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R0008-04926 · q-20261008-advance-20261011-r06-sample-space-0001
First-stage outcomes A=[0], second-stage outcomes B=[0]; 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=[0], second-stage outcomes B=[0]; 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=0;second-stage outcome=0
After
[0, 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
A=[0];B=[0]
After
[[0, 0]]
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, S002
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.[[0, 0]]
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: 41e361d43f17734f261cf8889a28da455603f884d4515e00a2da6c4ee32c4364candidate record SHA-256: 44b91c41d7a0c2cf5e1ce5da4308743c472d8549291ade3e1a04ccf6018ec037semantic review receipt SHA-256: b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289question-first witness SHA-256: caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67Lean: NOT_RUN · human review: NOT_PERFORMED