JOHNSTON, Iowa - s4story -- Big House Enterprise has published Theorem 3 of The Ontological Dominance Papers, extending its authority framework to businesses that compete across multiple product or service categories. The paper establishes that a business's total AI representation is not the simple average of its authority in each category, but a prominence-weighted average — meaning categories that account for a larger share of buyer queries carry disproportionate influence over how the whole entity is perceived.

The finding has direct implications for businesses that assume strength in a flagship category will offset weaker representation elsewhere. The paper's model suggests the opposite can also occur: weakness in a high-query-volume category can pull down an otherwise strong brand's overall standing.

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"A lot of businesses treat their product lines as separate scorecards," said Joseph Byrum, Founder, CEO and CTO of Big House Enterprise and author of the paper. "AI systems don't see it that way. If most of your buyer queries land in one category and you're weak there, that weakness is doing more damage to your brand than your strength in a smaller category is doing good."

The theorem also examines cross-category spillover, finding that authority signals transfer favorably between categories that share vocabulary and buyer types, but can actively work against each other when they don't. The paper specifies quarterly monitoring protocols for businesses managing authority across a portfolio. Upon internal adversarial review, the theorem was classified as a formally correct extension of the program's foundational law, with its practical validity still pending field confirmation.

"Knowing which categories reinforce each other and which ones compete for the same attention changes where a business should actually be investing," Byrum said.

Big House Enterprise plans to release Theorem 4, addressing how businesses defend AI authority against deliberate competitive attack, in the coming weeks.

Learn how to obtain Ontological Dominance at our website: https://bighouseenterprise.com