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R0008-04941 · q-20261008-advance-20261011-r06-sample-space-0016
First-stage outcomes A=[-15, 15], second-stage outcomes B=[0, 16]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.
G001 — First-stage outcomes A=[-15, 15], second-stage outcomes B=[0, 16]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
explicit finite possible-outcome protocol
After
no probability law,equiprobability or independence inferred
Conditions: none
These tasks list possible outcomes,recordings or event membership without assigning probabilities.All combinations being possible does not imply equiprobability or independence.
Rule: possible_outcomes_not_probabilities · Uses: G001
Before
first-stage outcome=-15;second-stage outcome=0
After
[-15, 0]
Conditions: none
Enumerate with A as the outer loop and B as the inner loop;stage order matters.
Rule: ordered_outcome_pair · Uses: G001, S001
Before
first-stage outcome=-15;second-stage outcome=16
After
[-15, 16]
Conditions: none
Enumerate with A as the outer loop and B as the inner loop;stage order matters.
Rule: ordered_outcome_pair · Uses: G001, S002
Before
first-stage outcome=15;second-stage outcome=0
After
[15, 0]
Conditions: none
Enumerate with A as the outer loop and B as the inner loop;stage order matters.
Rule: ordered_outcome_pair · Uses: G001, S003
Before
first-stage outcome=15;second-stage outcome=16
After
[15, 16]
Conditions: none
Enumerate with A as the outer loop and B as the inner loop;stage order matters.
Rule: ordered_outcome_pair · Uses: G001, S004
Before
A=[-15, 15];B=[0, 16]
After
[[-15, 0], [-15, 16], [15, 0], [15, 16]]
Conditions: none
After deduplication,pair each A-value with each B-value exactly once to list the protocol's full Cartesian product.
Rule: complete_cartesian_outcome_protocol · Uses: G001, S005
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.[[-15, 0], [-15, 16], [15, 0], [15, 16]]
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: 0f6d854b41c3ad41baed132284d63249d5fa7421315c14cdd74ed4be904465cccandidate record SHA-256: eb9e6aec6280f556478c7a7493c45e640de49659afe7bf0a642b5b8addbbfbf5semantic review receipt SHA-256: b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289question-first witness SHA-256: caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67Lean: NOT_RUN · human review: NOT_PERFORMED