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We present a distillation of contemporary research on information and system security with regards to the strength, quality and recommendations concerning secure password generation. Because all passwords are merely sequences of symbols, we have leveraged recent advances in the mathematics of transformatics\cite{Lutalo2025_transformatics_thesis} --- a work being spearheaded by the author, to develop general theory about the quality of any password sequence given what is currently known and agreed upon both in theory and by industry standards such as NIST. The results are several --- both in theory and tangible empirical artifacts; a new password quality measure; Password Quality Rank (PQR) based on sequence entropy and a standard minimum secure password length limit; two laws concerning the mathematically provable quality and strength of a password sequence; an original system architecture for a random secure password generator (RSPG) system that can generate secure passwords in three distinct classes; complex (shorter, traditional cryptic passwords); humane (longer, readily memorizable but hard to guess) and advanced (long, cryptic-word based, high-entropy, and high PQR). We have also gone ahead to implement a proof-of-concept implementation of the RSPG system using the cross-platform new general-purpose language, TEA (Transforming Executable Alphabet)\cite{cli_tttt}, that is also founded on transformatics and the paradigm of programming via text-processing and chaining sequence-transformers. This work should help other information security researchers, system administrators, password policy makers and cryptographers, to not only be able to mathematically gauge the quality of sample and existing passwords given what is standard, but also be able to leverage our proposed general theory and the RSPG algorithm to generate robust computer programs meant to facilitate the generation of high quality passwords that are sometimes not only provably hard to crack, but also which are quite easy for the human to memorize. This paper is intentionally left brief, because the theory, design and language specifics underlying TEA in which we present the RSPG algorithm reference implementation are already well catered for in the TEA TAZ\cite{Lutalo2024TEATAZ}.