{"schema_version":"task-form-representation.payload.v1","representation":{"schema_version":"task-form-representation.v2","task_form_ref":"task-form.logic.embedded-graph-predicate-panel-choice.v1","public_slug":"embedded-graph-predicate-panel-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.embedded-graph-predicate-panel-choice.v1","public_title":"Embedded-graph predicate panel choice","teacher_summary":"Embedded-graph predicate panel choice asks the player to inspect exact graph panels and choose the single panel whose topology satisfies the stated object-relation predicate.","teacher_purpose_md":"Inspect exact graph panels and choose the single panel whose topology satisfies the stated object-relation predicate.","player_action_public":"Inspect exact graph panels and choose the single panel whose topology satisfies the stated object-relation predicate.","answer_affordance_public":"Complete the embedded-graph predicate panel choice action.","visual_primitive_public_refs":["occupied_relation_board","graph_candidate_panels","marked_graph_vertices","exact_graph_edges","stable_panel_tokens","semantic_relation_highlights"],"player_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 changing the next route 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 after steady fresh solves."},{"id":"stretch_transfer","public_label":"Transfer","teacher_note_md":"Change representation or context after independent evidence stays strong."}],"presentation_profiles":[{"id":"presentation_compact","public_label":"Compact","teacher_note_md":"Use concrete objects, short prompts, and more visible support."},{"id":"presentation_standard","public_label":"Standard","teacher_note_md":"Use the same idea with more independent reading and representation."},{"id":"presentation_extended","public_label":"Extended","teacher_note_md":"Allow denser 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 player 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":["Embedded-graph predicate panel choice","task-form.logic.embedded-graph-predicate-panel-choice.v1","single_graph_panel_token","occupied_relation_board","graph_candidate_panels","marked_graph_vertices","exact_graph_edges","stable_panel_tokens","semantic_relation_highlights"],"teacher_questions":["What does Embedded-graph predicate panel choice mean?","How does Embedded-graph predicate panel choice adapt?","Can I see an example of Embedded-graph predicate panel choice?"],"keywords":["embedded-graph predicate panel choice","single_graph_panel_token","logic.proof-counterexample.artifacts","logic.constraints.elimination"],"short_answer_public":"Embedded-graph predicate panel choice asks the player to inspect exact graph panels and choose the single panel whose topology satisfies the stated object-relation predicate.","canonical_links":[{"label":"Embedded-graph predicate panel choice","url":"#taskform-embedded-graph-predicate-panel-choice"}],"safe_to_quote_snippets":["Embedded-graph predicate panel choice asks the player to inspect exact graph panels and choose the single panel whose topology satisfies the stated object-relation predicate."],"example_refs":[]}},"canonical_target":{"href":"/math/skills/logic/proof-counterexample-artifacts#taskform-embedded-graph-predicate-panel-choice","skill":{"schema_version":"teacher-skill-representation.v2","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","pattern-cluster.geom.transformations-composition-visualization.v1","pattern-cluster.ratio.scaling-rate-proportion.v1","pattern-cluster.measure.units-tools-conversions.v1","pattern-cluster.oa.additive-multiplicative-relations.v1","pattern-cluster.prealg.equations-expressions-digit-constraints.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-pattern.geometry.connected-grid-exact-cover-count.v1","task-pattern.logic.single-violation-repair.v1","task-pattern.logic.place-value-case-count.v1","task-pattern.decimal-percent.conserved-component-mixture.v1","task-pattern.logic.unique-perfect-matching-edge-extremum.v1","task-pattern.logic.sequential-private-information-elimination.v1","task-pattern.logic.orthogonal-grid-removal-counterexample-strategy.v1","task-pattern.geometry.geometric-network-optimization.v1","task-pattern.logic.bounded-semantic-rubric-response.v1","task-pattern.logic.bounded-reasoning-proof-workspace.v1","task-pattern.logic.switch-bulb-one-visit-identification.v1","task-pattern.geometry.equal-rope-knot-bundle-choice.v1","task-pattern.logic.embedded-graph-predicate-panel-choice.v1","task-pattern.logic.equal-sum-pair-omission-choice.v1","task-pattern.logic.finite-constraint-entailment-choice.v1","task-pattern.logic.region-doorway-trail-start-choice.v1","task-pattern.logic.symbol-strip-deletion-middle-token.v1","task-pattern.prealgebra.plus-minus-target-minus-count-choice.v1","task-pattern.logic.card-operation-move-count-pair-choice.v1","task-pattern.geometry.embedded-graph-triangle-count-proof.v1","task-pattern.geometry.segment-relocation-shape-transform.v1","task-pattern.logic.layered-path-consistency-proof.v1","task-pattern.logic.transport-crossing-sequence-proof.v1","task-pattern.logic.word-ladder-path-or-no-path-proof.v1","task-pattern.prealgebra.segment-relocation-equation-repair.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","task-form.geometry.grid-region-partition-count.v1","task-form.logic.violated-clue-and-repair-pair.v1","task-form.logic.place-value-case-count-numeric-entry.v1","task-form.decimal-percent.conserved-component-final-total.v1","task-form.logic.unique-perfect-matching-edge-extremum-proof.v1","task-form.logic.sequential-epistemic-rank-choice.v1","task-form.logic.orthogonal-grid-removal-counterexample-strategy.v1","task-form.geometry.network-optimization-cost-entry.v1","task-form.logic.bounded-semantic-rubric-response.v1","task-form.logic.bounded-reasoning-proof-workspace.v1","task-form.logic.switch-bulb-one-visit-identification.v1","task-form.geometry.equal-rope-knot-bundle-choice.v1","task-form.logic.embedded-graph-predicate-panel-choice.v1","task-form.logic.equal-sum-pair-omission-choice.v1","task-form.logic.finite-constraint-entailment-choice.v1","task-form.logic.region-doorway-trail-start-choice.v1","task-form.logic.symbol-strip-deletion-middle-token.v1","task-form.prealgebra.plus-minus-target-minus-count-choice.v1","task-form.logic.card-operation-move-count-pair-choice.v1","task-form.geometry.embedded-graph-triangle-count-proof.v1","task-form.geometry.segment-relocation-shape-transform.v1","task-form.logic.layered-path-consistency-proof.v1","task-form.logic.transport-crossing-sequence-proof.v1","task-form.logic.word-ladder-path-or-no-path-proof.v1","task-form.prealgebra.segment-relocation-equation-repair.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.","player_surface_summary_md":"This skill appears in 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, Connected grid exact-cover partition and count, Unique violated predicate and matching repair pair, Place-value property case-count entry, Conserved-component final-whole entry, Unique-perfect-matching edge extremum proof, Sequential epistemic ordered-value choice, Orthogonal-grid removal counterexample strategy, Geometric network minimum-cost entry, Bounded semantic rubric response, Bounded reasoning proof workspace, Switch-bulb one-visit identification, Equal-rope knot-bundle choice, Embedded-graph predicate panel choice, Equal-sum pair omission choice, Finite-constraint entailment choice, Region-doorway trail-start choice, Symbol-strip deletion middle token, Plus-minus target minus-count choice, Card-operation move-count pair choice, Embedded-graph triangle count with exhaustive witness proof, Segment relocation shape transform, Layered-path consistency proof, Transport-crossing sequence proof, Word-ladder path or no-path proof, Segment-relocation equation repair.","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 attention on the visible structure; reveals show the path without counting as independent evidence.","adaptation_summary_md":"Fresh independent work can move toward Core, Transfer, or Challenge routes; help use or confusion keeps support visible.","route_variant_refs":["support_repair","core","stretch_transfer","challenge_ready"],"presentation_profile_refs":["presentation_compact","presentation_standard","presentation_extended"],"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 player action","episodes with visible movement, fitting, nets, layers, grids, routes, or solid viewpoints","episodes where two quantities are linked by an explicit multiplicative scale or conserved proportion","episodes with a real scale, instrument, duration, unit, rate, or money quantity"],"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","Connected grid exact-cover partition and count","Unique violated predicate and matching repair pair","Place-value property case-count entry","Conserved-component final-whole entry","Unique-perfect-matching edge extremum proof","Sequential epistemic ordered-value choice","Orthogonal-grid removal counterexample strategy","Geometric network minimum-cost entry","Bounded semantic rubric response","Bounded reasoning proof workspace","Switch-bulb one-visit identification","Equal-rope knot-bundle choice","Embedded-graph predicate panel choice","Equal-sum pair omission choice","Finite-constraint entailment choice","Region-doorway trail-start choice","Symbol-strip deletion middle token","Plus-minus target minus-count choice","Card-operation move-count pair choice","Embedded-graph triangle count with exhaustive witness proof","Segment relocation shape transform","Layered-path consistency proof","Transport-crossing sequence proof","Word-ladder path or no-path proof","Segment-relocation equation repair"],"teacher_questions":["What does Proof and counterexample artifacts mean?","How does Proof and counterexample artifacts adapt?","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","task-form.geometry.grid-region-partition-count.v1","task-form.logic.violated-clue-and-repair-pair.v1","task-form.logic.place-value-case-count-numeric-entry.v1","task-form.decimal-percent.conserved-component-final-total.v1","task-form.logic.unique-perfect-matching-edge-extremum-proof.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":[]}}},"examples":[],"preview_artifacts":[]}