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R0011-06063 · q-20261009-advance-20261013-r06-event-0088
S=Fin(3)={0,…,2}; the event family is explicitly F=P(S). E=[1], ordered outcomes=[100, 101, 0]. Give (sample-eligibility mask, True/False/invalid-outcome occurrence list, first legal E hit’s zero-based index or none).
G001 — S=Fin(3)={0,…,2}; the event family is explicitly F=P(S). E=[1], ordered outcomes=[100, 101, 0]. Give (sample-eligibility mask, True/False/invalid-outcome occurrence list, first legal E hit’s zero-based index or none).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
S=Fin(3)=[0, 1, 2];declared event model=full_powerset
After
finite S alone does not specify its event family or a probability law
Conditions: none
A finite sample space does not automatically choose F=P(S).Use the declared event family;set data alone give no probabilities,equiprobability or independence.
Rule: declared_finite_event_family · Uses: G001
Before
observation position=0;candidate outcome=100;inside S=No
After
event occurrence=invalid sample
Conditions: none
First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ.
Rule: typed_event_occurrence_row · Uses: G001, S001
Before
observation position=1;candidate outcome=101;inside S=No
After
event occurrence=invalid sample
Conditions: none
First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ.
Rule: typed_event_occurrence_row · Uses: G001, S002
Before
observation position=2;candidate outcome=0;inside S=Yes
After
event occurrence=False
Conditions: none
First check whether the outcome lies in S,then event membership.An outside candidate is not assigned False occurrence;observation position and outcome value differ.
Rule: typed_event_occurrence_row · Uses: G001, S003
Before
legal event hits among ordered candidates;E=[1]
After
first hit position=none
Conditions: none
Return the first0-based position of a legal E-hit in the ordered list;an empty list or no hit gives none,without invented observations.
Rule: first_legal_event_hit_position · Uses: G001, S004
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.([No, No, Yes], [invalid-outcome, invalid-outcome, False], none)
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: fc8f93ab2f354c11e3afe1f873154d068278c97c241ad4c8cf54276a3b28d681candidate record SHA-256: 56ac017ef121232993a7be14d0e455de1cde020d21cee59fba46d83d59570bb1semantic review receipt SHA-256: b9bbc1c947f477a9c4bb5a579368ac5265f2da4572ce612c30f3633ecaf4ae80question-first witness SHA-256: 93f720df3ab3af13a792a3e6b443728e3c2a56276df839911f36569333236c55Lean: NOT_RUN · human review: NOT_PERFORMED