Use declared mean=8/9, positive finite variance=9/10, and iid_certificate=finite_simulation_only. In the symbolic theorem families this marker supplies the premise of common mean/variance and IID for every finite subfamily of the whole sequence; a token or finite simulation is not independent proof of that premise. Independence then gives Var(sample mean_n)=variance/n and Chebyshev controls P(|sample mean_n−mean|≥epsilon). This finite-variance WLLN slice claims convergence in probability, not the strong law, CLT or finite-n equality with a limit. Positive epsilon=1/10, finite prefix of sample means=[9/10, 10/11, 11/12]. The supplied marker is finite_simulation_only, not the symbolic whole-sequence premise. Give (mean, epsilon, prefix_sample_means, sufficient, boundary).
G001 — Use declared mean=8/9, positive finite variance=9/10, and iid_certificate=finite_simulation_only. In the symbolic theorem families this marker supplies the premise of common mean/variance and IID for every finite subfamily of the whole sequence; a token or finite simulation is not independent proof of that premise. Independence then gives Var(sample mean_n)=variance/n and Chebyshev controls P(|sample mean_n−mean|≥epsilon). This finite-variance WLLN slice claims convergence in probability, not the strong law, CLT or finite-n equality with a limit. Positive epsilon=1/10, finite prefix of sample means=[9/10, 10/11, 11/12]. The supplied marker is finite_simulation_only, not the symbolic whole-sequence premise. Give (mean, epsilon, prefix_sample_means, sufficient, 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.
Retain the historical interface marker in the original snapshot while listing ordered source fields here,without JavaScript or external lookup.Field names are not mathematical evidence,and No retains the operation's specific claim scope.
original declared mean=8/9;positive variance=9/10;epsilon=1/10;original finite prefix=[9/10, 10/11, 11/12];certificate=finite_simulation_only
After
finite simulation alone supplies NO whole-sequence IID premise or all-n probability tail;finite_simulation_not_IID_certificate_or_WLLN_proof
Conditions: none
Retain even an empty prefix.Finite values or proximity to a mean do not certify IID for arbitrary finite subfamilies,common moments or all-later probability bounds.The No does not prove an unspecified sequence divergent or refute the WLLN.
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.
Result
(8/9, 1/10, [9/10, 10/11, 11/12], No, finite_simulation_not_IID_certificate_or_WLLN_proof)
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.