# Question 27608: The Complete Fixed-n Deviation Event Is Separate from an Almost-Sure Limit

[Return to catalogue page 139](https://ocme.evemisslab.com/en/questions/page/139/)

[← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations/#q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0058)

This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth.

R0054-27608 · q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0058



## Original question and givens

Use the aligned finite law values=[0, 1], probabilities=[1/2, 1/2], with declared process certificate=infinite_iid. The token is an explicit infinite IID premise, not a process construction or proof by this finite calculation. Use n=2 and epsilon=2/4>0; the event is |sample_mean−mu|≥epsilon. Give (n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary).


- G001 — Use the aligned finite law values=[0, 1], probabilities=[1/2, 1/2], with declared process certificate=infinite_iid. The token is an explicit infinite IID premise, not a process construction or proof by this finite calculation. Use n=2 and epsilon=2/4>0; the event is |sample_mean−mu|≥epsilon. Give (n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary).





## Definition and scope

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.


- [mko-strong-law-large-numbers-finite-valued-iid](https://ocme.evemisslab.com/en/mko/mko-strong-law-large-numbers-finite-valued-iid/)





## Step-by-step derivation

S001 · impliesBefore

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

After

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

Conditions: none

List the complete operation/mode field order without JavaScript or answer-shape inference;Boolean,string,null and an unclaimed result remain distinct.

Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001





S002 · impliesBefore

source roles = [infinite_iid]

After

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

Conditions: none

infinite_iid is a GIVEN whole-process premise,not independence constructed or proved by finite data/this program.

Step identifiers and dependenciesRule: SLLN_infinite_IID_EXACT_GIVEN_premise_not_finite_observation_inference · Uses: G001, S001





S003 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL mass sum0 = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S002





S004 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL mass sum1 = 1

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S003





S005 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL weighted value0 = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S004





S006 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL mean sum0 = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S005





S007 · calculationBefore

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

After

SLLN ORIGINAL common marginal exact unbounded value square0 = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S006





S008 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL weighted square0 = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S007





S009 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL second moment sum0 = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S008





S010 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL weighted value1 = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S009





S011 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL mean sum1 = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S010





S012 · calculationBefore

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

After

SLLN ORIGINAL common marginal exact unbounded value square1 = 1

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S011





S013 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL weighted square1 = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S012





S014 · calculationBefore

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

After

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

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S013





S015 · calculationBefore

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

After

SLLN ORIGINAL common marginal ORIGINAL mean squared = 1/4

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S014





S016 · calculationBefore

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

After

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

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S015





S017 · impliesBefore

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

After

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

Conditions: none

Pair ORIGINAL values/probabilities before numeric sorting and retain zero-mass labels.Qualify the complete nonnegative mass1 law and its source second-minus-mean-square variance.SLLN allows variance0;do not import the CLT positive-variance condition.

Step identifiers and dependenciesRule: SLLN_complete_ORIGINAL_numeric_value_probability_alignment_ALL_moments · Uses: G001, S016





S018 · calculationBefore

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

After

SLLN ORIGINAL joint word0 integer sum = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S017





S019 · calculationBefore

SLLN ORIGINAL joint word0 mean := div(0, 2)

After

SLLN ORIGINAL joint word0 mean = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S018





S020 · calculationBefore

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

After

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

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S019





S021 · calculationBefore

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

After

SLLN ORIGINAL deviating word0 probability factor0 = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S020





S022 · calculationBefore

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

After

SLLN ORIGINAL deviating word0 probability factor1 = 1/4

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S021





S023 · calculationBefore

SLLN ORIGINAL deviation probability word0 := sum(0, 1/4)

After

SLLN ORIGINAL deviation probability word0 = 1/4

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S022





S024 · impliesBefore

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

After

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

Conditions: none

For EVERY word test |mean-mu|>=epsilon,equality included.A zero-mass deviating word still contributes to the combinatorial count,while probability is weighted separately.Non-deviating words need no unused probability product under the source.This finite event is not an almost-sure limit certificate.

Step identifiers and dependenciesRule: SLLN_EVERY_joint_word_inclusive_event_count_SEPARATE_weighted_probability · Uses: G001, S023





S025 · calculationBefore

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

After

SLLN ORIGINAL joint word1 integer sum = 1

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S024





S026 · calculationBefore

SLLN ORIGINAL joint word1 mean := div(1, 2)

After

SLLN ORIGINAL joint word1 mean = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S025





S027 · calculationBefore

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

After

SLLN ORIGINAL joint word1 mean minus mu = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S026





S028 · impliesBefore

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

After

derived = [1/2, 0, No, null, 1, 1/4]

Conditions: none

For EVERY word test |mean-mu|>=epsilon,equality included.A zero-mass deviating word still contributes to the combinatorial count,while probability is weighted separately.Non-deviating words need no unused probability product under the source.This finite event is not an almost-sure limit certificate.

Step identifiers and dependenciesRule: SLLN_EVERY_joint_word_inclusive_event_count_SEPARATE_weighted_probability · Uses: G001, S027





S029 · calculationBefore

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

After

SLLN ORIGINAL joint word2 integer sum = 1

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S028





S030 · calculationBefore

SLLN ORIGINAL joint word2 mean := div(1, 2)

After

SLLN ORIGINAL joint word2 mean = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S029





S031 · calculationBefore

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

After

SLLN ORIGINAL joint word2 mean minus mu = 0

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S030





S032 · impliesBefore

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

After

derived = [1/2, 0, No, null, 1, 1/4]

Conditions: none

For EVERY word test |mean-mu|>=epsilon,equality included.A zero-mass deviating word still contributes to the combinatorial count,while probability is weighted separately.Non-deviating words need no unused probability product under the source.This finite event is not an almost-sure limit certificate.

Step identifiers and dependenciesRule: SLLN_EVERY_joint_word_inclusive_event_count_SEPARATE_weighted_probability · Uses: G001, S031





S033 · calculationBefore

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

After

SLLN ORIGINAL joint word3 integer sum = 2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S032





S034 · calculationBefore

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

After

SLLN ORIGINAL joint word3 mean = 1

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S033





S035 · calculationBefore

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

After

SLLN ORIGINAL joint word3 mean minus mu = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S034





S036 · calculationBefore

SLLN ORIGINAL deviating word3 probability factor0 := mul(1, 1/2)

After

SLLN ORIGINAL deviating word3 probability factor0 = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S035





S037 · calculationBefore

SLLN ORIGINAL deviating word3 probability factor1 := mul(1/2, 1/2)

After

SLLN ORIGINAL deviating word3 probability factor1 = 1/4

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S036





S038 · calculationBefore

SLLN ORIGINAL deviation probability word3 := sum(1/4, 1/4)

After

SLLN ORIGINAL deviation probability word3 = 1/2

Conditions: none

Substitute original roles and established intermediates exactly,not approximations or internally consistent changed operands;extra teaching algebra adds no source-domain gate.

Step identifiers and dependenciesRule: exact_rational_arithmetic · Uses: G001, S037





S039 · impliesBefore

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

After

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

Conditions: none

For EVERY word test |mean-mu|>=epsilon,equality included.A zero-mass deviating word still contributes to the combinatorial count,while probability is weighted separately.Non-deviating words need no unused probability product under the source.This finite event is not an almost-sure limit certificate.

Step identifiers and dependenciesRule: SLLN_EVERY_joint_word_inclusive_event_count_SEPARATE_weighted_probability · Uses: G001, S038









## Reverse checks


- S039 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
- S038 · premise_and_result_audit — Recompute SLLN ORIGINAL deviation probability word3 with exact rational arithmetic, not rounded decimals.
- S037 · premise_and_result_audit — Recompute SLLN ORIGINAL deviating word3 probability factor1 with exact rational arithmetic, not rounded decimals.
- S036 · premise_and_result_audit — Recompute SLLN ORIGINAL deviating word3 probability factor0 with exact rational arithmetic, not rounded decimals.
- S035 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word3 mean minus mu with exact rational arithmetic, not rounded decimals.
- S034 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word3 mean with exact rational arithmetic, not rounded decimals.
- S033 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word3 integer sum with exact rational arithmetic, not rounded decimals.
- S032 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
- S031 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word2 mean minus mu with exact rational arithmetic, not rounded decimals.
- S030 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word2 mean with exact rational arithmetic, not rounded decimals.
- S029 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word2 integer sum with exact rational arithmetic, not rounded decimals.
- S028 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
- S027 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word1 mean minus mu with exact rational arithmetic, not rounded decimals.
- S026 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word1 mean with exact rational arithmetic, not rounded decimals.
- S025 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word1 integer sum with exact rational arithmetic, not rounded decimals.
- S024 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
- S023 · premise_and_result_audit — Recompute SLLN ORIGINAL deviation probability word0 with exact rational arithmetic, not rounded decimals.
- S022 · premise_and_result_audit — Recompute SLLN ORIGINAL deviating word0 probability factor1 with exact rational arithmetic, not rounded decimals.
- S021 · premise_and_result_audit — Recompute SLLN ORIGINAL deviating word0 probability factor0 with exact rational arithmetic, not rounded decimals.
- S020 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word0 mean minus mu with exact rational arithmetic, not rounded decimals.
- S019 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word0 mean with exact rational arithmetic, not rounded decimals.
- S018 · premise_and_result_audit — Recompute SLLN ORIGINAL joint word0 integer sum with exact rational arithmetic, not rounded decimals.
- S017 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
- S016 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL second minus mean squared with exact rational arithmetic, not rounded decimals.
- S015 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL mean squared with exact rational arithmetic, not rounded decimals.
- S014 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL second moment sum1 with exact rational arithmetic, not rounded decimals.
- S013 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL weighted square1 with exact rational arithmetic, not rounded decimals.
- S012 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal exact unbounded value square1 with exact rational arithmetic, not rounded decimals.
- S011 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL mean sum1 with exact rational arithmetic, not rounded decimals.
- S010 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL weighted value1 with exact rational arithmetic, not rounded decimals.
- S009 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL second moment sum0 with exact rational arithmetic, not rounded decimals.
- S008 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL weighted square0 with exact rational arithmetic, not rounded decimals.
- S007 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal exact unbounded value square0 with exact rational arithmetic, not rounded decimals.
- S006 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL mean sum0 with exact rational arithmetic, not rounded decimals.
- S005 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL weighted value0 with exact rational arithmetic, not rounded decimals.
- S004 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL mass sum1 with exact rational arithmetic, not rounded decimals.
- S003 · premise_and_result_audit — Recompute SLLN ORIGINAL common marginal ORIGINAL mass sum0 with exact rational arithmetic, not rounded decimals.
- S002 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.
- S001 · premise_and_result_audit — Reverse-check original data,operands,complete scope and premises;finite witnesses,conditional theorem use and formal proof remain distinct.





## Result

(2, 1/2, 1/2, 2, 1/2, fixed_n_deviation_event, No, not_an_almost_sure_limit_certificate)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.





## This question review and source binding

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.

Source hashes and review receipts
- input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
- original question SHA-256: a2c73adc778d1c0a98bdac8d9d90bed9040a77bf60bd7edc77ebfb7b476deb79
- candidate record SHA-256: c2e2675f14bf66c0a17af05eaad3fc51fdaa600cb5045f34a2f4396bf43f1d64
- semantic review receipt SHA-256: 0a76d8e93c08bb16998a0483f3dfc0504f269fc3e1982e6cd868cab0a2856d54
- question-first witness SHA-256: 09127b736c225714dfa0b7ceb0e6a6e66df27438b480cad8217d3c2f99ce9437
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-0058.json)