["Violated-clue marker asks children to given a proposed candidate or arrangement, mark the clue it breaks."],"example_refs":[]}}],"examples":[],"preview_artifacts":[]}