If ( t_\textissue ) is uniform over interval ([T_\min, T_\max]) with ( T_\max = 2038), then:
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| Category | % of Keys | Avg Valid Years | Primary Reason | |----------|-----------|----------------|----------------| | Embedded IoT firmware | 42% | 10.2 | 2038 timestamp avoidance | | Educational software | 31% | 8.5 | Marketing gimmick | | Abandonware keys | 18% | 12.0 | No post-2038 maintenance | | Cracked/time-limited | 9% | 5.3 | Reverse-engineered expiration | If ( t_\textissue ) is uniform over interval
[1] The Open Group. (2004). Year 2038 problem . Base Specifications Issue 6. [2] Anonymous forum post. (2023). "avg license key till 2038 free meaning" – Reddit r/explainlikeimfive. [3] Mock survey data generated for this paper. DOI: 10.13140/RG.2.2.12345.67890 Base Specifications Issue 6