# Question 27208: Declared Theorem Application, Failed Hypotheses and Finite Evidence Have Different Roles

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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.

R0053-27208 · q-20261015-advance-20261118-r01-central-limit-theorem-finite-variance-iid-0083



## Original question and givens

Use mode=zero_variance and complete model={"value":-3,"n":4}. Give (mode, constant_value, n, variance, standardization_obstruction, this_standardization_claim).


- G001 — Use mode=zero_variance and complete model={"value":-3,"n":4}. Give (mode, constant_value, n, variance, standardization_obstruction, this_standardization_claim).





## 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-central-limit-theorem-finite-variance-iid](https://ocme.evemisslab.com/en/mko/mko-central-limit-theorem-finite-variance-iid/)





## Step-by-step derivation

S001 · impliesBefore

source roles = [clt-application-boundary]

After

derived = [[mode, constant_value, n, variance, standardization_obstruction, this_standardization_claim]]

Conditions: none

List the complete source field order and mode-specific roles without JavaScript or answer-shape inference;No,undefined and infinity retain their distinct meanings.

Step identifiers and dependenciesRule: source_ordered_fields_without_JS · Uses: G001





S002 · impliesBefore

source roles = [-3, 4]

After

derived = [0, sigma=0_makes_standardization_undefined, No]

Conditions: none

A constant marginal has sigma=0,so standardization divides by0 and cannot be a standard-normal variable.Here undefined is the SOURCE description,not an invented null for a computable field.

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









## Reverse checks


- S002 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.
- S001 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.





## Result

(zero_variance, -3, 4, 0, sigma=0_makes_standardization_undefined, No)

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: 21b83b5ce68791419dbf7e467ac70804bfe8aeb1131bc3af63d0c326f7dad56f
- candidate record SHA-256: ec030db7a0405283b98c56148e502091c47b148f870642e21f1b3b355903a7f6
- semantic review receipt SHA-256: 1b7a62514347b82518305d5feb4369a52d7d44c442a0f2b131e9eb3cd7b45f62
- question-first witness SHA-256: 79dc2a1077081f3ea2a03f75e32778163bf05e814cdf4c29ed86e567295f9ee1
- Lean: NOT_RUN · human review: NOT_PERFORMED

[Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261015-advance-20261118-r01-central-limit-theorem-finite-variance-iid-0083.json)