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R0056-28911 · q-20261005-advance-20261006-r07-descriptive-statistics-0086
The nonempty observation list is D=[13, 0, 0, 0, -12, -12]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.
G001 — The nonempty observation list is D=[13, 0, 0, 0, -12, -12]. Retain every repetition. Under the explicit all-frequency-maximizers convention, give every value with maximum frequency as an increasing set, including all values if every frequency is one.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
source roles = [qf-statistics-maximal-frequency-set, maximal_frequency_set]
After
derived = [ALL_frequency_maximizers_numeric_set]
Conditions: none
Use the declared scalar/set/Yes-No/fraction answer role;integer fractions retain/1.Do not add an undeclared domain or change original bilingual data,formulas or questions.
Rule: R56_source_answer_role_and_EXACT_family_interface · Uses: G001
Before
source roles = [[13, 0, 0, 0, -12, -12]]
After
derived = [[-12, -12, 0, 0, 0, 13], 6]
Conditions: none
Retain EVERY observation,including repeated values.Numeric sorting changes order only,not n or the sum;do not deduplicate as a set or sort lexically.These are sample summaries,not inferred population laws.
Rule: Statistics_FULL_observations_MULTIPLICITY_and_numeric_order · Uses: G001, S001
Before
Statistics ORIGINAL ALL indicators for value-12 := sum(0, 0, 0, 0, 1, 1)
After
Statistics ORIGINAL ALL indicators for value-12 = 2
Conditions: none
Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
Statistics ORIGINAL ALL indicators for value0 := sum(0, 1, 1, 1, 0, 0)
After
Statistics ORIGINAL ALL indicators for value0 = 3
Conditions: none
Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
Statistics ORIGINAL ALL indicators for value13 := sum(1, 0, 0, 0, 0, 0)
After
Statistics ORIGINAL ALL indicators for value13 = 1
Conditions: none
Perform exact rational arithmetic on the ORIGINAL roles.SAFE bounds raw inputs only;derived integers are unbounded and never approximated by floats.
Rule: exact_rational_arithmetic · Uses: G001, S004
Before
source roles = [[13, 0, 0, 0, -12, -12], all_frequency_maximizers]
After
derived = [[[-12, 2], [0, 3], [13, 1]], 3, [0], {0}]Conditions: none
Count ALL occurrences in the complete list for each distinct value,and retain EVERY maximum-frequency tie.Under the EXPLICIT all_frequency_maximizers convention,an all-distinct sample returns every value,not another textbook no-mode convention.
Rule: Statistics_EXPLICIT_ALL_frequency_maximizers_ALL_ties · Uses: G001, S005
S006 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.S005 · premise_and_result_audit — Recompute Statistics ORIGINAL ALL indicators for value13 with exact rational arithmetic, not rounded decimals.S004 · premise_and_result_audit — Recompute Statistics ORIGINAL ALL indicators for value0 with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute Statistics ORIGINAL ALL indicators for value-12 with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.S001 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.{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: f8e1babfb635a60f009b9676409110d4bdda80823871a493eb7bdd5aef22da08candidate record SHA-256: ac9493550dcb4410171537560b1430d62407d3995802d2cff6ebdc1d8153a0easemantic review receipt SHA-256: 8bbda4edbed7078634ae88342998c79bcfb95de96187fac119c3b08e0adb0bc8question-first witness SHA-256: 3edafa72d63d16a22414892b55806430e0a25b15b926d04f312550179607759fLean: NOT_RUN · human review: NOT_PERFORMED