第 27623 題：有限值IID強大數律

原題與已知條件

無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-strong-law-large-numbers-finite-valued-iid

逐步推導

source roles = [slln-fixed-n-deviation]

derived = [[n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary]]

source roles = [infinite_iid]

derived = [ASSUME whole infinite sequence is IID with this common marginal]

SLLN ORIGINAL common marginal ORIGINAL mass sum0 := sum(0, 1/2)

SLLN ORIGINAL common marginal ORIGINAL mass sum0 = 1/2

SLLN ORIGINAL common marginal ORIGINAL mass sum1 := sum(1/2, 1/2)

SLLN ORIGINAL common marginal ORIGINAL mass sum1 = 1

SLLN ORIGINAL common marginal ORIGINAL weighted value0 := mul(0, 1/2)

SLLN ORIGINAL common marginal ORIGINAL weighted value0 = 0

SLLN ORIGINAL common marginal ORIGINAL mean sum0 := sum(0, 0)

SLLN ORIGINAL common marginal ORIGINAL mean sum0 = 0

SLLN ORIGINAL common marginal exact unbounded value square0 := mul(0, 0)

SLLN ORIGINAL common marginal exact unbounded value square0 = 0

SLLN ORIGINAL common marginal ORIGINAL weighted square0 := mul(0, 1/2)

SLLN ORIGINAL common marginal ORIGINAL weighted square0 = 0

SLLN ORIGINAL common marginal ORIGINAL second moment sum0 := sum(0, 0)

SLLN ORIGINAL common marginal ORIGINAL second moment sum0 = 0

SLLN ORIGINAL common marginal ORIGINAL weighted value1 := mul(1, 1/2)

SLLN ORIGINAL common marginal ORIGINAL weighted value1 = 1/2

SLLN ORIGINAL common marginal ORIGINAL mean sum1 := sum(0, 1/2)

SLLN ORIGINAL common marginal ORIGINAL mean sum1 = 1/2

SLLN ORIGINAL common marginal exact unbounded value square1 := mul(1, 1)

SLLN ORIGINAL common marginal exact unbounded value square1 = 1

SLLN ORIGINAL common marginal ORIGINAL weighted square1 := mul(1, 1/2)

SLLN ORIGINAL common marginal ORIGINAL weighted square1 = 1/2

SLLN ORIGINAL common marginal ORIGINAL second moment sum1 := sum(0, 1/2)

SLLN ORIGINAL common marginal ORIGINAL second moment sum1 = 1/2

SLLN ORIGINAL common marginal ORIGINAL mean squared := mul(1/2, 1/2)

SLLN ORIGINAL common marginal ORIGINAL mean squared = 1/4

SLLN ORIGINAL common marginal ORIGINAL second minus mean squared := sub(1/2, 1/4)

SLLN ORIGINAL common marginal ORIGINAL second minus mean squared = 1/4

source roles = [SLLN ORIGINAL common marginal, [0, 1], [[1, 2], [1, 2]]]

derived = [[[0, 1/2], [1, 1/2]], 1, 1/2, 1/2, 1/4]

SLLN ORIGINAL joint word0 integer sum := sum(0, 0, 0, 0, 0)

SLLN ORIGINAL joint word0 integer sum = 0

SLLN ORIGINAL joint word0 mean := div(0, 5)

SLLN ORIGINAL joint word0 mean = 0

SLLN ORIGINAL joint word0 mean minus mu := sub(0, 1/2)

SLLN ORIGINAL joint word0 mean minus mu = -1/2

SLLN ORIGINAL deviating word0 probability factor0 := mul(1, 1/2)

SLLN ORIGINAL deviating word0 probability factor0 = 1/2

SLLN ORIGINAL deviating word0 probability factor1 := mul(1/2, 1/2)

SLLN ORIGINAL deviating word0 probability factor1 = 1/4

SLLN ORIGINAL deviating word0 probability factor2 := mul(1/4, 1/2)

SLLN ORIGINAL deviating word0 probability factor2 = 1/8

SLLN ORIGINAL deviating word0 probability factor3 := mul(1/8, 1/2)

SLLN ORIGINAL deviating word0 probability factor3 = 1/16

SLLN ORIGINAL deviating word0 probability factor4 := mul(1/16, 1/2)

SLLN ORIGINAL deviating word0 probability factor4 = 1/32

SLLN ORIGINAL deviation probability word0 := sum(0, 1/32)

SLLN ORIGINAL deviation probability word0 = 1/32

source roles = [5, 0, [0, 0, 0, 0, 0], 1/2, 1/2]

derived = [0, 1/2, 是, 1/32, 1, 1/32]

SLLN ORIGINAL joint word1 integer sum := sum(0, 0, 0, 0, 1)

SLLN ORIGINAL joint word1 integer sum = 1

SLLN ORIGINAL joint word1 mean := div(1, 5)

SLLN ORIGINAL joint word1 mean = 1/5

SLLN ORIGINAL joint word1 mean minus mu := sub(1/5, 1/2)

SLLN ORIGINAL joint word1 mean minus mu = -3/10

source roles = [5, 1, [0, 0, 0, 0, 1], 1/2, 1/2]

derived = [1/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word2 integer sum := sum(0, 0, 0, 1, 0)

SLLN ORIGINAL joint word2 integer sum = 1

SLLN ORIGINAL joint word2 mean := div(1, 5)

SLLN ORIGINAL joint word2 mean = 1/5

SLLN ORIGINAL joint word2 mean minus mu := sub(1/5, 1/2)

SLLN ORIGINAL joint word2 mean minus mu = -3/10

source roles = [5, 2, [0, 0, 0, 1, 0], 1/2, 1/2]

derived = [1/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word3 integer sum := sum(0, 0, 0, 1, 1)

SLLN ORIGINAL joint word3 integer sum = 2

SLLN ORIGINAL joint word3 mean := div(2, 5)

SLLN ORIGINAL joint word3 mean = 2/5

SLLN ORIGINAL joint word3 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word3 mean minus mu = -1/10

source roles = [5, 3, [0, 0, 0, 1, 1], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word4 integer sum := sum(0, 0, 1, 0, 0)

SLLN ORIGINAL joint word4 integer sum = 1

SLLN ORIGINAL joint word4 mean := div(1, 5)

SLLN ORIGINAL joint word4 mean = 1/5

SLLN ORIGINAL joint word4 mean minus mu := sub(1/5, 1/2)

SLLN ORIGINAL joint word4 mean minus mu = -3/10

source roles = [5, 4, [0, 0, 1, 0, 0], 1/2, 1/2]

derived = [1/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word5 integer sum := sum(0, 0, 1, 0, 1)

SLLN ORIGINAL joint word5 integer sum = 2

SLLN ORIGINAL joint word5 mean := div(2, 5)

SLLN ORIGINAL joint word5 mean = 2/5

SLLN ORIGINAL joint word5 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word5 mean minus mu = -1/10

source roles = [5, 5, [0, 0, 1, 0, 1], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word6 integer sum := sum(0, 0, 1, 1, 0)

SLLN ORIGINAL joint word6 integer sum = 2

SLLN ORIGINAL joint word6 mean := div(2, 5)

SLLN ORIGINAL joint word6 mean = 2/5

SLLN ORIGINAL joint word6 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word6 mean minus mu = -1/10

source roles = [5, 6, [0, 0, 1, 1, 0], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word7 integer sum := sum(0, 0, 1, 1, 1)

SLLN ORIGINAL joint word7 integer sum = 3

SLLN ORIGINAL joint word7 mean := div(3, 5)

SLLN ORIGINAL joint word7 mean = 3/5

SLLN ORIGINAL joint word7 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word7 mean minus mu = 1/10

source roles = [5, 7, [0, 0, 1, 1, 1], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word8 integer sum := sum(0, 1, 0, 0, 0)

SLLN ORIGINAL joint word8 integer sum = 1

SLLN ORIGINAL joint word8 mean := div(1, 5)

SLLN ORIGINAL joint word8 mean = 1/5

SLLN ORIGINAL joint word8 mean minus mu := sub(1/5, 1/2)

SLLN ORIGINAL joint word8 mean minus mu = -3/10

source roles = [5, 8, [0, 1, 0, 0, 0], 1/2, 1/2]

derived = [1/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word9 integer sum := sum(0, 1, 0, 0, 1)

SLLN ORIGINAL joint word9 integer sum = 2

SLLN ORIGINAL joint word9 mean := div(2, 5)

SLLN ORIGINAL joint word9 mean = 2/5

SLLN ORIGINAL joint word9 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word9 mean minus mu = -1/10

source roles = [5, 9, [0, 1, 0, 0, 1], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word10 integer sum := sum(0, 1, 0, 1, 0)

SLLN ORIGINAL joint word10 integer sum = 2

SLLN ORIGINAL joint word10 mean := div(2, 5)

SLLN ORIGINAL joint word10 mean = 2/5

SLLN ORIGINAL joint word10 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word10 mean minus mu = -1/10

source roles = [5, 10, [0, 1, 0, 1, 0], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word11 integer sum := sum(0, 1, 0, 1, 1)

SLLN ORIGINAL joint word11 integer sum = 3

SLLN ORIGINAL joint word11 mean := div(3, 5)

SLLN ORIGINAL joint word11 mean = 3/5

SLLN ORIGINAL joint word11 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word11 mean minus mu = 1/10

source roles = [5, 11, [0, 1, 0, 1, 1], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word12 integer sum := sum(0, 1, 1, 0, 0)

SLLN ORIGINAL joint word12 integer sum = 2

SLLN ORIGINAL joint word12 mean := div(2, 5)

SLLN ORIGINAL joint word12 mean = 2/5

SLLN ORIGINAL joint word12 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word12 mean minus mu = -1/10

source roles = [5, 12, [0, 1, 1, 0, 0], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word13 integer sum := sum(0, 1, 1, 0, 1)

SLLN ORIGINAL joint word13 integer sum = 3

SLLN ORIGINAL joint word13 mean := div(3, 5)

SLLN ORIGINAL joint word13 mean = 3/5

SLLN ORIGINAL joint word13 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word13 mean minus mu = 1/10

source roles = [5, 13, [0, 1, 1, 0, 1], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word14 integer sum := sum(0, 1, 1, 1, 0)

SLLN ORIGINAL joint word14 integer sum = 3

SLLN ORIGINAL joint word14 mean := div(3, 5)

SLLN ORIGINAL joint word14 mean = 3/5

SLLN ORIGINAL joint word14 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word14 mean minus mu = 1/10

source roles = [5, 14, [0, 1, 1, 1, 0], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word15 integer sum := sum(0, 1, 1, 1, 1)

SLLN ORIGINAL joint word15 integer sum = 4

SLLN ORIGINAL joint word15 mean := div(4, 5)

SLLN ORIGINAL joint word15 mean = 4/5

SLLN ORIGINAL joint word15 mean minus mu := sub(4/5, 1/2)

SLLN ORIGINAL joint word15 mean minus mu = 3/10

source roles = [5, 15, [0, 1, 1, 1, 1], 1/2, 1/2]

derived = [4/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word16 integer sum := sum(1, 0, 0, 0, 0)

SLLN ORIGINAL joint word16 integer sum = 1

SLLN ORIGINAL joint word16 mean := div(1, 5)

SLLN ORIGINAL joint word16 mean = 1/5

SLLN ORIGINAL joint word16 mean minus mu := sub(1/5, 1/2)

SLLN ORIGINAL joint word16 mean minus mu = -3/10

source roles = [5, 16, [1, 0, 0, 0, 0], 1/2, 1/2]

derived = [1/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word17 integer sum := sum(1, 0, 0, 0, 1)

SLLN ORIGINAL joint word17 integer sum = 2

SLLN ORIGINAL joint word17 mean := div(2, 5)

SLLN ORIGINAL joint word17 mean = 2/5

SLLN ORIGINAL joint word17 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word17 mean minus mu = -1/10

source roles = [5, 17, [1, 0, 0, 0, 1], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word18 integer sum := sum(1, 0, 0, 1, 0)

SLLN ORIGINAL joint word18 integer sum = 2

SLLN ORIGINAL joint word18 mean := div(2, 5)

SLLN ORIGINAL joint word18 mean = 2/5

SLLN ORIGINAL joint word18 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word18 mean minus mu = -1/10

source roles = [5, 18, [1, 0, 0, 1, 0], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word19 integer sum := sum(1, 0, 0, 1, 1)

SLLN ORIGINAL joint word19 integer sum = 3

SLLN ORIGINAL joint word19 mean := div(3, 5)

SLLN ORIGINAL joint word19 mean = 3/5

SLLN ORIGINAL joint word19 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word19 mean minus mu = 1/10

source roles = [5, 19, [1, 0, 0, 1, 1], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word20 integer sum := sum(1, 0, 1, 0, 0)

SLLN ORIGINAL joint word20 integer sum = 2

SLLN ORIGINAL joint word20 mean := div(2, 5)

SLLN ORIGINAL joint word20 mean = 2/5

SLLN ORIGINAL joint word20 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word20 mean minus mu = -1/10

source roles = [5, 20, [1, 0, 1, 0, 0], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word21 integer sum := sum(1, 0, 1, 0, 1)

SLLN ORIGINAL joint word21 integer sum = 3

SLLN ORIGINAL joint word21 mean := div(3, 5)

SLLN ORIGINAL joint word21 mean = 3/5

SLLN ORIGINAL joint word21 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word21 mean minus mu = 1/10

source roles = [5, 21, [1, 0, 1, 0, 1], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word22 integer sum := sum(1, 0, 1, 1, 0)

SLLN ORIGINAL joint word22 integer sum = 3

SLLN ORIGINAL joint word22 mean := div(3, 5)

SLLN ORIGINAL joint word22 mean = 3/5

SLLN ORIGINAL joint word22 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word22 mean minus mu = 1/10

source roles = [5, 22, [1, 0, 1, 1, 0], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word23 integer sum := sum(1, 0, 1, 1, 1)

SLLN ORIGINAL joint word23 integer sum = 4

SLLN ORIGINAL joint word23 mean := div(4, 5)

SLLN ORIGINAL joint word23 mean = 4/5

SLLN ORIGINAL joint word23 mean minus mu := sub(4/5, 1/2)

SLLN ORIGINAL joint word23 mean minus mu = 3/10

source roles = [5, 23, [1, 0, 1, 1, 1], 1/2, 1/2]

derived = [4/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word24 integer sum := sum(1, 1, 0, 0, 0)

SLLN ORIGINAL joint word24 integer sum = 2

SLLN ORIGINAL joint word24 mean := div(2, 5)

SLLN ORIGINAL joint word24 mean = 2/5

SLLN ORIGINAL joint word24 mean minus mu := sub(2/5, 1/2)

SLLN ORIGINAL joint word24 mean minus mu = -1/10

source roles = [5, 24, [1, 1, 0, 0, 0], 1/2, 1/2]

derived = [2/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word25 integer sum := sum(1, 1, 0, 0, 1)

SLLN ORIGINAL joint word25 integer sum = 3

SLLN ORIGINAL joint word25 mean := div(3, 5)

SLLN ORIGINAL joint word25 mean = 3/5

SLLN ORIGINAL joint word25 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word25 mean minus mu = 1/10

source roles = [5, 25, [1, 1, 0, 0, 1], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word26 integer sum := sum(1, 1, 0, 1, 0)

SLLN ORIGINAL joint word26 integer sum = 3

SLLN ORIGINAL joint word26 mean := div(3, 5)

SLLN ORIGINAL joint word26 mean = 3/5

SLLN ORIGINAL joint word26 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word26 mean minus mu = 1/10

source roles = [5, 26, [1, 1, 0, 1, 0], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word27 integer sum := sum(1, 1, 0, 1, 1)

SLLN ORIGINAL joint word27 integer sum = 4

SLLN ORIGINAL joint word27 mean := div(4, 5)

SLLN ORIGINAL joint word27 mean = 4/5

SLLN ORIGINAL joint word27 mean minus mu := sub(4/5, 1/2)

SLLN ORIGINAL joint word27 mean minus mu = 3/10

source roles = [5, 27, [1, 1, 0, 1, 1], 1/2, 1/2]

derived = [4/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word28 integer sum := sum(1, 1, 1, 0, 0)

SLLN ORIGINAL joint word28 integer sum = 3

SLLN ORIGINAL joint word28 mean := div(3, 5)

SLLN ORIGINAL joint word28 mean = 3/5

SLLN ORIGINAL joint word28 mean minus mu := sub(3/5, 1/2)

SLLN ORIGINAL joint word28 mean minus mu = 1/10

source roles = [5, 28, [1, 1, 1, 0, 0], 1/2, 1/2]

derived = [3/5, 1/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word29 integer sum := sum(1, 1, 1, 0, 1)

SLLN ORIGINAL joint word29 integer sum = 4

SLLN ORIGINAL joint word29 mean := div(4, 5)

SLLN ORIGINAL joint word29 mean = 4/5

SLLN ORIGINAL joint word29 mean minus mu := sub(4/5, 1/2)

SLLN ORIGINAL joint word29 mean minus mu = 3/10

source roles = [5, 29, [1, 1, 1, 0, 1], 1/2, 1/2]

derived = [4/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word30 integer sum := sum(1, 1, 1, 1, 0)

SLLN ORIGINAL joint word30 integer sum = 4

SLLN ORIGINAL joint word30 mean := div(4, 5)

SLLN ORIGINAL joint word30 mean = 4/5

SLLN ORIGINAL joint word30 mean minus mu := sub(4/5, 1/2)

SLLN ORIGINAL joint word30 mean minus mu = 3/10

source roles = [5, 30, [1, 1, 1, 1, 0], 1/2, 1/2]

derived = [4/5, 3/10, 否, null, 1, 1/32]

SLLN ORIGINAL joint word31 integer sum := sum(1, 1, 1, 1, 1)

SLLN ORIGINAL joint word31 integer sum = 5

SLLN ORIGINAL joint word31 mean := div(5, 5)

SLLN ORIGINAL joint word31 mean = 1

SLLN ORIGINAL joint word31 mean minus mu := sub(1, 1/2)

SLLN ORIGINAL joint word31 mean minus mu = 1/2

SLLN ORIGINAL deviating word31 probability factor0 := mul(1, 1/2)

SLLN ORIGINAL deviating word31 probability factor0 = 1/2

SLLN ORIGINAL deviating word31 probability factor1 := mul(1/2, 1/2)

SLLN ORIGINAL deviating word31 probability factor1 = 1/4

SLLN ORIGINAL deviating word31 probability factor2 := mul(1/4, 1/2)

SLLN ORIGINAL deviating word31 probability factor2 = 1/8

SLLN ORIGINAL deviating word31 probability factor3 := mul(1/8, 1/2)

SLLN ORIGINAL deviating word31 probability factor3 = 1/16

SLLN ORIGINAL deviating word31 probability factor4 := mul(1/16, 1/2)

SLLN ORIGINAL deviating word31 probability factor4 = 1/32

SLLN ORIGINAL deviation probability word31 := sum(1/32, 1/32)

SLLN ORIGINAL deviation probability word31 = 1/16

source roles = [5, 31, [1, 1, 1, 1, 1], 1/2, 1/2]

derived = [1, 1/2, 是, 1/32, 2, 1/16]

逐步反向核對

• S157 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S156 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviation probability word31，不以小數近似替代。
• S155 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word31 probability factor4，不以小數近似替代。
• S154 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word31 probability factor3，不以小數近似替代。
• S153 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word31 probability factor2，不以小數近似替代。
• S152 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word31 probability factor1，不以小數近似替代。
• S151 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word31 probability factor0，不以小數近似替代。
• S150 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word31 mean minus mu，不以小數近似替代。
• S149 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word31 mean，不以小數近似替代。
• S148 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word31 integer sum，不以小數近似替代。
• S147 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S146 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word30 mean minus mu，不以小數近似替代。
• S145 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word30 mean，不以小數近似替代。
• S144 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word30 integer sum，不以小數近似替代。
• S143 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S142 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word29 mean minus mu，不以小數近似替代。
• S141 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word29 mean，不以小數近似替代。
• S140 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word29 integer sum，不以小數近似替代。
• S139 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S138 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word28 mean minus mu，不以小數近似替代。
• S137 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word28 mean，不以小數近似替代。
• S136 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word28 integer sum，不以小數近似替代。
• S135 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S134 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word27 mean minus mu，不以小數近似替代。
• S133 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word27 mean，不以小數近似替代。
• S132 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word27 integer sum，不以小數近似替代。
• S131 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S130 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word26 mean minus mu，不以小數近似替代。
• S129 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word26 mean，不以小數近似替代。
• S128 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word26 integer sum，不以小數近似替代。
• S127 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S126 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word25 mean minus mu，不以小數近似替代。
• S125 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word25 mean，不以小數近似替代。
• S124 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word25 integer sum，不以小數近似替代。
• S123 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S122 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word24 mean minus mu，不以小數近似替代。
• S121 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word24 mean，不以小數近似替代。
• S120 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word24 integer sum，不以小數近似替代。
• S119 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S118 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word23 mean minus mu，不以小數近似替代。
• S117 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word23 mean，不以小數近似替代。
• S116 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word23 integer sum，不以小數近似替代。
• S115 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S114 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word22 mean minus mu，不以小數近似替代。
• S113 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word22 mean，不以小數近似替代。
• S112 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word22 integer sum，不以小數近似替代。
• S111 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S110 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word21 mean minus mu，不以小數近似替代。
• S109 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word21 mean，不以小數近似替代。
• S108 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word21 integer sum，不以小數近似替代。
• S107 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S106 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word20 mean minus mu，不以小數近似替代。
• S105 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word20 mean，不以小數近似替代。
• S104 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word20 integer sum，不以小數近似替代。
• S103 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S102 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word19 mean minus mu，不以小數近似替代。
• S101 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word19 mean，不以小數近似替代。
• S100 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word19 integer sum，不以小數近似替代。
• S099 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S098 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word18 mean minus mu，不以小數近似替代。
• S097 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word18 mean，不以小數近似替代。
• S096 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word18 integer sum，不以小數近似替代。
• S095 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S094 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word17 mean minus mu，不以小數近似替代。
• S093 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word17 mean，不以小數近似替代。
• S092 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word17 integer sum，不以小數近似替代。
• S091 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S090 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word16 mean minus mu，不以小數近似替代。
• S089 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word16 mean，不以小數近似替代。
• S088 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word16 integer sum，不以小數近似替代。
• S087 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S086 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word15 mean minus mu，不以小數近似替代。
• S085 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word15 mean，不以小數近似替代。
• S084 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word15 integer sum，不以小數近似替代。
• S083 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S082 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word14 mean minus mu，不以小數近似替代。
• S081 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word14 mean，不以小數近似替代。
• S080 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word14 integer sum，不以小數近似替代。
• S079 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S078 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word13 mean minus mu，不以小數近似替代。
• S077 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word13 mean，不以小數近似替代。
• S076 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word13 integer sum，不以小數近似替代。
• S075 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S074 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word12 mean minus mu，不以小數近似替代。
• S073 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word12 mean，不以小數近似替代。
• S072 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word12 integer sum，不以小數近似替代。
• S071 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S070 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word11 mean minus mu，不以小數近似替代。
• S069 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word11 mean，不以小數近似替代。
• S068 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word11 integer sum，不以小數近似替代。
• S067 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S066 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word10 mean minus mu，不以小數近似替代。
• S065 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word10 mean，不以小數近似替代。
• S064 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word10 integer sum，不以小數近似替代。
• S063 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S062 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word9 mean minus mu，不以小數近似替代。
• S061 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word9 mean，不以小數近似替代。
• S060 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word9 integer sum，不以小數近似替代。
• S059 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S058 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word8 mean minus mu，不以小數近似替代。
• S057 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word8 mean，不以小數近似替代。
• S056 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word8 integer sum，不以小數近似替代。
• S055 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S054 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word7 mean minus mu，不以小數近似替代。
• S053 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word7 mean，不以小數近似替代。
• S052 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word7 integer sum，不以小數近似替代。
• S051 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S050 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word6 mean minus mu，不以小數近似替代。
• S049 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word6 mean，不以小數近似替代。
• S048 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word6 integer sum，不以小數近似替代。
• S047 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S046 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word5 mean minus mu，不以小數近似替代。
• S045 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word5 mean，不以小數近似替代。
• S044 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word5 integer sum，不以小數近似替代。
• S043 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S042 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word4 mean minus mu，不以小數近似替代。
• S041 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word4 mean，不以小數近似替代。
• S040 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word4 integer sum，不以小數近似替代。
• S039 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S038 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word3 mean minus mu，不以小數近似替代。
• S037 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word3 mean，不以小數近似替代。
• S036 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word3 integer sum，不以小數近似替代。
• S035 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S034 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word2 mean minus mu，不以小數近似替代。
• S033 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word2 mean，不以小數近似替代。
• S032 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word2 integer sum，不以小數近似替代。
• S031 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S030 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word1 mean minus mu，不以小數近似替代。
• S029 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word1 mean，不以小數近似替代。
• S028 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word1 integer sum，不以小數近似替代。
• S027 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S026 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviation probability word0，不以小數近似替代。
• S025 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word0 probability factor4，不以小數近似替代。
• S024 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word0 probability factor3，不以小數近似替代。
• S023 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word0 probability factor2，不以小數近似替代。
• S022 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word0 probability factor1，不以小數近似替代。
• S021 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word0 probability factor0，不以小數近似替代。
• S020 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word0 mean minus mu，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word0 mean，不以小數近似替代。
• S018 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word0 integer sum，不以小數近似替代。
• S017 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S016 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL second minus mean squared，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mean squared，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL second moment sum1，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL weighted square1，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal exact unbounded value square1，不以小數近似替代。
• S011 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mean sum1，不以小數近似替代。
• S010 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL weighted value1，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL second moment sum0，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL weighted square0，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal exact unbounded value square0，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mean sum0，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL weighted value0，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mass sum1，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mass sum0，不以小數近似替代。
• S002 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S001 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。

結論

(5, 1/2, 1/2, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。